Photonic, Electronic and Atomic Collisions: Proceedings of the XXIV International Conference

editors

Pablo D Fainstein Marco Aurelio P Lima Jorge E Miraglia Eduardo C Montenegro Roberto D Rivarola

Photonic, Electronic and Atomic Collisions Proceedings of the XXIV International Conference

Photonic, Electronic and Atomic Collisions Proceedings of the XXIV International Conference

Photonic, Electronic and Atomic Collisions Proceedings of t h e XXIV International C o n f e r e n c e

Rosario, Argentina

20 - 26 July 2005

editors

Pablo D Fainstein (Centro Atomico Bariloche,

Argentina},

Marco Aurelio P Lima (Universidade Estadual de Campinas, Brasitj,

Jorge E Miraglia (Instituto de Astronomia y Fisica del Espacio,

Argentina),

Eduardo C Montenegro (Universidade Federal do Rio de Janeiro, Brasil) &

Roberto D Rivarola (Universidad Nacional de Rosario, Argentina)

\[p World Scientific NEW JERSEY • LONDON

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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

PHOTONIC, ELECTRONIC AND ATOMIC COLLISIONS Proceedings of the XXIV International Conference Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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PREFACE

The 24th edition of the International Conference on Photonic, Electronic and Atomic Collisions (XXIV ICPEAC) was held in Rosario, Argentina, from July 20 to July 26, 2005. It was the first time that an edition of this series of biennial conferences was hosted in Latin America, and only the second time that the event took place in the Southern Hemisphere. The meeting was organized by a Local Committee made up of physicists from Argentina and Brazil, together with a representative from Mexico. The conference was attended by 485 delegates from 42 countries, composed of 355 regular participants and 130 students. In addition, 63 accompanying persons registered for the social programme. The conference followed the traditional format of five full days of scientific activities. The themes were divided into three broad areas: Heavy Particle Collisions, Lepton Collisions, and Photon Collisions. Five Plenary Lectures were presented at the respective openings of the daily sessions and four Review Lectures were offered during the course of the programme. In addition, 86 oral communications were given during the conference, including 62 Progress Reports and 24 Special Reports (the former Hot Topics). The results of 761 contributed papers were presented as poster communications. Finally, an Argentinian paleontologist of international repute delivered a public lecture on Updating Patagonic Dinosaurs: A New Look to an Ancient Story. A wide range of subjects comprising a balanced mix of topics were covered throughout the course of the conference. They include collisions of heavy particles and electrons with atoms, molecules and clusters, the coherent control of reaction dynamics using lasers and electromagnetic pulses, different processes involving exotic particles, the interaction of strong electromagnetic fields with molecules, clusters and liquids, the collisions of electrons and heavy particles with surfaces, and the transport of particles through solids and cold-atom/molecule collisions, among others. This publication contains most of the lectures given by the guest speakers. The XXIV ICPEAC was a resounding success for the international and local communities, from the scientific point of view as well as social. v

VI

Participants were delighted with the local cultural and social activities offered during the event. Five satellite meetings were organized after the main conference in the cities of Buenos Aires, Argentina, and Campinas and Rio de Janeiro, Brazil. The Local Committee would like to recognize the generous contributions made by various institutions: International Union for Pure and Applied Physics (IUPAP), Centro Latino Americano de Fisica (CLAF), Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Agencia Nacional de Promotion Cientifica y Tecnologica (ANPCyT), Comision Nacional de Energia Atomica (CNEA), Municipalidad de Rosario (MR), Universidad Nacional de Rosario (UNR), Facultad de Ciencias Exactas, Ingenieria y Agrimensura of the UNR, Fundacion para el Apoyo de las Ciencias Fisicas (ACIFIR) and the companies Transdatos S.A. and Investigation Aplicada S.E. (INVAP). On a personal level, I would like to express my gratitude to the local Co-chairs Jorge Miraglia, Eduardo Montenegro and Marco Aurelio Lima, with whom we initiated this truly challenging and exciting project. I also wish to extend my thanks to all the physicists from Rosario, Buenos Aires, Bariloche and Bahia Blanca who worked so hard in the organization of the conference, in particular to Alejandra Martinez, Maria Silvia Gravielle, Heriberto Fabio Busnengo, Pablo Fainstein, Flavio Colavecchia, Juan Fiol and Raul Barrachina. The generous collaboration received from Gustavo Gasaneo, Omar Fojon, Dario Mitnik, Daniel Fregenal, Renata Delia Picca and Geraldo Sigaud must also be mentioned. Finally, my warm thanks go to Albert Crowe, Chair of the ICPEAC Executive Committee for the period 2003-2005, who so strongly and actively supported Rosario as the host city of the XXIV ICPEAC.

Roberto D. Rivarola Local Chair, XXIV ICPEAC November 2005

SPONSORS

The Local Committee gratefully acknowledges financial support from: • • • • • • • •

Municipalidad de Rosario Universidad Nacional de Rosario Agenda Nacional de Promocion Cientifica y Tecnoldgica Consejo Nacional de Investigaciones Cientificas y Tecnicas Centro Latinoamericano de Fisica International Union of Pure and Applied Physics INVAPS.E. TRANSDATORS S.A.

The X X I V ICPEAC was held under the auspices of: • Secretaria de ciencia, Tecnologia e Innovacion Productiva, Ministerio de Educacion, Ciencia y Tecnologia la Repuhlica Argentina • Facultad de Ciencias, Exactas, Ingenieria y Arimensura, Universidad Nacional de Rosario • Instituto de Fisica de Rosario • Fundacion para el Apoyo de las Ciencias Fisicas de Rosario • Comisidn Nacional de Energia Atomica The X X I V I C P E A C has been declared of interest by: • Municipalidad de Rosario • Provincia de Santa Fe • Senado de la Provincia de Santa Fe

vn

International Conference on Photonic, Electronic and Atomic Collisions

Committee Chair

Vice Chair

Albert Crowe Department of Physics University of Newcastle Newcastle, NE1 7RU, United Kingdom Tel: +44-191-222-7401 Fax: +44-191-222-7361 Email: [email protected]

Yasunori Yamazaki Institute of Physics University of Tokio Komaba, Tokyo, 153-8902, Japan Tel: +81-3-5454-6521 Fax: +81-3-5454-6433 Email: [email protected]

Secretary

Treasurer

Klaus Bartschat Department of Physics and Astronomy Drake University Des Moines, IA 50311, USA Tel: +1-515-271-3750 Pax: +1-515-271-1943 Email: [email protected]

Henrik Cederquist Department of Physics Stockholm University SE-106 91, Stockholm, Sweden Tel: +46-8-5537-8626 Fax: +46-8-5537-8601 Email: [email protected]

Members A. Huetz, France M. Larsson, Sweden M. A. P. Lima, Brazil E. Lindroth, Sweden F. Martin, Spain J. E. Miraglia, Argentina E. C. Montenegro, Brazil

R. D. Rivarola, Argentina R. Schuch, Sweden A. Stelbovics, Australia J. Tanis, USA J. Ullrich, Germany C. Whelan, USA

International Conference on Photonic, Electronic and Atomic Collisions

General Committee ARGENTINA R. 0 . Barrachina

ISRAEL Z. Amitay

AUSTRALIA J. Lower P. Teubner

ITALY A. Borghesani JAPAN T. Azuma M. Kimura N. Kouchi H. Tanaka K. Yamanouchi

AUSTRIA P. Scheier BRAZIL G. Sigaud CANADA A. Bandrauk

P.R. CHINA K. Xu

DENMARK L. Andersen

POLAND M. Pajek

FRANCE K. Wohrer

RUSSIA A. N. Grum-Grzhimailo V. K.Ivanov

GERMANY R. Dorner D. Gerlich H. J. Ludde M. Drescher

SPAIN G. Garcia SWEDEN D. Hanstorp

INDIA K. Baluja

SWITZERLAND M. Allan

IRELAND E. Kennedy

IX

X

THE NETHERLANDS T. Schlatholter UNITED KINGDOM „ , G. TKing T ,, „ J. JVLcCann _ . .. G. TLariccnia

UNITED STATES B. Esry 'Fl *?!? . M. Khakoo ,, „ , , M - Schulz _ „ . ., D. Schultz _ _ , C. hurko

International Conference on Photonic, Electronic and Atomic Collisions

Local Organizing Committee Chair R. D. Rivarola (IFIR-UNR, Argentina) Co-chairs M. A. P. Lima (UNICAMP, Brazil) J. E. Miraglia (IAFE-UBA, Argentina) E. C. Montenegro (UFRJ, Brazil) Member R. 0 . Barrachina (CAB-IB, Argentina) H. F. Busnengo (IFIR-UNR, Argentina) C. Cisneros (UNAM, Mexico) F. Colavecchia (CAB-IB, Argentina) P. D. Fainstein (CAB-IB, Argentina) J. Fiol (CAB-IB, Argentina) O. A. Fojon (IFIR-UNR, Argentina) G. Gasaneo (UNSur, Argentina) P. L. Grande (UFRGS, Brazil) M. S. Gravielle (IAFE-UBA, Argentina) M. C. A. Lopes (UFJF, Brazil) A. E. Martinez (IFIR-UNR, Argentina) D. Mitnik (IAFE-UBA, Argentina) R. D. Piacentini (IFIR-UNR, Argentina) G. M. Sigaud (PUC, Brazil) M. T. do N. Varela (UNICAMP, Brazil)

XI

CONTENTS

PLENARY Electron Collisions — Past, Present and Future J. W. McConkey

3

Collisions of Slow Highly Charged Ions with Surfaces J. Burgdorfer, C. Lemell, K. Schiessl, B. Solleder, C. Reinhold, K. Tokesi and L. Wirtz

16

Atomic Collisions Studied with "Reaction-Microscopes" R. Moshammer, D. Fischer, A. Rudenko, T. Ergler, B. Feuerstein, K. Zrost, C. D. Schroter, A. Voitkiv, B. Najjari, A. Dora, M. Diirr, Ch. Dimopoulou, T. Ferger, J. Ullrich and M. Schulz

46

Rydberg Atoms: A Microscale Laboratory for Studying Electron-Molecule Interactions F. B. Dunning

64

COLLISIONS INVOLVING P H O T O N S Quantum Control of Photochemical Reaction Dynamics and Molecular Functions M. Yamaki, M. Abe, Y. Ohtsuki, H. Kono and Y. Fujimura Manipulating and Viewing Rydberg Wavepackets R. R. Jones Angle-Resolved Photoelectrons as a Probe of Strong-Field Interactions M. Vrakking Ultracold Rydberg Atoms in a Structured Environment I. C. H. Liu and J. M. Rost xm

79

87

95

104

Synchrotron-Radiation-Based Recoil Ion Momentum Spectroscopy of Laser Cooled and Trapped Cesium Atoms L. H. Coutinho, R. L. Cavasso-Filho, M. G. P. Homem, D. S. L. Figueira, F. C. Cruz and A. Naves de Brito Reconstruction of Attosecond Pulse Trains Y. Mairesse, P. Agostini, P. Breger, B. Carre, A. Merdji, P. Monchicourt, P. Salieres, K. Varju, E. Gustafsson, P. Johnsson, J. Mauritsson, T. Remetter, A. L'Huillier and L. J. Frasinski Selective Excitation of Metastable Atomic States by Femtoand Attosecond Laser Pulses A. D. Kondorskiy Accurate Calculations of Triple Differential Cross Sections for Double Photoionization of the Hydrogen Molecule W. Vanroose, F. Martin, T. N. Rescigno and C. W. McCurdy

108

112

120

128

Double and Triple Photoionization of Li and Be J. Colgan, M. S. Pindzola and F. Robicheaux

132

Few/Many Body Dynamics in Strong Laser Fields J. Zanghellini and T. Brabec

136

Rescattering-Induced Effects in Electron-Atom Scattering in the Presence of a Circularly Polarized Laser Field A. V. Flegel, M. V. Frolov, N. L. Manakov and A. F. Starace Multidimensional Photoelectron Spectroscopy P. Lablanquie, F. Penent, J. Palaudoux, L. Andric, T. Aoto, K. Ro, Y. Hirosaka, R. Feifel and J. H. D. Eland Few Photon and Strongly Driven Transitions in the XUV and Beyond P. Lambropoulos, L. A. A. Nikolopoulos and S. I. Themelis Ionization Dynamics of Atomic Clusters in Intense Laser Pulses U. Saalmann and J. M. Rost

144

148

152

160

On the Second Order Autocorrelation of an XUV Attosecond Pulse Train E. P. Benis, L. A. A. Nikolopoulos, P. Tzallas, D. Charalambidis, K. Witte and G. D. Tsakiris

168

Evidence for Rescattering in Molecular Dissociation /. D. Williams, J. McKenna, M. Suresh, B. Srigengan, E. M. L. English, S. L. Stebbings, W. A. Bryan, W. R. Newell and I. C. E. Turcu

172

Photoionizing Ions Using Synchrotron Radiation R. Phaneuf

176

Photo Double Ionization of Fixed in Space Deuterium Molecules T. Weber, R. Dorner, A. Czasch, O. Jagutzki, H. Schmidt-Bo eking, A. Muller, V. Mergel, M. Prior, T. Osipov, S. Daveau, E. Rotenberg, G. Meigs, L. Cocke, A. Landers, A. Kheifets, J. Feagin and R. Diez Muino Coherence and Intramolecular Scattering in Molecular Photoionization U. Becker Experimental Observation of Interatomic Coulombic Decay in Neon Dimers T. Jahnke, A. Czasch, M. Schoffter, S. Schossler, A. Knapp, M. Kdsz, J. Titze, C. Wimmer, K. Kreidi, R. E. Grisenti, A. Staudte, O. Jagutzki, U. Hergenhahn, H. Schmidt-Bo eking and R. Dorner Ionization by Short UV Laser Pulses: Secondary ATI Peaks of the Electron Spectrum V. D. Rodriguez, E. Cormier and R. Gayet Molecular Frame Photoemission in Photoionization of H2 and D2: The Role of Dissociation on Autoionization of the Qi and Q 2 Doubly Excited States D. Dowek, M. Lebech and J. C Houver

184

192

198

206

214

XVI

3p Photoemission of 3d Transition Metals — Atoms, Molecules and Clusters M. Martins

224

COLLISIONS INVOLVING ELECTRONS Spin-Resolved Collisions of Electrons with Atoms and Molecules G. F. Hanne

235

Calculation of Ionization and Excitation Processes Using the Convergent Close-Coupling Method D. V. Fursa, I. Bray and A. T. Stelbovics

245

The B-Spline R-Matrix Method for Electron and Photon Collisions with Atoms and Ions 0. Zatsarinny and K. Bartschat

253

Absolute Angle-Differential Cross Sections for Excitation of Neon Atoms by Electrons of Energy 16.6-19.2 eV M. Allan, K. Franz, H. Hotop, O. Zatsarinny and K. Bartschat Studies of QED and Nuclear Size Effects with Highly Charged Ions in an EBIT J. R. Crespo Lopez-Urrutia, J. Braun, G. Brenner, H. Bruhns, A. J. Gonzalez Martinez, A. Lapierre, V. Mironov, R. Soria Oris, H. Tawara, M. Trinczek, J. Ullrich, A. Artemyev, J. H. Scofield and I. I. Tupitsyn Recombination of Astrophysically Relevant Ions: Be-like C, N, and O M. Fogle, R. Schuch, N. R. Badnell, S. D. Loch, Sh. A. Abdel-Naby, M. S. Pindzola and P. Glans Dissociation and Excitation of Molecules and Molecular Ions by Electron Impact A. E. Orel and J. Royal

261

265

273

281

XV11

State-Selective X-Ray Study of the Radiative Recombination of U 9 2 + Ions with Cooling Electrons M. Pajek, Th. Stohlker, D. Bancs, H. F. Beyer, S. Bbhm, F. Bosch, C. Brandau, M. Czarnota, S. Chatterjee, J.-CI. Dousse, A. Gumberidze, S. Hagmann, C. Kozhuharov, D. Liesen, A. Miiller, R. Reuschl, E. W. Schmidt, D. Sierpowski, U. Spillmann, J. Szlachetko, S. Tashenov, S. Trotsenko, P. Verma, M. Walek, A. Warczak and A. Wilk

289

Electron Collisions with Trapped, Metastable Helium L. J. Uhlmann, R. G. Dall, K. G. H. Baldwin and S. J. Buckman

293

Non-Dipole Effects in Electron and Photon Impact Ionization N. L. S. Martin

297

Electron Driven Processes in Atmospheric Behaviour L. Campbell, M. J. Brunger and P. J. 0. Teubner

305

Calculation of Excitatioiiand Ionization for Electron-Molecule Collisions at Intermediate Energies J. D. Gorfinkiel Absolute Total Cross Sections for Electron-CH4 Scattering at Intermediate Energies M. C. A. Lopes, M. P. Gomes, H. Couto, W. de Souza Melo and L. L. de Lima

313

320

Electron-CC-2 Scattering in a Cluster Environment /. I. Fabrikant

324

Isomer Effect in Electron Collisions with Small Hydrocarbons M. H. F. Bettega, A. R. Lopes, S. D'A. Sanchez, M. T. do N. Varella, M. A. P. Lima and L. G. Ferreira

328

Low Energy Electron Interactions with Bio-Molecules B. P. Marinkovic, D. M. Filipovic, V. Pejcev, D. Sevic, A. R. Milosavljevic, D. Pavlovic, S. Milisavljevic, P. Kolarz and M. Pardovska

336

xvm Narrow Resonances in Dissociative Electron Attachment and Vibrational Excitation in H2 M. Cizek

344

(e,2e) Experiments with Randomly Oriented and Fixed-in-Space Hydrogen Molecules M. Takahashi

352

Initial and Final State Correlation Effects in (e,3e) Processes G. Gasaneo, S. Otranto and K. V. Rodriguez An (e,72e) Experiment for Simultaneous lonization-Excitation of Helium to the He + (2p) 2 P States by Electron Impact A. Dorn, G. Sakhelashvili, C. Hohr, J. Ullrich, A. S. Kheifets, J. Lower and K. Bartschat

360

364

COLLISIONS INVOLVING EXOTIC PARTICLES Antihydrogen in the Laboratory M. Charlton

371

Atomic Collisions Involving Positrons H. R. J. Walters and C. Starret

381

Ionization and Positronium Formation in Noble Gases J. P. Marler, J. P. Sullivan and C. M. Surko

391

Study of Inner-Shell Ionization by Low-Energy Positron Impact Y. Nagashima, W. Shigeta, T. Hyodo, F. Saito, Y. Itoh, A. Goto and M. Iwaki

399

Positron-Atom Bound States and Interactions M. W. J. Bromley, J. Mitroy, S. A. Novikov, A. T. Le and C. D. Lin

407

Extraction of Ultra-Slow Antiproton Beams for Single Collision Experiments H. A. Torii, N. Kuroda, M. Shibata, Y. Nagata, D. Barna, M. Hori, J. Eades, A. Mohri, K. Komaki and Y. Yamazaki

415

XIX

Positronium Formation from Valence and Inner Shells in Noble Gases L. J. M. Dunlop and G. F. Gribakin Molecular Effects in Neutrino Mass Measurements N. Doss, J. Tennyson, A. Saenz and S. Jonsell

419

423

COLLISIONS INVOLVING HEAVY PROJECTILES Probing the Solar Wind with Cometary X-Ray and Far-Ultraviolet Emission R. Hoekstra, D. Bodewits, R. Morgenstern, C. M. Lisse and A. G. G. M. Tielens Production of 0 2 + + Neutrals from the Collision of C3+ with Water H. Luna, P. M. Y. Garcia, G. M. Sigaud, M. B. Shah and E. C. Montenegro

429

439

Vector Correlation of Fragment Ions Produced by Collision of Ar 1 1 + with Dimethyldisulfide T. Matsuoka, N. Machida, H. Shiromaru and Y. Achiba

450

Slow Multiply Charged Ion-Molecule Collision Dynamics Studied Through a Multi-Coincidence Technique T. Kaneyasu, T. Azuraa and K. Okuno

454

Recent Developments in Proton-Transfer-Reaction Mass Spectrometry A. Wisthaler, A. Hansel, A. Jordan and T. D. Mark

462

Interferences in Electron Emission from H2 Induced by Fast Ions N. Stolterfoht

470

Atomic Realization of the Young Single Electron Interference Process in Individual Autoionization Collisions R. O. Barrachina and M. Zitnik

478

XX

Multiple Ionization Processes Related to Irradiation of Biological Tissue M. E. Galassi, R. D. Rivarola, M. P. Gaigeot, B. Gervais, M. Beuve, R. Vuilleumier, P. D. Fainstein, C. R. Stia and M. F. Politis

482

Atom-Diatom Collisions at Cold and Ultra-Cold Temperatures F. D. Colavecchia, G. A. Parker and R. T. Pack

486

Interactions of Ions with Hydrogen Atoms A. Luca, G. Borodi and D. Gerlich

494

Analysis of All Structures in the Elastic and Charge Transfer Cross Sections for Proton-Hydrogen Collisions in the Range of 10- 1 0 -10 2 eV P. S. Krstic, D. R. Schultz, J. H. Macek and S. Yu. Ovchinnikov

502

Ab-initio Ion-Atom Collision Calculations for Many-Electron Systems 3. Anton and B. Fricke

506

Fully Differential Studies on Single Ionization of Helium by Slow Proton Impact A. Hasan, N. V. Maydanyuk, M. Foster, B. Tooke, E. Nanni, D. H. Madison, M. Schulz, A. Voitkiv and B. Najjari Dipole Polarization Effects on Highly-Charged-Ion-Atom Electron Capture C. C. Havener, S. L. Hough, R. Rejoub, D. W. Savin and M. Schnell Proton-, Antiproton-, and Photon-He Collisions in the Context of Ultra Fast Processes T. Morishita, S. Watanabe, M. Matsuzawa and C. D. Lin

514

522

531

XXI

Impact Parameter Dependent Charge Exchange Studies with Channeled Heavy Ions D. Dauvergne, M. Chevallier, J.-C. Poizat, C. Ray, E. Testa, A. Brauning-Demian, F. Bosch, S. Hagmann, C. Kozuharov, D. Liesen, P. Mokler, Th. Stohlker, M. Tarisien, P. Verma, C. Cohen, A. L'Hoir, J.-P. Rozet, D. Vernhet, H. Brauning and M. Toulemonde Crystal Assisted Atomic Physics Experiments Using Heavy Ions K. Komaki

539

548

COLLISIONS INVOLVING CLUSTERS A N D SURFACES Structure and Dynamics of Van der Waal Complexes: From Triatomic to Medium Size Clusters G. Delgado Barrio, D. Lopez-Durdn, A. Valdes, R. Prosmiti, M. P. de Lara-Castells, T. Gonzalez-Lezana and P. Villarreal Evaporation, Fission and Multifragmentation Processes of Multicharged Ceo Ions Versus Excitation Energies S. Martin, L. Chen, B. Wei, J. Bernard and R. Bredy

559

569

Fragmentation of Collisionally Excited Fullerenes M. Alcami, S. Diaz-Tendero and F. Martin

583

Lifetimes of Cj?^ and C ^ Dianions in a Storage Ring S. Tomita, J. U. Andersen, B. Concina, P. Hvelplund, B. Liu, S. Br0ndsted Nielsen, H. Cederquist, J. Jensen, H. T. Schmidt, H. Zettergren, O. Echt, J. S. Forster, K. Hansen, B. A. Huber, B. Manil, L. Maunoury and J. Rangama

591

Clusters and Clusters of Clusters in Collisions B. Manil, V. Bernigaud, P. Boduch, A. Cassimi, O. Kamalou, J. Lenoir, L. Maunoury, J. Rangama, B. A. Huber, J. Jensen, H. T. Schmidt, H. Zettergren, H. Cederquist, S. Tomita, P. Hvelplund, F. Alvarado, S. Bari, A. Lecointre and T. Schlatholter

599

XXII

Fragmentation of Small Carbon Clusters M. Chabot, F. Mezdari, G. Martinet, K. Wohrer-Beroff, S. Delia Negra, P. Desesquelles, H. Hamrita, A. LePadellec and L. Montagnon Collective Excitations in Collisions of Photons and Electrons with Metal Clusters and Pullerenes A. V. Solov'yov Dynamics of H2 Chemisorption on Metal Surfaces H. F. Busnengo, C. Diaz, P. Riviere, M. A. Di Cesare, F. Martin, W. Dong and A. Salin Interaction of Slow Multiply Charged Ions with Insulator Surfaces W. Meissl, J. Stockl, M. Fiirsatz, HP. Winter, F. Aumayr, J. R. Crespo Lopez-Urrutia, J. Simonet, W. Chen, H. Tawara and J. Ullrich

607

615

625

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Electron Emission During Grazing Impact of Atoms on Metals Surfaces H. Winter

641

Inner-Shell Collective Effects for Protons Backscattered from the Al(110) Surface P. L. Grande, A. Hentz and G. Schiwietz

649

Guiding of Highly Charged Ions by Si0 2 Nano-Capillaries M. B. Sahana, P. Skog, Gy. Vikor, R. T. Rajendra Kumar and R. Schuch Low-Energy Electron Impact on Hydrogenated Polycrystalline Diamond and Condensed Molecules A. Lafosse, D. Cdceres, M. Bertin, D. Teillet-Billy, R. Azria and A. Hoffman Low Energy Spin-Polarized Electron-Pair (e,2e)-in-Reflection from Various Surfaces J. F. Williams, S. N. Samarin, A. D. Sergeant, A. A. Suvorova and 0. M. Artamonov List of Contributors

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PLENARY

ELECTRON COLLISIONS - PAST, PRESENT AND FUTURE. J.W.McCONKEY. Department of Physics, University of Windsor, Ontario N9B 3P4, Canada.

Abstract After broadly surveying the field of electron collisions over the past century and giving some of the highlights which have driven the field, the topic of electron spectroscopy is considered and its development outlined. As an example of current research, measurements of Cs cross sections in a magneto-optical trap are discussed in detail. Suggestions are given regarding possible future directions in the field.

Introduction. Electron-driven processes abound in practically every area of our experience. Electrons deposited from the solar wind, or released by solar photoionization, interact with upper atmosphere atoms and molecules to produce familiar auroral and airglow effects. At lower altitudes, lightning storms provide vivid illustrations of how electrons create powerful, natural releases of electrostatic energy. Missions such as Voyager and Galileo have revealed that electron collisions are important also in the atmospheres of other planets in our solar system, while the plasmas which abound in the deep space environment send a wealth of spectroscopic and other information to planet earth, much of which is electron driven. It is of interest to recall that it was in an attempt to explain the plasma, which resulted when an electric current was passed through a low pressure gas, that the electron was actually discovered (by J J Thomson in 1897). Everywhere an electrical discharge is initiated, whether it is in a fluorescent light fixture or a flat panel display system, a tokamak high current thermonuclear device or a high powered, laser-inertial-confinement device, we find examples of where high technology industry is putting electrons to work for our benefit. Electron driven discharges are essential components of Plasma-Enhanced Chemical Vapour Deposition (PECVD) and Plasma-etching technologies that are vital for the manufacture of micro-electronic components and devices. Plasmas are also used for safe destruction and disposal of toxic wastes (Becker et al, 2000). Another area where electron-driven processes are of importance is in the field of radiation damage. When high-energy radiation, such as X-rays or y-rays, enters the body, low energy secondary electrons are produced, which interact strongly, and often destructively, with biological material. Boudaiffa et al (2000) and Martin et al

3

4

(2004) have shown that dissociative attachment of low energy electrons can lead to both single and double strand-breaking processes in DNA. Recently, studies of the interaction of ultra-short, high-intensity laser pulses with atoms and molecules have produced startling effects in which the interaction of the electron with the radiation field of the laser plays a dominant role (see e.g. Niikura et al (2003), Weckenbrock et al (2003)). Comprehensive discussions on electron-atom (molecule) collision physics can be found in the books of Massey and Burhop (1969), Massey et al (1969), McDaniel (1989) and in the volumes of Advances in Atomic and Molecular (since 1990 Atomic, Molecular and Optical) Physics. Recent reviews on various aspects of the topic are those of Brunger and Buckman (2002), [electron-molecule cross sections], Surko et al (2005), [positron interactions], Hotop et al (2003), [low energy electron molecule collisions], Christophorou and Olthoff (2001), [interactions with excited targets], Andersen and Bartschat (2001) [alignment and orientation effects], and Zecca et al (1996, 2001), [integral cross sections]. We note the special data publications of relevance to the plasma science community, Christophorou and Olthoff (2001a), Kimura and Itikawa (2001) and Inokuti (2000). The latest developments are usually published in Physical Review A, Journal of Physics B, Journal of Chemical Physics and Journal of Physical and Chemical Reference Data. The main forum for presenting results at the cutting edge of the field is the biannual International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC). About one third of the papers presented at this conference are related to lepton collision research. This fraction has stayed approximately constant over the past 45 years. It is noteworthy that four of the five satellite meetings to this conference are partially or totally devoted to lepton collisions. Surveying the Past - Historical Highlights. Over the past century of electron collisions, it is possible to highlight many major advances and discoveries. Some of the more significant are listed below. Detailed references may be obtained from the books listed in the previous paragraphs. 1903. First electron scattering experiment (Lenard). 1914. Franck-Hertz experiment. Birth of electron energy-loss spectroscopy. 1921. Discovery of Ramsauer-Townsend effect. 1925. Electron spin proposed (Uhlenbeck and Goudsmit) 1927. Dirac Equation. - Electron spin, magnetic moment, anti-particle. 1927. Electron wave effects. Interference and Diffraction phenomena. (Davisson & Germer, G P Thomson).

5

1922-30. Early attempts at cross-beam measurements. 1927-36. Total ionization X-section measurements with static gas targets. 1930-2005. Continuous development of theoretical methods and models. 1932. Positron Discovered. (Anderson). 1954-63. Development of electrostatic energy analysers, 127° &1800. 1957-2005. H-atom used as test bed. (Fite, Williams, ....) 1957-62. Introduction of modern cross-beam methods. 1963. First resonance (He,19.37eV) in electron scattering discovered (Schulz) 1969. Complete scattering experiments proposed (Bederson) 1969. First e-2e experiments. (Ehrhardt, Amaldi). 1970. First experiments involving excited targets. 1971-3. First e-hv coincidence work yielding atomic alignment and orientation. 1980. Development of high intensity spin-polarized electron beams. 1987. Development of EBIT machine for electron-ion interactions,(Levine, Marrs) 1987. Development of COLTRIMS technique for complete momentum imaging of collision fragments, (Schmidt-Bocking, Cocke, Ullrich). 1987. Development of ELECTRON COOLERS in ion storage rings for highresolution recombination studies, (Danared et al). 1988. Introduction of "natural" parameters to define excited states (Andersen et al) 1992. Sub-meV resolution achieved for first time in gas phase (Hotop). 1995. MOTs used for e-collisions for first time (Lin). In many cases the field was driven by technological advances which stimulated a need for quantitative electron collision data or the development of electron optical devices. This has been ongoing since Lee de Forest invented the first vacuum tube amplifier in 1906. Since about 1930 the development of Fluorescent Lamps and other forms of lighting, has provided a continual stimulus for electron collision measurements. World War II stimulated the development of microwave technology, semi-conductors, and digital computers, while a short time later in 1947 the transistor was invented. The 1950s saw the development of the Maser and the declassification (in 1958) of high-current (thermonuclear) plasma research. The 1960s and 70s saw the invention of various types of gas lasers which fuelled a need for understanding the processes involved, many of which involved electron impact in a plasma environment. The 1970s and 80s saw many successful missions to study the environments of other planets in our solar system. Huge bodies of data were accumulated which demanded accurate electron cross section data to aid interpretation of the processes involved. 1984 saw the development of the PlasmaEnhanced Chemical Vapour Deposition (PECVD) process and this was followed in 1992 by the development of Plasma Etching technology. Both of these are important in the manufacture of microelectronics components and devices. Again a wide body of electron collision data are required for device optimization. Research into thermo-nuclear plasmas has continued steadily over the past 50 years with a steady demand for collision related data. This demand will continue for the next

6

few decades as the building and commissioning of the International ITER machine gets under way in 2005. The last decade has seen enormous strides in photonics development so that it rivals or exceeds electronics in technological importance. Electron Spectroscopy - Birth and Development The field of electron collisions has depended on the development of suitable measurement technology or, in the case of theory, of computational power. One of the key developments on the experimental side was in the area of electron energy loss spectroscopy. It is interesting to consider the earliest experiment in this field [Franck and Hertz, (1914)], because it was not until many decades later that the results were fully understood. The experiment was very simple in principle. Electrons were accelerated through a low pressure mercury gas towards a grid. On the other side of the grid was a collector biased slightly negatively relative to the grid. The current to the collector was monitored as a function of the accelerating potential between the electron source and the grid. If an electron lost energy, for example in an inelastic collision with a mercury atom, it could not overcome the negative bias, reach the collector and be measured. The result of the experiment was a series of peaks on the current-voltage graph. The peaks were separated by approximately 4.9 V. The experiment was interpreted (correctly) as demonstrating the existence of energy levels in the mercury atom with an excitation energy of approximately 5 eV. The experiment was a key to development of early ideas about atomic structure. As the spectroscopy of the mercury atom unfolded in subsequent years, it was established that there were indeed some energy levels with an excitation energy of around 5 eV. However these levels were designated 6 3Po,i,2 whereas the ground state was 6'S0. Excitation of a triplet level from the ground state necessitated an exchange process in which a projectile electron took the place of a target electron of opposite spin. It was some 60 years after the original experiment that Kessler, Hanne and colleagues at Munster did an experiment with spin polarized electrons to demonstrate that such an exchange process did indeed take place. Also, using a combination of sophisticated experimental and theoretical tools, they established the magnitude and near threshold variation of the excitation cross sections of the individual 6 3Po,i,2 states with incident electron energy. A number of important facts became evident. First, the 3P0 cross section was very small. This explained why the peaks in the Franck-Hertz experiment were not separated by 4.7 eV (the 3Po excitation energy). Second, the 3P] excitation cross section was dominated by a strong resonance enhancement right at its 4.9 eV threshold. Thus the reason why the Franck-Hertz experiment worked so dramatically was because of a phenomenon which was not discovered until some 60 years later!

7

Little progress in improving the resolution of energy loss spectroscopy occurred until mid-20th century when a surge of development work occurred leading to the so-called 127° cylindrical, the 180° hemispherical and various other analysers [see e.g. McDaniel (1989) for details]. Energy resolutions of 50 meV were readily obtained and this figure was rapidly reduced to below 10 meV as the century progressed. The current state of the art in gas-phase electron spectroscopy is probably represented by Allan (2004) with resolutions as low as 7 meV. Allan's instrument incorporates a Wien filter to allow discrimination between electrons and negative ions and also a magnetic angle changing device [Read and Charming, (1996)] that allows the backscattering region to be accessed and thus differential cross sections to be measured over the entire angular range. Incident energies in the tens of meV are routinely possible. Use of laser photoionization techniques have enabled electron sources of very narrow energy spreads to be achieved and electron attachment studies to be carried out at sub meV resolutions, [see Hotop et al, (2003) for details and references]. In parallel with all the experimental advances in instrumentation and techniques, there have been equally impressive developments in theoretical methods. These are highlighted in the cited reviews and in many of the invited presentations at this Conference. The interplay between experiment and theory is demonstrated in the many publications which deal with both the experimental and theoretical aspects of the particular scattering problem under consideration. These close collaborations bode well for the future health and development of the field. Case Study from the Present - Measuring Electron Cross Sections in MOTs. Use of MOTs for collision cross section determinations is based on very similar ideas to those present in the atomic beam experiments carried out at NYU in the 1960s. Rubin et al (1960) pioneered the use of the so-called "atomic beam recoil" technique for measuring electron scattering cross sections and Visconti et al (1970) applied it in a systematic study of the total cross sections for electron scattering from the alkalis. Lin and co-workers at the University of Wisconsin recognised that the sensitivity of the atom recoil technique could be greatly enhanced if optically trapped atoms rather than an atomic beam were used as the target. In a series of elegant, pioneering papers [Schappe et al, 1995, 1996, Keeler et al, 2000], they presented measurements of both total and ionization cross sections from ground state rubidium and also ionization cross sections out of the 52P excited state of this atom. The alkalis are particularly suitable for measurements using a MOT because of the availability of suitable diode lasers matching the wavelengths of the resonance transitions of these species. Further, because the act of trapping results in the preparation of a target with a large fraction of excited species, it is possible (as

8

demonstrated by Keeler et al, 2000) to obtain absolute cross section data involving these excited species. Interest in such data is intense, particularly from the plasma physics and industrial communities. Cesium is perhaps the most interesting alkali target because of its use in atomic clocks and in studies of thermo-ionic conversion in plasmas [Kuehn et al, 1978]. Further, being the heaviest of the alkalis, Cesium is also of great interest from a theoretical point of view because relativistic and atomic structure effects should be strong. In addition, significant disagreements existed between experimental measurements and between experiment and available theory, (see Zecca e? a/, (1996)). Principle of Method. When a collection of trapped atoms is irradiated by a beam of electrons and collisions occur, momentum is transferred to the atoms causing them to be ejected from the trap. Atoms are ejected from the trap due to the electron-atom collisions at a rate:

Te=oJ/e

(l)

where a is the cross section for ejecting atoms from the trap, J is the electron current density and e the electronic charge. Measurements of Te and J yield a directly. For very small scattering angles where the transfer of momentum in the collision is below some limiting value, the collision will not be violent enough to remove the atom from the trap. Calculations show that for our system (laser beam diameter, timing sequence etc) with elastically scattered electrons of 5 eV energy, electrons scattered at angles smaller than about 5° will not impart enough momentum to eject atoms from the trap. This is a negligible portion of the total solid angle. At higher impact energies the ranges of low angle scattering, which result in no contribution to the loss of atoms from the trap, become even smaller. Experimental Considerations. These have been outlined in detail in publications from our group, MacAskill et al (2002), Lukomski et al (2005) and so will only be briefly summarized here. We note also that a comprehensive review of the various techniques needed for measuring different types of cross sections using MOTs is available [Schappe et al, 2002]. The MOT is of a standard design except the anti-Helmholtz pair of coils, providing the magnetic trapping field, is positioned inside the ultra high vacuum vessel. They provide an axial field gradient of approximately 10 G/cm for an operating current of 2A. A specially designed pulsing circuit is used with these coils to allow the current to be switched rapidly by a TTL signal. This circuit also provides a means of rapidly dissipating the coil current to minimize the decay time of the magnetic field during switching.

9

The optical set-up for laser cooling of the atoms is standard so the reader is referred to our earlier publications for details. The atom cloud was monitored using two infra-red sensitive cameras positioned in the same, horizontal, plane. This allowed accurate monitoring of the position of the atom cloud which was vital in insuring proper overlap of the electron beam with the trapped atoms. The multi-element electron gun was designed to produce a broad near-parallel beam in the 5-400eV electron energy range. An oxide coated cathode was used and two pairs of electrostatic deflectors allowed accurate control and steering of the electron beam. Since accurate knowledge of the current density in the region of the MOT was necessary, two movable, 0.010" diameter, wire probes were arranged so that the electron beam profile could be monitored in two dimensions in a plane perpendicular to the e-beam direction. After scanning the e-beam diameter the wire probes could be retracted so that they did not interfere with the trapping laser beams. At each electron energy the gun controls were optimized so that the two measured diameters were as similar as possible. The measured profiles were then compared with a theoretical model where uniform density over the cross-sectional area of the beam was assumed. Good agreement between the measured and theoretical profiles was always obtained. A Faraday Cup system was used to monitor the total beam current. From the measurements of e-beam profile (discussed in the previous paragraph) and total beam current, the current density, J, (Equation 1), in the region of the atom cloud, was obtained.The MOT trapped atom fluorescence is collected and monitored continuously using a cooled EMI 9558 photomultiplier (PM) tube. The analogue output of the PM is digitized and monitored using a multichannel scaling plug-in card in the control computer. Thus the time variation of the trap fluorescence was recorded and displayed. Since it is not possible to introduce the electron beam while the trapping magnetic field is on, the experiment proceeds in a pulsed mode. The timing sequence for this is as follows. First the trap is turned off for a time, TB, (typically 20 msec) by switching off the magnetic field and the re-pumping laser. During alternate trap-off times an electron beam pulse is introduced for a time, Te (typically 8 msec) after a delay Te (1 msec). Trap fluorescence is monitored continuously with alternate cycles being stored in separate memories. The time evolution of the trap fluorescence, both with and without the presence of the electron beam pulse, is obtained and processed as discussed later. All of the measurements presented here are determined by recording two fluorescence signals. The first is measured in the absence of the electron beam pulse, and is necessary to establish a net background loss rate. This background loss rate is a combination of factors including thermal expansion, inelastic collisions

10

within the trap, gravitational acceleration, time-varying magnetic fields that occur during switching, and collisions with vacuum residuals. The second signal is measured in the presence of the electron beam pulse, and displays a larger loss rate that includes the net background losses, mentioned earlier, and also losses due to electron collisions. These fluorescence signals are measured sequentially. This ensures consistency in trapping parameters during data collection and minimizes longer term variations in background fluorescence, electron beam current, laser intensity and frequency detuning. Since, in this work, we are interested in cross sections involving ground state Cs atoms, the re-pumping laser is switched off prior to the introduction of the electron beam. Rapid optical pumping to a dark hyperfine level of the ground state occurs immediately, thus ensuring a total ground state target. Data Analysis During continuous operation of the trap, in the absence of an electron beam, the steady state trap population is given by: dN

r

r *r

— = L-r0N at

(2)

for a loading rate L from the atomic vapor, and a loss rate T0 which takes into account various trap loss mechanisms including inelastic collisions within the trap and collisions with vacuum residuals. Eliminating the trapping magnetic field or the output from either laser, effectively removes any loading and so the term is dropped from the differential equation leaving: d

N

^

A.

-=-rtN

(3)

In the presence of an electron beam, the loss rate is altered to T = T0 + T e , where Te is the loss rate due to electronic collisions, presented in Eqn.(l). From this, we obtain the following equations describing trap populations:

N(t) = N0 e-T«' N(t) = N0 e'^^'

(4a) (4b)

where N(t) describes the trap population as a function of time in the absence of an electron beam, and N(t) describes populations in the presence of an electron beam. To isolate the electron induced trap loss rate one takes the ratio of these two equations obtaining:

11

-*r-L = -JL e e N(t) N0

(5)

Due to the long 500ms time period of our pulsing scheme, the steady state populations with and without the electron beam are the same and, consequently, N0 IN0 = 1. As the electron beam is present for a time Te, the loss rate is obtained directly from:

In this work the cross section for ground state (62S1/2) Cs is measured using the fluorescence during the reloading phase. As the re-pumping laser must be off while the electron beam is pulsed on to ensure only the 62Si/2 state is populated, the trap is "dark" during the expansion phase. Following the removal of the re-pumping laser, the trap ceases to fluoresce in approximately 0.5 ms. While the actual response of the trap is not directly observable during the electron interaction time, the effect is reflected in the net difference of the trap populations during the initial reloading. The difference in the fluorescence, observed at the beginning of the reloading phases for the electron beam off and on, is due solely to the electron collisions that occurred during the expansion phase. We note that for each measurement, evaluation of any background fluorescence (from untrapped atoms or scattered laser light) had to be carried out. This was obtained by repeating the measurements using the same timing sequence as before but with the trapping magnetic field permanently off. By subtracting the resultant background signal we obtain the fluorescence yield due only to the population of trapped atoms. Results and Discussion. The figure gives our experimental data for the total cross section out of the Cs 62Si/2 ground state. Also included are data sets from earlier work. A number of points are immediately evident. Very good agreement exists between all the high-energy experimental results, (even those of Brode, 1929) above 100 eV. Below 100 eV Brode's data are clearly spurious. Our data agree very well with those of Surdutovich et al (2004) over the entire energy range covered by both data sets. Agreement with the early data of Jaduszliwer and Chan (1992) in the region below 20 eV is also very good. With the convergence of the experimental results obtained using three very different techniques, it is possible to assess the accuracy of the calculations. The figure suggests that although the CCC calculations yield accurate data at the higher energies, this is not the case as the energy is reduced below 75 eV. Divergence from

12 experiment continues down to at least 5 eV. The Breit-Pauli R-Matrix calculations of Bartschat (1993, 2000) and, particularly the CCC results, MacAskill et al, (2002), indicate a "shoulder" in the cross section at around 10 eV. This feature is largely absent from the experimental data. Below 9 eV the two theoretical curves diverge from one another. Some of this divergence is possibly due to structure differences or inner shell effects. It is an unavoidable fact that with increasing complexity of the target, the structure approximations become of increasing importance relative to the scattering approximations.

i i i IT|

'"I

i "I' riii"("|

I

I

i t"

a

o

1

'•§ w 1 for w Yg. 1. The attractive image force leads to an acceleration, and thus to a bending of the trajectory towards the surface. At a critical distance R = Rc the electronic response is no longer confined to a polarization within the surface but results in transfer of electrons into high lying states of the projectile. The formation of "hollow atoms" 9 (more precisely, hollow ions) marks this second stage. As the projectile approaches the surface, part of the potential energy is released by electron emission in Auger processes involving both electrons localized around the ion as well as near the surface. The relaxation during this stage is, however, too slow to render the projectile in its ground state. In vicinity to the surface, quasi-resonant capture from inner shells' ("side feeding" 10) as well as two-center Auger capture u begin to fill inner! shells marking the fourth stage of this process. The key feature of the slow deexcitation is that a significant fraction of the incident potential energy remains to be relaxed as the ion hits the surface. Consequently, dissipation will involve the electronic degrees of freedom of the Itopmost layers and, by way of electron-phonon coupling, of atoms and ions near the surface] The final stage is then the creation of defects, heating of the lattice, and ablation of surface material ("potential sputtering" 1 2 ' 1 3 ). Developing a quantitative description with predictive) power for such a complex array of processes has remained a challenge. Nevertheless, some progress made to date! will be highlighted in the following.

20 3. Theoretical M e t h o d s 3 . 1 . Classical

Over Barrier

Model

Classical models for the electronic dynamics have a long-standing tradition in atomic collision physics going back to Bohr's! account of energy loss of charged particles 14 . This tradition was continued with Thomas' genius analysis of electron capture in 1927 15 and later with the binary encounter model for ionization 16J For problems with one active1 electron, the "classical trajectory Monte Carlo (CTMC) Method" 17 was developed as an efficient algorithm with, quite often, quantitative predictive power. Classical methods are appealing in view of their simplicity compared to quantum calculations, even for simple systems. MQiile for fundamental atomic collision process, such as one-electron ionization and capture, quantum ab initio calculations are possible 18 - 19 , resorting to a classical descriptions is almost in inevitable for complex many-body (systems such as collisions with s u t faces. Among classical models, the classical over-barrier (COB) model has proven to be versatile and remarkably successful. The COB model was originally developed for one-electron capture into highly charged ions in ion-atom collisions by Ryufuku et al. 20 based on earlier work by Bohr and Lindhard 2 1 and later extended by Barany et al. 22 and Niehaus ^ 16 incorporate multi-electron transfer. Its extension to ion-surface collisions 1 , 2 , a provides a simple framework for the description of ion-surface interactions] The physical significance of the COB model Is derived from the fact that only classically allowed over-the-barrier processes as opposed to tunneling are sufficiently fast to be effective within the characteristic interaction time of the ion with the surface. An 'active' electron crossing the barrier is subject to the potential V(r, R), V(f, R) = Ve (f) + Vp{ (f, R) + Vpe (r, R)

(4)

where f — (x, y, z) id the position of the electron, with x and y parallel to the surface and z perpendicular to She (surface, and R = (Rx,Ry,Rz) is the position of the projectile (an HCI). The direct interaction between the electron and the HCI, Vpe, is given for hydrogenic projectiles by

VveftiL) = - - £ - . \r-R\ Corresponding single-particle core potentials available in the literature 2 4 . The interaction tron and the surface in absence of the HCI is potential" due to the presence of the HCI is

(5)

for non-hydrogenic ions are potential between the elecdenoted by Ve. The "image denoted by VJe. The latter

21 two potentials are markedly different for metals and for insulators 3.25>26. Choosing for simplicity pure Coulomb potentials the electronic self-image potential (Eq. (3 )} as the large-2 limit of Ve for metals, the position of Ithe saddle point z„,dV(zs)dz = 0 and the barrier height V(z„,R) can be determined analytically. The critical distance follows from 1>2'3'4, V(zs,Rc)=ET

= -W,

(6)

where W is the work function of the surface, as

Sott)*^-

(7)

The COH model predicts, furthermore, the critical quantum! number nc into which the first resonant capture event takes place, i / ^

(8)

These predictions pertain to the Hirst stages of the neutralization scenario

0

l l l l l l l l l t l l l l l l l l l l t l l t l l l l — I

10

20

30 initial charge 0

tiI

t

I

f—L

40

Figure 2. Scaled energy gain AE/W due to fmage acceleration for different targets. Experimental data: O : Al; A,D,Au(110),», Au. Also shown are the COB model (see Eg. 9) and the classical lower bound, from Ref. 28 and refs. therein.

22

and were initially difficult to verify since the subsequent violent relaxation processes tend to erase the memory on eadiexj stages J Eq. (7) mm first Indirectly tested (Fig. 2) by measurements 27,28 of the energy gain due to the Image acceleration! (Eq. (3)). Since the charge of the) projectiles is reduced |by one unit (Ql = Q,Q — 1...) I&t each successive critical distance, RC[Q') (Eq, (7)), the energy gain along the neutralization sequence ("staircase") follows as [2]

ra = ^ » "

(9)

in agreement with experimental data ?Ir??!?!L Similar estimates can be derived for insulators [3]. Direct test became available with the help of novel targets, metallic laanocapillaries, pioneered by the group of Yamazaki et al. 30 . Interaction with the! internal walls of capillaries allows to select trajectories that avoid a close encounter with the surface (trajectories of type 3 (Fig. 3)) thus allowing spectroscopic as well as charge-state analysis of the early stages bf the leutializatioi scenario. Application of the COB allows' tie determ¥ nation of the charge state fractions proportional to the areas of concentric tings whose thicknesses are determined by [Eq. (7). Good agreement of the COB simulations 31 , even when relaxation processes are neglected clearly

-Ml) •M3!

[Figure 3. Sketch of nanocapillary a n d typical ion trajectories (aspect ratio n o t t o scale), trajectories leaving t h e capillary in its initial charge s t a t e ( t y p e 1); trajectories underfeeing grazing incidence scattering (type 2), a n d trajectories leaving capillary before touching down probing early stages of hollow-atom formation (type 3).

23 100

I"*"!'"""""

Re = $QiW

©

•

without ftupti

01

•

o

0

1

•

*

0.01 2

'

•

0

*

•,.,J

,.,

3

*

A(1) 5

i?i 2 >

8

Figure 4. left) Final state charge fraction of JV6+ penetrating Ni nanocapillary. Open circles: expj (ref. 29), triangle: prediction by geometric cross sections (right), full circle: COB simulation (ref. 30), right] Decomposition of cross section into rings corresponding to sequential capture of electrons at the critical distance for each charge state.

supports the validity! of Eq~. (7) (Fig. 4). Very recently, much more detailed evidence on the early stages of hollow atom formation became available through spectroscopy of optical emission from high Rydberg states in Ar®(Q = 8 - 12). From the line intensity along the transitions n -»• n - 1, fche population of n shells could be determined 32 (Fig. 5). The peak in the initial state occupation! follows the prediction (EqJ 8). 3.2. Quantum Mechanical

Foundations

The COB model hinges on several Approximations. The most drastic ones include: tunneling (i.e. below barrier) transitions are neglected since they have small rates compared to over-barrier processes so that they give only a minor contribution to the reaction rate. Atomic states are assumed to exist as resonances near and above the barrier when the electron is classically allowed to escape. Optical dipole transitions within the projectile driven by dynamical polarization fields in the target (e.g. plasmon excitations) are negligible since these processes are intrinsically non-classical 33 . Furthermore, despite the slow velocities involved (vj. >_

-

i

i

-0.48

top Of baiifel -0.5 i

I

J

i ,,•

.1

«

I

i

1

»

I

i

i

(Figure 6. a) Position of the H(ls) resonance [Er =Re(B)] near an Al as function of R : —, A and 0 different complex-rotation calculations (ref. 25 and refs. therein), image Ishift formula Eia(oo) + [l/4(fl - zo)]- Also shown is the energy of the top of the barrier as a function of R (...). b) As in a) but for width of the if (Is) resonance [r = 2 Im(£)] tts a fnnrtinn of R.

be attempted for one-electron problems, either employing coupled-channel methods 39,40 or wavefunction propagation or a grid 41>42. The latter was

27

primarily used for the simulation of H~ detachment, which can be reduced Ito an effective one-electron problem. The electronic ground state of the surface, e.g. of LiF, provides an adequate representation of the channel potential. Quantum calculations for this problems have yielded valuable insights into the1 role1 of the Madelung potential for the detachment near LiF 41 and the influence of the projected bandgap of Cu 42 . Extensions to HCI have1 not yet been attempted. A potentially promising avenue for treating the time-dependent multielectron dynamics is time-dependent density functional theory (TDDFT). As a matter of principle, time-dependent density functional theory 43 provides a highly efficient method to solve the time-dependent quantum manybody problem] It yields directly the time-dependent one-particle density n(f, t) of the many-body system. IWithin TDDFT, the time-dependent density is represented through the time-dependent Kohn-Sham spin-orbitals $„,j (f, t) as

n(f, 0 = £ MF, 0 = E £ l*^(r, t)\2 ,

(10)

where N„ denotes the number of electrons of spin a. The one-particle spin-orbitals $CT]j (f, t) evolve Recording to the time-dependent Kohn-Sham equation governed by the one-particle Kohn-Sham Hamiltonian / / f 5 [ n t , n j = - i v 2 + Vext{f\ + V(r,t) +VH[n](f,t) +

(11)

Vxc[nt,rn](x,t),

which includes the external one-particle potential, the Hartree potential and the exchange-correlation potential. The initial states \$a,j(t -> — oo)) = \$o,j) a r e the occupied Kohn-Sham orbitals of stationary ground state density functional theory (DFT). In practice, however, applications are hampered by the lack of knowledge about the exact exchange-correlation potentiall VIC[n]. Its form is a priori not known and a convergent algorithm for its calculation to increasingly higher degree of accuracy has toot yet been proposed. Moreover, the rrarrp ber of occupied orbitals needed to adequately represent the density of states of a surface of a simple metal is large {Na > 103), thus represent a major numerical challenge. This is most likely the reason whyj only few [applications of TDDFT to ion-surface Scattering 44 ' 45 have been reported to date. A recent example for the1 time-dependent density fluctuation induced by a (triply Charged ion (Q = 3) in front of a jellium surface is shown in Fig.

28

7. At the surface1 the polarization (charge density giving rise to the image potential can he Qhsersoedt Simultaneously, the onset of charge transfer to the projectile becomes visible. At this farge; distance, R = 25, capture still proceeds by tunneling which is reflected in thd low electron density, JYe = Jv ndnr < 1 when intepating over a volume enclosing the projectile. Only neai Rc for over barrier processes reaches Ne « I". A major conceptually difficulty is that, even if n^t) would be exactly Icnown, a read-out functional to extract occupation numbers of excited pro-

^^%pf

^

figure 7. Potential energy surface (top picture) and induced TDDFT1 density change (bottom picture) for a triply charged ion approaching a jellium surface with r a = 3 and W = 0.33 a.u. for HCI-surface distance of ft = 25 a.u..

29 jectile and target states is still fussing. Only very recently, some progress in the construction of a. functional that, allow, to extract the S-matrix from the density, S[n], has been made 4 6 . 3.3. Hybrid Classical-Quantum Transport Theory

Simulations:

Classical

Going beyond simple one-electron (or mean field) descriptions requires novel concepts. We have recently introduced a classical transport! theory (CTT) which is based on a multi-particle Liouville master equation 4 7 . It invokes four major ingredients: a) the explicit treatment of multi-electron processes by following the time evolution of the joint phase space density p(h,R, { P ' p ' } , {P^}) that depends on population strings of ./V-electron states in the projectile { P ' p ' } and {P^} target, b) the usage of transition rates in the relaxation (or transport) kernel, that are derived from quantum calculations (mostly, first-order perturbation! theory) wherever available, e.g. two-center Auger capture and deexcitation rates 4 8 , and c) the embedding of these processes within the framework of a classical phase space transport simulation for the ion. The equation of motion of p is of the form of a Liouville master equation

where the "relaxation" (collision) operator includes single and double particle-hole (de) excitation processes which represent resonant capture, resonant loss, hold hopping, ionization by promotion through the continuum, Auger capture, Auger deexcitation and autoionization which depend on both the local position of the ion, R, and the population strings {p( p )} and {p' T )}. A detailed discussion of the rates1 entering |Eq. (12) is given in Ref. 47>48J The effective projectile potential Vp that governs the ionic motion will depend, in general, on the strings as well, i.e. Vp (R,{P(p'},{P(p'}J. Direct integration of the Liouville master equation (Eq. (12)) appears to be extremely difficult in view of the large number of degrees of freedom involved. Here, the fourth ingredient, d) solution by test particle discretization and a Monte Carlo sampling for ensembles of stochastic realizations of trajectories comes into play. We follow a large number of ionic trajectories with identical initial conditions for the phase space variables (R, vp) along an event - by - event sequence of stochastic electronic processes whose probability laws are governed by the rates of the

30

Underlying Liouville master equation. The probability for any process with transition rate Ta within a_time internal At to occur is determined by Wa(At) = 1 - exp(-A*r a ).

(13)

In order to decide which electronic transition (if any) takes place during the time period At, we use the rejection method for each of the distributions. At the same time the coordinate and velocity of the HCI are propagated in time according to a Langevin equation of motion. The resulting population strings {Pn {t)}» and {P^(t)}i\ for a single stochastic trajectory fi are discontinuous functions of time. After sampling a large number! of trajectories, one obtains smooth ensemble averages representing solutions of Eq. (12). Earlier and less complete simulations of the Neutralization scenario were given in Refs. 49 ' 50 . Variants of the present approach have been previously employed for energetic electron transport through solids 51 , ion transport through nanocapillaries to be discussed below, and very recently for the interaction of strong laser fields with large clusters 52 . For illustration, we present an application of Eq. (12) to the interaction of Ne 10+ with a LiF surface in vertical incidence. We focus on the existence of the f'trampoline effect". A microscopic trampoline effect! was proposed by Briand et al. 53 for insulators. As the HCI Approaches the surface, the formation of a hollow atom is accompanied by the microscopic charge up of the surface in the vicinity of the impact region. As surface charges (i.e.holes) feature only a slow mobility, the ion may be repelled by the charge patch without actually! touching down. The simulation of the average ion velocity (Fig. 8) requires a simultaneous simulation of the random walk of the electronic holes on the F~ sublattice which represent in this case the target strings {P^}The average velocity [uj_ of the projectile remains always [negative, meaning movement towards the surface. At distances larger than the critical distance for first electron capture, the projectile] is1 accelerated by the self-image interaction. As electron capture begins to contribute, the acceleration still continues but is reduced because the charge state of the projectile and its image has decreased and because the repulsion due to holes generated by capture increases. At around 11 a.u., the hole repulsion starts to dominate over the image acceleration and the projectile slows down. The repulsive force can offset the image acceleration. However, it |s, on the average, not strong enough to lead to a complete) stop and to a reversal of the projectile above the surface. Only 2 % of all trajectories are reflected at distances larger than 3 a.u. from the topmost layer and no

31 0.000 -0.002

- T -0.004 3

•5> -0.006

with hole hopping

-0.008

-0.010 0

5

10

15

20

R (a.u.) Figure 8. EvolutionI of the average vertical velocity vz of a N e l u + ion with an initial energy E/,in = 1 a.u. starting at a distance of 20 a.u. as a function of the distance from the surface. Solid line: with hole hopping; dashed line: hole hopping switched off.

fuming point was observed at a distance larger than 3.5 a.uj Such small distances of closest approach correspond already to the fringes of the binary collision regime and imply an (almost) complete neutralization of the highly charged! ion. IWhile we conclude that for a Ne 10+ vertically incident on an LiF surface, tthe trampoline effect, i.e., the above surface reflection leaving the ion in a multiply charged state, is absent, its occurrence for very high charge states where repulsion by slow holes should play a more prominent role remains an open question to be explored in the near future 54 .

4. Ion Transport Through Nanocapillaries Nanocapillaries play currently a very prominent role in HCI-surface interaction well beyond the original goal to study the early stages of the hollow atom formation. The focus has shifted towards transport through capillaries, particularly of ions in their original charge statesJ For metallic capillaries trajectories of type 11 (see Fig. 3) transport promises new information

32

t>n the stopping power (or friction force) |at unprecedentedly large distances from the surface 55 . For insulating capillaries a recently discovered ion guiding effect 58 due to self-organized charge up suggests the opportunity to build ion-optical devices for forming and guiding nano-sized beams.

4.1. Energy Loss in Metallic

Nanocapillaries

Calculation of the friction force for ions propagating parallel to the surface at large distances has remained a puzzle. Linear response (LR) theory for an electron gas within the framework of TDDFT yields an R~4 distance dependence from the surface caused by particle-hole excitations 57 . The apparently much simpler approach of the socalled specular reflection model pioneered by Ritchie et al. 58 predicts a much stronger friction force S decaying as R^3. This difference is of crucial importance for transport ^>f highly charged ions through nanocapillaries because of the high charge state Q > 1, S oa Q2 and the long interaction time during the propagation over mesoscopic distances (ss 1 — 10 /xm). This puzzle was recently solved 65 by noting that TDDFT-LR lacks the contribution of plasmon excitation k>f a jellium at large distances. In distant collisions, the long-wavelength or Optical limit (Q —• 0) is probed. Because of the lack of electron-phonon coupling in a jellium, the width ry of the plasmon peak vanishes as Q —> 0. Consequently, plasmons| can neither decay nor be excited. By correcting for the finite width at ^(Q —• 0) within a modified TDDFT calculation, the proper large distance behavior could be restored. Fig. 9 displays the correlated energy loss scattering angle {AE6) distribution of slow Kr30+ ions penetrating a metallic Ni nanocapillary. The predicted energy loss is found to be sufficiently large as to be accessible by future experiments. 4.2. Guiding through Insulating

Capillaries

CapilTaries"through insulating foils (PET or "Mylar", 56 and SIC^j 59) have been studied in several laboratories 60,61 . Unexpectedly, considerable transmission probabilities for projectiles in ftheir initial charge state were measured for incidence angles as large as « 20°. Apparently, ions' are guided along the capillary axis with a spread (FWHM) of A0OU( of several degrees for mylar 56 but close to geometric opening 80 for SiC>2 59 . Keeping the Initial charge state, contrary to the expected neutralization upon approach of the internal capillary surface, suggests that the ions bounce off the walls at distances' larger than the critical distance R^ ft y/2Q/W (Eq. (7)). We

33

•J

#.f»

S «

Figure 9. 2D correlation pattern between the energyi loss and the scattering angle of Kr 3 0 + ions passing through an Ni nanocapillary at 2.5 eV/amu energy. The distancedependent stopping power is calculated by the SRM (see text).

refer to this effect as a mesoscopic trampoline. Key to this process is the charging up of the internal insulator walls due to preceding ion impacts. Ion guiding through the capillary ensues as soon as a dynamical equilibrium of self-organized charge up by the ion beam, charge relaxation, and reflection is established. A theoretical description and simulation of this process poses a considerable challenge in view of the widely disparate time! scales simultaneously present in this problem: The microscopic charge-up and hole transport due to the impact of individual ion impact takes place on a time scale of sub-/s to fs with a typical hole hopping time rh < l ( T 1 5 s . The transmission time rt of a projectile ion through the capillary for typical ion energies of « 2QQ eV/u is of the order of n » 10~ 10 sJ Typical average time intervals 2 1 between two

34

subsequent transmission (or [impact) events in thel same capillary are, for present experimental current densities of nA/mm/\ of the order of At « 0.1 s, and finally, characteristic (bulk) discharge times1 n for these highly insulating materials, can be1 estimated from conductivity data to typically texceed r;, > 103 s and can even reach days. This multi-scale problem spans a remarkable 18 orders of magnitude. A fully microscopic ab initio simulation covering all relevant scales is undoubtedly! out of reach. The method of choice is therefore a simulation based on the classical transport theory discussed above, modified such that the discharge characteristics deduced from data fori macroscopic material Ipropertiesj of the nanocapillary material can be incorporated. Specifically, the bulk discharge time TJ, or bulk diffusion constant £>(, as well surface charge diffusion constant Ds arill he estimated from surface and bulk cour ductivity data for mylar 62 . The present approach represents a mean-field classical transport theory

Figure 10. Illustration) of transmission through insulating! nanocapillaries, schematically. Array of nanocapillaries oriented along the surface normal, inset: close-up of an individual capillary. Anl insulating foil (PET) with dielectric! constant e is covered on both sides with gold layers (dark shaded) preventing charge up of the target during experiment. Capillaries with radius a = 50 nm and L = 10/im are typically D = 500 nm &part. Projectiles enter and exit the capillary under angles 6i„ and Qout with respect to the capillary axis respectively] The capillary axis is either! normal to the surface or Gaussian distributed with A0a < 2° (FWHM).

35 63

based on a microscopic classical-trajectory Monte Carlo (CTMC) simulation for the ion transported, self-consistently coupled to the charge-up of and charge diffusion near the internal capillary wallsJ Initially, each ion impact at the surface deposits Q charges. The charged-up micro-patch will undergo surface diffusion with diffusion constant D3 as well diffusion into the bulk with diffusion constant Db- Bulk diffusion is extremely slow for highly insulating materials while the surface diffusion towards the grounded metallic layers (Fig. 10) will be a factor = 100 faster, thus governing the overall discharge process. Self-organized guiding sets in when a dynamical equilibrium betweenl charge-up by a series of ion impact^ at internal walls is established such that the electrostatic repulsion prevents further impacts and the ion is reflected at distances from the wall larger than the critical distance (Eq. 7) from the surface. The wall forms then an effective mesoscopic "trampoline" for subsequent ions and guides the projectile towards the exit, as shown for a few sample trajectories in Fig. 11.

Figure 11. Scatter plot of deposited charges in the interior of an individual capillary and resulting trajectories for 9i„ = 3 ° . a) zig-zag distribution leading to blocking for an Unrealistic choice (D3 =~T>b)\ 5) patch distribution leading to transmission for realistic lvalues (Ds = 100D6)-

A first quantitative comparison of the CTT simulation with experimental data can be made for the transmission probability as a function of the incident tilt angle 6in relative to the capillary axis (Fig. 12). Transmission occurs for $in well outside the geometric opening angle 0Q « QJj? bf the capillary. Theoretically predicted 63 efficiency in ion guiding agrees reason-

36 i

0.4-

i

i

i

-

0.35-V=fiT-V^^ 500

1000

-20 r 10

!

I

1500

kinetic energy (eV)

1000

1500

2000

kinetic energy (eV) Figure 14. Mass! removal due to sputtering bf (a) LiF and (b) of MgO x by highly Icharged ions as a function of ion impact energy. Left ordinate: in atomic mass units per incident projectile (as measured by the quartz crystal microbalance). Right ordinate: Corresponding sputter yield (in molecules per incident ion). Solid lines for guidance only; dashed lines: extrapolation to zero kinetic energy (from refs. 12 and 71).

it is the kinetic energy of the incident projectile that causes defects (e.g. lattice dislocations) along its track which then serve as transient trapping

41

centers for electronic defects caused by the accompanying potential energy. This interplay, which can be operative in a broad range of materials, mates potential energy induced sputtering a much more wide-spread phenomena. 5.3. Towards

Nanostructuring

The impact oFaTHpily charged ion creates a strong dislocation in the surface (Fig. 15) which, contrary to naive expectation, is not necessarily a

Ar* (SSS eV) on A1203

Ar7* (600 eV) on M2%

Figure 15. (a) UHV7CPM contact mode image of sapphire (XliiUaTTs-plane 0001)'bom^ barded with 500 eV Ar+ionsi The defects are topographic features; all dimensions in Manometers, (b) as in (a) but bombarded with 500 eV Ar7"*" ions. Nanodefects induced (by these ions with same kinetic but higher potential energy as compared to A r + , from ref. (74).

crater buti can take on the shape of a "blister"or "hillock" 75>74, as seen in AFM pictures. Clearly, the appearance on an AFM image may not accurately mirror the morphology of the defect as a clear-cut separation between microscopy and spectroscopy is difficult to achieve. In other words, an electronic delect may appear as a topographic defect 76 . Moreover, the size of Ithe tip may be* insufficient to distinguish the crater from its rim. Fig. 15 also illustrates size dependence of the nanodefect on the charge. HCI are therefore excellent tools to inscribe nano-sized structures into the Surface with the charge| as control parameter of its size. Future applications! hinge on the availability of additional elements of control for nanostructuring. This is a largely unexplored area of research for potential sputtering. For kinetic sputtering, self-organization of defect structures have been analyzed 77 and, in part, experimentally veriled

42 78

. Bradley and Harper (BHJ |have introduced a phenomenological diffusion (equation for the height ¥ariation h(x, y) the x — y plane, 77 ^h{x,y,t)

= -vo + vV2h(x,y,t)-DV2

(V2ft(*>V.*)) ,

(14)

Iwhere VQ is the constant ablation rate, v is the (negative) surface tension hvhile D is the diffusion fate for the surface curfalure. Eq. (14) applies to normal incidence. Additional terms with odd powers of the derivate |would appear for oblique incidence. Key to nanostructuring is the negative surface tension which describes, on a phenomenological level, the tendency towards spontaneous roughening of the surface under ion impact, i.e. randomly appearing depressions are deepened as they become more susceptible to further ablations than ^earby hills. The microscopic justification for Negative surface tension relies on the spike-like energy deposition pattern for kinetic sputtering. The balance of curvature diffusion which tends to smooth the surface and kinetic roughening results in self-organized nanostructuring. Ordered waveEke patterns have been predicted for oblique incidence. For normal incidence, a near-ordered hexagonal spatial correlation pattern in h{x,y} has been recently bbserved 78 , clearly pointing towards seli^organlzed ordered nanostructuring (Fig. 16). However, such a (pattern formation has not been theoretically accounted for! in detail. Moreover, translating these observations to [potential sputtering is1 not straightforward. Its primary energy deposition is expected to be markedly different

200 nm figure 16. SEM image of highly ordered cone-shaped dots on a (100) GaSb surface formed by ion impact, (a) The extract of a SEM image and (b) the corresponding two(dimensional autocorrelation reveal the regularity and hexagonal ordering of the dots (from ref. 77).

43 from Spikes along tracks. The challenge for the1 future is thus to develop a theory in analogy to the BH approach Eq. (14) for potential sputtering, in particular to explore the existence (or Absence) of the negative surface tension and to improve the BH equation such as td account for "crystallization" of defects in ordered hexagonal patterns. Work supported by the Austrian Fonds zur Forderung der wissenschaftlichen Forschung under proj. nos. FWF-SFB016 "ADLIS" and PT7449-TSTO2, by the EU under contract No. HPRI-CT-2001-50036, by the Hungarian Scientific Research Found: OTKA Nos. T038016, T046454, the grant f'Bolya" from the Hungarian Academy of Sciences, and the TeT Grant No. A-15/04J References 1. 2. 3. 4~.

JL Burgdorfer, P. Lerner, and F. W_ Meyer, PhysJ Rear. A44, 5624 (1991). J. Burgdorfer and F. Meyer, Phys. Rev. A47, R20 (1993). J. Hagg, C. Reinhold, and J. Burgdorfer, phys. Rev. A55 (1997). T. Burgdorfer in Review of Fundamental Processes and Applications of Atoms and Ions, ed. C. Lin (World (Scientific, Singapore 1993) p. 517-614. 5. H. Winter, Phys. Rep. 367, 387 (2002). 6. HP. Winter and F. Aumayr, J. Phys. B 32, R39 (1999). 7. A. Arnau et al., Surf. Sci. Rep. 27, 113 (1997). 8. F. Aumayr and HP. Winter, Nucl. Instr. & Meth. B 233, 111 (2005). 9. J.P. Briand, et al., Phys. Rev. Lett. 65, 159 (1990). 10. L. Folkerts and R. Morgenstern, Europhys. Lett. 13, 377 (1990). 11. H.D. Hagstrum, PhysJ Rev. 96 (1954) 336; Electron and Ion Spectroscopy of Solids, eds. L. Fiermans at al. (Plenum, NY, 1978) p. 273. 12. E. Parilis, Proc. Int. Conf. Phenomena in Ionized Gases, Editura Akademiei Repulicii Socialistic Romania, Buckarest, 1969, p. 24; I. Bitensky and E. Parilis, J. de Physicle C2, 227 (1989). 13. T. Neidhart, F. Pichler, F. Aumayr, HP. Winter, M. Schmid, and P. Varga, Phys. Rev. Lett. 74 5280 (1995). T. Neidhart, F. Pichler, F. Aumayr, HP. Winter, M. Schmid, and P. Varga, Nucl. Instr. & Meth. B 98, 465 (1995). 14. N. Bohr, Kgl. Danske Videnskab. Selska B. Mat-fys. Medd. XVIII, No. 8

riT48y. 15. 16. 17. 18.

L.H. Thomas, Proc. Roy. Soc. A114, 5611 (1927). T. Bonsen and L. Vriens, Physica 47, 307 (1970). R. Abrines and I.C. Percival, Proc. Phys. Soc. 88, 861, 873 (1966). see e.g. T. Winter, Phys. Rev. A 25, 697 (1982); N. Toshima, Phys. Rev. A 50, 3940 (1994). 19. see e.g. T. Minami et al. J. Phys. B 37, 4025 (2004). 20. H. Ryufuku, K. Sasaki, and T. Watanabe, Phs. Rev. A21 745 (1980). 21. N. Bohr and J. Lindhard, Dan. Vid. Sel. Mat. Phys. Medd. 78. No. 7 (1954).

44 22. A. Bardny, G. Astner, H. Cederquist, H. Danared, S. Huldt, PJ Hvelplund, A. Johnson, H. Knudsen, L. Liljeby, and K.GJ Rensfelt, Nucl Instr. & Meth. B9, 397 (1985). 23. A. Niehaus, J. Phys. B19, 2925 (1986). 24. R.H. Garvey, C.H. Jackman, and A.E.S. Green, Phys. Rev. A12, 1144 (1975), and references therein. 25. P.J. Jennings] R.O. Jones, and M. Weinert, Phys. Rev. B37, 6113 (1988); P.J. Jennings and R.O. Jones, Advances in Physics! 37, 3411 (1988). 26. S. Peutscher, X. Yang, and J. Burgdorfer, Phys. Rev. A55, 466 (1997). 27". H. Winter, C. Auth, R. Schuch and E. BeebeJ Phys. Rev. Lett. 7T, 1539 (1993T28. F. Aumayr, H. Kurz, D. Schneider, M.A. BriereJ J.W. McDonald, C.E. Cunningham and HP Winter, Phys. Rev. Lett. 71, 1943 (1993). 29. C. Lemell, HP. Winter, F. Aumayr, J. Burgdorfer, and F. Meyer, Phys. Rev. A53, 880 (1996). 30. S. Ninomya, Y. Yamazaki, F. Koike, H. Masuda, T. Azuma, K. Komaki, K. Kuroki, and M. Sekiguchi, Phys. Rev. Lett. [78, 4557 (1997). 31. K. T6k6si, L. Wirtz, C. Lemell, fend J. Burgdorfer, Phys. Rev. A 61, 020901 (R) (2000)i Phys. Rev. A 62, 042902 (2001). 32. Y. Morishita, R. Hutton, H.A. Torii, K. Tomaki, T. Brage, K. Ando, K. Ishii, and Y. Yamazaki, Phys. Rev. A 70", 012902 (2004). 33. C. Reinhold and J. Burgdorfer, J. phys. B 26, 3101 (1993). 34. P. Nordlander and J.C. Tully, Phys. Rev. Lett. 6 1 , 990 (1988); Surf. Sci. 211/212, 207 (1989); PEys: Rev. B 42, 5564 (1990). 35. A.B. Borisov and V. Sidis, Phys. Rev. B56, 10628 (1997). 36. E.A. Garcia et al., Phys. Rev. B59, 13370 (1999). 37. L. Wirtz et al^ Phys. Rev. A68, 032902 (2003). 38. G. Hayderer et al., Phys. Rev. Lett. 83, 3948 (1999). 39. S. Peutscher, Ph.D. Thesis, Ell Berlin, Shaker-Verlag (1998). 40. A. Borisov et al., Phys. Rev. B63, 045407 (2001). 41. A. Borisov and J. Gauyacq, Phys. Rev. B62, 4265 (2000). 42. EL Chakraborty et al., Phys. Rev. A 70, 052903 (2004). 43. E. Runge, E.K.U. GrossJ Phys. Rev. Lett. 52, 997 (1984). E.K.U. Gross, W. Kohn, Phys. Rev. Lett. 55, 2850 (1985). 44. K. SnafeF, N. Kwong, and J. GafciaT, SurT. Sci 199, 132 (1988). 45. C. Lemell et al., Nucl. Instr. Meth. B235, 425 (2005). 46. N. Rohringer, S. Peter, and J. Burgdorfer, submitted td Phys. Rev. Lett. (2005). 47. L. Wirtz, C. Reinhold, C. Lemell, and J. Burgdorfer, Phys. Rev. A67, 012903 (2003). 48. J. Burgdorfer, C. Reinhold, and F. Meyer, Nucl. Instr. Meth. B205, 690 (2003). 49. S. Winecki, M. Stockli, and C. Cocke, phys. Rev. A55, 4310 (1997). 50. J. Burgdorfer, C. Reinhold, and F. Meyer, Nucl. Instr. Meth. B98, 415 (1995). 51. J. Burgdorfer and J. Gibbons, Phys. Rev. A 42, 1206 (1990), J. Burgdorfer in Proceedings of 16th ICPEAC (eds. A. Dalgarno| et al.) AIP Conf. Proc.

45 205, 476 (1990). 52. C. Deiss, N. Rohringer, and J. Burgdorfer, Phys. Rev. Lett (2005, in press). 53. J.-P. Briand, S. Thuriez, G. Giardino, G. Porsoni, M. Froment, M. Eddrief, and C. S 1 ms have also been measured following free electron attachment in the Penning trap. Statistical arguments17 suggest that the autodetachment rate should increase as the internal energy in the ion is increased. This energy is governed by the electron affinity of the parent neutral, by the kinetic energy of the captured electron, and by the initial internal vibrational energy of the neutral which depends on its temperature. It is thus reasonable to attribute some of the variation in the observed lifetimes to differences in the initial internal energies of the target molecules and in the energy of the captured electrons. Despite this, significant discrepancies remain that merit further study. Paradoxically, some of the shortest lifetimes have been reported using jet-cooled targets,18 leading to speculation that IVR might be enhanced for vibrationally-excited molecules.19 At low n, the lifetime of ions formed in Rydberg atom collisions increases. This results because the size of the electron cloud becomes such that the product positive and negative ions must be formed in close proximity when their postattachment interactions become important. This is especially true for thermalenergy collisions where a significant fraction of the product ion pairs are electrostatically bound and unable to separate.20 Furthermore, post-attachment interactions can lead to transfer of internal energy from the negative ion into translational energy of the products. This can result in stabilization of the ion (or in an increase in its lifetime) and can increase the fraction of the product ion

69

pairs that are able to separate and be detected. While post-attachment interactions are of considerable intrinsic interest in their own right, they also provide a powerful means to measure the lifetimes (on a picosecond timescale) of excited intermediates. This results because electrostatic interactions between the product ions modify their trajectories and final velocities by an amount that depends on the lifetime of the intermediate and the energetics of its dissociation. Intermediate lifetimes can be determined by measuring the angular distribution of the product ions formed in low-n collisions.21'23 The velocity distribution of fragment ions formed in high-rc collisions, where post-attachment interactions are negligible, provides a direct measure of the translational energy release distribution and of the distribution of the excess energy of reaction between internal and translational motions of the fragments. To improve the kinematic specificity of the measurements, velocity-selected Rydberg atoms are employed. Arrival time gating is exploited to identify product ion pairs formed traveling in a desired plane. The ability to examine collisions in two-dimensions (2D) provides a clearer picture of the reaction dynamics and better highlights their characteristics. The ion angular and velocity distributions are analyzed using a Monte Carlo collision code based on the independent particle model. The capabilities of this approach are illustrated in Fig. 3 which shows the (2D) angular distribution of Br-, ions produced through dissociative capture in K(14p)/CH2Br2 collisions expressed as a function of the angle 8 between the initial K(«p) velocity vector and final Br - trajectory.23 A pronounced minimum is evident in the forward direction. This results because the mean velocity of the product Br - ions is comparable to that of the K+ core ions. Thus, if the K+ and Br - ions are initially formed traveling in the same general direction, their kinetic energy of relative motion will be small and a sizable fraction of the ion pairs

Fig. 3. 2D angular distribution of Br" ions produced through dissociative attachment in K(14p)/CH2Br2 collisions (ref. 23). • , experimental data. The lines show model predictions for assumed CH2Br2~" lifetimes of 0 ( — ), 3( ), and 6 ( — ) picoseconds.

-150

-100

-50

0

50

ANGLE (degrees)

100

150

70

will be electrostatically bound. If, however, the ions initially travel in opposite directions, their relative kinetic energy is much greater permitting a larger fraction to separate. Figure 3 includes the results of simulations that assume CH2Br2-* intermediate lifetimes of T = 0, 3 and 6 ps. As T increases, the asymmetry in the predicted distribution decreases because electrostatic interactions between the K + and CH2Br2-* ions lead to increasing deflection of the K + ion prior to dissociation. Post-attachment interactions still occur but the initial velocity of the K + ion becomes more random reducing the angular asymmetry. Although the angular distribution is not especially sensitive to T, the data do point to a very short intermediate lifetime and are well reproduced by assuming T ~ 0. This is consistent with the velocity distribution of the Br ions observed following high-K collisions. This is strongly peaked and corresponds to a narrow translational energy release distribution centered on -0.3 eV. This indicates that the intermediate must be sufficiently short lived that dissociation occurs before significant redistribution of the excess energy of reaction to internal motions can occur. 3. Dipole-Bound Anions Dipole-bound negative ions have been the subject of much recent experimental and theoretical interest.24,25 It is now generally accepted that neutral molecules with dipole moments > 2.5D can form dipole-bound negative ions in which the extra electron is weakly bound by the dipole potential of the neutral molecule in a diffuse orbital localized near the positive end of the dipole. Such species can be conveniently created through electron transfer in collisions with Rydberg atoms. In contrast to the behavior observed with targets like SF^ that attach electrons to form valence-bound negative ions, the production of dipole-bound ions is strongly peaked over a narrow range of n, behavior that can be accounted for using a curve crossing model.24 Given their weak binding (typically < 20 meV) and relatively large size, it is reasonable to expect that they will be quite reactive and display many of the behaviors characteristic of Rydberg atoms and that these might be analyzed using an independent-particle free-electron model. Indeed, recent work26 shows that dipole-bound ion collisions with attaching targets can lead to electron transfer reactions of the type -» CH3CN + ABC"

(7a)

-> CH3CN + AB + C -

(7b)

-

CH3CN~ + ABC -» CH3CN + ABC *

71 Such reactions are studied by injecting dipole-bound ions into the Penning trap in the presence of target gas and monitoring the time evolution of the total ion population. Data pertaining to CH3CN~7SF6 collisions are shown in Fig. 4. In the absence of SF6 the CHbCN- population decreases exponentially at a rate that corresponds to an effective lifetime 1 ~ 65 ms, a consequence of photodetachment induced by background thermal black-body radiation.27 With SF6 in the trap the total (CH3CN~~ plus SF6~) ion signal initially decays but a long-lived SF6~ signal remains at late times whose size increases with the target gas pressure. The electron transfer rates required to account for this signal are large, 1

< z

•

0.5

V)

'

z

V

"—

o 02

e

Fig. 4. Time development of the total trapped ion population following injection of CH3CN~ ions with: • , no target gas present; and o , • , v , SF6 target gas present at pressures of -2.8, 5.5 and 8.2 x 10-7 cm3 (see ref. 26).

• 0,1

-

"• 0

1

2

3

TIME (ms)

~2 x 10"7 cm3 s"1, yet somewhat less than those predicted by the free-electron model, i.e., Eq. (4). Earlier work concerning application of the free-electron model to Rydberg atom collisions has shown that Eq. (4) only applies when the probability that a molecule captures the electron during its passage through the electron cloud is small.28 This "transparency" condition can be satisfied if the electron cloud is large, if the target molecule has a small capture cross section, or if the relative heavy particle collision velocity is high. Theoretical calculations suggest that dipole-bound ions are relatively compact24 and, therefore, that this transparency condition is not satisfied in a significant fraction of collisions. The reaction rate is thus smaller than predicted by Eq. (4) and limited by the "hard-sphere" collision cross section. Initial capture, however, can still be viewed in terms of a binary electron-target interaction suggesting that dipole-bound ions might provide a valuable tool to explore electron-molecule interactions. In contrast to Rydberg atom collisions, there are

72

no long-range electrostatic interactions in the exit channel, meaning that postattachment interactions are reduced. Of particular interest are molecules like CH3NO2 that can form valencebound negative ions yet also possess dipole moments sufficient to support dipole-bound states. Questions then arise as to which type of anion might be formed and under what conditions, as well as to the extent to which the two states are coupled. Such questions can be addressed using Rydberg atom techniques.29'30 For example, studies of Rydberg electron transfer in K(np)/CH3N02 collisions show that whereas initial electron capture might be facilitated by formation of a diffuse dipole-bound "doorway" state this rapidly evolves, on a timescale < 50 ps, into a state with predominantly valence-bound character. This is consistent with theoretical work demonstrating that the coupling between dipole-bound and valence states in CH3N02~ is strong. 4. Elastic and Quasi-Elastic Electron Scattering Scattering of the Rydberg electron in its orbit leads to a variety of collision processes. Emphasis is placed here on those that occur with high-n atoms and the insights they provide into ultra-low-energy electron-molecule scattering. Quasi-elastic Rydberg electron scattering can lead to level shifts and broading and to changes in the electron orbital angular momentum, so-called t -changing collisions. Quasi-elastic scattering also causes irreversible dephasing of coherently excited Rydberg wavepackets. Such decoherence is of importance for all atomic systems considered as potential carriers of quantum information or for quantum control protocols. Recent theory31 indicates that measurements of the decoherence rate for wavepackets comprising a coherent superposition of neighboring Stark states can provide a sensitive tool for examining elastic electron-molecule scattering. The transfer of rotational energy to the Rydberg electron through reaction (2) can populate groups of higher-^ states (w-changing collisions) or cause ionization. For sufficiently high n, all rotational transitions will lead to ionization. Figure 5 shows the rate constant for destruction of an £ -mixed population of K(n£) Rydberg atoms in collisions with CH3CI.10 The rate constant is large and increases rapidly with n. In slow electron-polar molecule scattering molecular rotation is important and can average out all or part of the target dipole moment as observed in a laboratory-fixed frame. CH3C1 is a symmetric top with a dipole moment of 1.89D, too small to support a dipolebound state. The time-averaged space projection of its dipole moment is even smaller because at room temperature states with large J but small K tend to be

73

populated. In addition to the long-range term associated with this non-averaged residual component of the dipole moment, the electron-target potential also contains shorter-range terms arising from electron-induced dipole interactions. If the resulting total effective potential is able to support a virtual state, the cross section for super-elastic free electron scattering assumes the form10 o,(v e )oe-

1 1/

2x

.

2x\

0 e +K )

(8)

where -K /2 is the energy of the state and x is a parameter related to the nonaveraged component of the dipole moment. (When the latter is small, x ~ 1.) The best fit to the experimental data obtained using an expression of this form (and x = 0.95) in Eq. (4) is included in Fig. 5 and corresponds to a virtual (or

12 Fig. 5. Rate constants for destruction of an I -mixed population in collisions with CHjCl. • , experimental data; , fit using Eq. (8) (see ref. 10).

IS

b z z o o

< CE

0

200 400 600 BOO 1000 PRINCIPAL QUANTUM NUMBER, n

bound) state energy of-55 meV. The data, however, pertain to a distribution of rotational states and this energy must represent some average over this distribution. Theory confirms the existence of a dipole supported virtual state which (for J = K. = 0) is predicted to lie between 30 and 40 meV.32 Detailed studies of I -changing and ionization in K(np)/HF collisions at high n have also been reported.33 HF (|o, = 1.94D) is a particularly simple rotor allowing detailed analysis of the data. Comparison between theory and experiment points to the existence of a (J=0) dipole-supported virtual state with an energy of -1 to 1.5 meV further highlighting the role of dipole-supported states in electron-polar molecule scattering.

74

5. Conclusions As evident from the above examples, Rydberg atoms provide a powerful laboratory in which to examine low-energy electron-molecule interactions at energies that extend below those accessible using any alternate technique. These techniques can be applied to a broad range of target species and can provide new insights into a wide variety of collision process. Acknowledgments The research by the author and his colleagues described here was supported by the National Science Foundation and the Robert A. Welch Foundation. References 1. See, for example, Electron-Molecule Interactions and their Applications, edited by L. G. Christophorou (Academic Press, Orlando, 1984). 2. P. G. Datskos, L. G. Christophorou and J. G. Carter, J. Chem. Phys. 98, 7875 (1993). 3. D. Smith and P. Spanel, Adv. In At. Mol. Opt. Phys. 32, 307 (1994). 4. H. Shimamori, Y. Tatsumi, Y. Ogawa and T. Sunagawa, J. Chem. Phys. 97,6335(1992). 5. D. Klar, M.-W. Ruf and H. Hotop, Int. J. Mass Spectrom. 205, 93 (2001); A. Schramm, J. M. Weber, J. Kreil, M.-W. Ruf and H. Hotop, Phys. Rev. Lett. 81, 778 (1998). 6. J.-P. Ziesel, J. Randell, D. Field, S. L. Lunt, G. Mrotzek and P. Martin, J. Phys. B: At. Mol. Opt. Phys. 26. 527 (1993). 7. P.-T. Howe, A. Kortyna, M. Darrach and A. Chutjian, Phys. Rev. A 64, 042706(2001). 8. F. B. Dunning, J. Phys. B: At. Mol. Opt. Phys. 28, 1645 (1995). 9. See, for example, the articles by M. Matsuzawa and by A. P. Hickman, R. E. Olson and J. Pascale in Rydberg States of Atoms and Molecules, edited by R. F. Stebbings and F. B. Dunning (Cambridge, New York, 1983). 10. M. T. Frey, S. B. Hill, K. A. Smith, F. B. Dunning and I. I. Fabrikant, Phys. Rev. Letts., 75, 810 (1995). 11. X. Ling, B. G. Lindsay, K. A. Smith and F. B. Dunning, Phys. Rev. A 45, 242 (1992). 12. A. Chutjian and S. H. Alajajian, Phys. Rev. A 31, 2885 (1985). 13. C. E. Klots, Chem. Phys. Lett. 38, 71 (1976).

75 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

L. Suess, R. Parthasarathy and F. B. Dunning, J. Chem. Phys. 118, 6203 (2003). Y. Liu, L. Suess andF. B. Dunning,/ Chem. Phys.,122, 214313 (2005). L. Suess, Y. Liu and F. B. Dunning, Rev. Sci. Instrum. 76, 026116 (2005). L. G. Christophorou, Adv. Electron. Electron Phys. 46, 55 (1978). J. L. LeGarrec, D. A. Steinhurst and M. A. Smith, J. Chem. Phys. 114, 8831 (2001). H. Hotop - private communication. L. Suess, R. Parthasarathy and F. B. Dunning, J. Chem. Phys. 118, 10919 (2003). R. Parthasarathy, L. Suess, S. B. Hill and F. B. Dunning, J. Chem. Phys. 114, 7962 (2001). C. D. Finch, R. Parthasarathy, S. B. Hill and F. B. Dunning, J. Chem. Phys. 111,7316(1999). R. Parthasarathy, C. D. Finch, J. Wolfgang, P. Nordlander and F. B. Dunning, J. Chem. Phys. 109, 8829 (1998). C. Desfrancois, H. Abdoul Carime and J.-P. Schermann, Int. J. Mod. Phys. 5 1 0 , 1339(1996). R. N. Compton and N. I. Hammer, Adv. Gas-Phase Ion Chem. 4, 257 (2001). Y. Liu, L. Suess and F. B. Dunning, Chem. Phys. Lett, (submitted). L. Suess, Y. Liu, R. Parthasarathy and F. B. Dunning, J. Chem. Phys. 119, 12890(2003). Z. Zheng, X. Ling, K. A. Smith and F. B. Dunning, J. Chem. Phys. 92, 285 (1990). L. Suess, R. Parthasarathy and F. B. Dunning, J. Chem. Phys. 119, 9532 (2003). R. N. Compton et al, J. Chem. Phys. 105, 3472 (1996). C O . Reinhold, J. Burgdorfer, and F. B. Dunning, Nucl. Inst. Meth. Phys. Res. B 233, 48 (2005). I. I. Fabrikant and R. S. Wilde, J. Phys. B: At. Mol. Opt. Phys. 32, 235 (1999). S. B. Hill, M. T. Frey, F. B. Dunning and I. I. Fabrikant, Phys. Rev. A 53, 3348 (1996).

COLLISIONS INVOLVING PHOTONS

QUANTUM CONTROL OF PHOTOCHEMICAL REACTION DYNAMICS AND MOLECULAR FUNCTIONS* M. YAMAKI, M. ABE, Y. OHTSUKI, H. KONO, AND Y. FUJIMURA* Department of Chemistry, Graduate School of Science, Tohoku University, Sendai, 980-8578Japan A theoretical study is presented on the quantum control of two different types of molecular dynamics: cis-trans photoisomerization of retinal in rhodopsin and unidirectional rotational motions of chiral molecular motors. The former is characterized by nuclear wave packets propagation through a conical intersection. The latter is characterized by a rotational angular momentum of a functional group of a chiral molecular motor. One can control its rotation in the intuitive direction or that in the unintuitive direction by using the quantum control treatment. The mechanisms of these controls are clarified by analyzing time-dependent behaviors of nuclear wave packets.

1. Introduction Quantum control of molecular reaction dynamics has been attracted considerable attention [1,2]. In quantum control, atoms or groups in reaction species can be guided to a desired target state by using tailored electric fields of laser [3], This is greatly indebted to recent progress in laser technology such as pulse shaping techniques with adaptive feedback algorithm [4,5]. The effectiveness of quantum control originates from the fact that wave functions relevant to reaction dynamics are directly controlled through a coherent interaction between the molecule of interest and laser fields. Quite recently, there is an increased interest in control of molecular motors due to their important roles in functional molecular devices [6]. Particularly, molecular motors driven by optical fields are interesting because their control can be carried out within a ultrashort time scale [7]. In this paper, we present results of the theoretical study on quantum control of two different types of molecular dynamical systems: cis-trans photoisomerization and unidirectional rotational motions of a molecular motor " This work is supported by a Grant-in-Aid for Scientific Research on Priority Areas "Control of Molecules in Intense Laser Fields" from the Ministry of Education, Science, Sports, Culture and Technology, Japan. * Work partially supported by a Grant from Japan Society for the Promotion of Science for a JapanGerman Research Cooperation Program.

79

80

driven by laser pulses. The former is a typical example of photochemical reactions via a conical intersection in a multidimensional potential surface between the ground and excited electronic states [8]. The latter is one of the examples of molecular functioning such as acceleration or gearing in molecular motors [9]. 2. Cis-trans isomerization of photo-excited retinal in rhodopsin Cis-trans isomerization of retinal in photo-excited rhodopsin is the initial event of vision as shown in Fig. 1. The reaction takes place via conical intersections of the multidimensional potential surfaces between the ground and excited electronic states. Here, the potential consists of the cis-tarns isomerization reaction mode denoted by, which is a torsional vibratinal one and an effective coupling mode denoted by x, which is a CC stretching mode.

^UH*

11-cis retinal

"*HH+

all-trans retinal

Figure 1. Cis-trans isomerization of retinal in rhodopsin.

In the diabatic representation, the total Hamiltonian is expressed as

H=

2/ dip2 2m dx2

V 21

-fi'E(t).

V

(1)

r

22j

Here, I(m) is the reduced moment of inertia ( reduced mass). Vx/ (k and / = 1,2) denotes the diabatic coupling matrix elements, n denotes the dipole moment. E(t) is an electric field of laser pulse. An electric field of the optimal pulse E(t) is given as E{t) = -A\m< £{t)\W \V(i)>

(2)

where W is the target operator. *?(?), the wave function, is obtained by solving the time-dependent Schrodinger equation,

81

ihl\V(t)) = H\nt))

0)

t,(i) is the solution of Eq.(3) with the final condition, \4(tf)) = w\¥{tf)) at t = tf. The initial state of the photochemical reaction is set to be the lowest vibronic state of the cis isomer. The target is the ground state of the trans isomer restricted to a small range along the reaction coordinate. In the quantum control of this system, nuclear wave packet is localized in the target region 0e [0.97t, 1.1rc]in the adiabatic ground electronic state of the trans isomer.

Figure 2. (a) The optimal pulses obtained by the quantum control procedure and (b) the time evolutions of the cis-trans photoisomerization of retinal in rhodopsin; the target expectation value is denoted by a bold solid line, the ground-state population and the excited state population are denoted by solid and dotted lines, respectively.

Figure 2(a) and 2(b) show the optimal control pulses and the time evolutions of the reaction, which are calculated in the quantum control procedure, respectively. The target expectation value increases with yield of 38.3 % rapidly around the final time, tf= 500 fs. The subpulses created before ca. 400 fs are used to adjust the shape of the wave packet within the Franck-Condon region of

82

the cis isomer through multiple electronic transitions between the ground and excited states. To discuss the mechanisms of the cis-trans isomerization, Fig. 3(a) and 3(b) show the time evolution of population in the electronic excited state and that in the ground state in the reaction coordinate space, respectively [10].

200 300 time + i|65»/>/2 , respectively. Here, 165) and | 66) are eigenstates whose frequencies are equal to each other within 0.001 cm" Figure 5 shows the time-dependent behaviors of expectation values of instantaneous angular momentum [tit)) of the molecular motor driven by locally optimized laser pulses. The instantaneous angular momentum, (£(t)) , is defined as

{l(t))= £'daV\t)(-lh-p\v(t) da J

(4)

84

0

100

200

300

//ps Figure 5. Instantaneous angular momentum, {((,!)), of the molecular motor driven by controlled laser pulses: (a) rotation in the intuitive direction, and (b) rotation in the unintuitive direction.

The sign and absolute quantity of the expectation value represent the direction of the angular momentum and its magnitude, respectively. Figure 5 indicates that rotational directions of the motor are controlled well at the final time of 300 ps. It should be noted that there exists time difference in ignition between intuitive and unintuitive rotational directions. Figure 6 shows time-frequency-resolved spectra of the optimized electric fields to rotate the motor in the intuitive and unintuitive directions shown in Fig. 5(a) and 5(b), respectively. This figure indicates that the electric fields consist of four components in a global sense. The first two components simultaneously operate at the initial stage of motor ignition ( 0 - 160 ps). The third component dominates in the low-frequency regime of the torsional motion whose potential is highly anharmonic. The third component bridges between the initial stage and the final stage of ignition (180 - 250 ps) at which unidirectional rotation starts. The fourth component accelerates the rotational motion.

85 (a)

E o

(b)

100

150

200

250

300

t /ps Figure 6. Time-frequency-resolved spectra of the electric fields of laser pulses obtained by using a locally optimized control procedure: (a) for the intuitive direction of rotation and (b) for the unintuitive direction of rotation.

4. Conclusion In this paper, we have presented a theoretical study on quantum control of two types of molecular dynamics, cis-trans photoisomerization and unidirectional rotational motions of molecular motor driven by lasers. In the case of cis-trans photoisomerization, the subpulses designed by using the optimal control procedure work for adjustment of the shape of the wave packet within the Franck-Condon region of the cis isomer through multiple electronic transitions. We have theoretically shown that unidirectional motions of a chiral molecular motor can be controlled by using designed mid-infrared laser pulses. Their pulses are designed by using a local control method. The direction of rotation is determined by the phase of a coherent superposition of rotational eigenstates created by designed pulses.

86

Acknowledgments We thank Prof. S. Koseki and Dr. K. Hoki for their critical comments and suggestions. References 1. G. Vogt, G. Krampert, P. Niklaus, P. Nuemberger and G. Gerber, Phys. Rev. Lett. 94,068305-1(2005). 2. R. A. Gordon and Y. Fujimura, "Coherent control of chemical reactions", in Encyclopedia ofPhysical Science and Technology (Academic Press, San Diego, 2002) p. 207. 3. J. R. Levis, G. M. Menkir, and H. Rabitz, Science, 292,709(2001). 4. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle and G. Gerber, Science, 282, 919(1998). 5. R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68,1500(1992). 6. J,-P, Sauvage, volume editor, Molecular machine and motors (Springer,Berlin,2001). 7. K. Hoki, M. Yamaki and Y. Fujimura, Angew. Chem. Int. Ed., 42, 2975(2003). 8. W. Domcke, D. R. Yarkony and H. Koeppel, editors, Conical Intersections (World Scientific, Singapore, 2004). 9. K. Hoki, M. Yamaki, S. Koseki and Y. Fujimura, J. Chem. Phys. 118, 497( 2003). 10. M. Abe, Y. Ohtsuki, Y. Fujimura and W. Domcke, in Ultrafast Phenomena XIVedited by T. Kobayashi et al. (Springer-Verlag, Berlin, 2995), p.613. 11. Y. Ohtsuki, H. Kono and Y. Fujimura, J. Chem. Phys. 109,9318(1998).

MANIPULATING AND VIEWING RYDBERG WAVEPACKETSt ROBERT R. JONES Physics Department, University of Virginia, 382 McCormick Road Charlottesville, VA 22904-4714, USA Essentially all processes within atoms and molecules, as well as the interaction between atoms/molecules and applied fields, depend critically on the relative positions and/or momenta of the particles and their orientation with respect to external fields. Yet in most experiments these key parameters are not well defined, but instead, are distributed over a range of values according to a quantum probability amplitude or statistical ensemble. However, ultra-short laser pulses (or pulse sequences) can be used to create coherent superposition states in which the reactants are localized in specific coordinates at particular times. In Rydberg atoms, the electronic eigenstates serve as the building blocks for creating specific time-dependent structures, i.e. wavepackets, within atoms. The manner in which the wavepacket evolves is determined by which eigenstates are superimposed, and the time scales over which the evolution occurs is determined by the inverse of the energy differences between eigenstates. Recent experiments performed using appropriately designed wavepackets have enabled our investigation of nonperturbative dynamics as a function of the initial values of key parameters such as relative distance, momenta, and/or orientation.

1. Introduction During the past decade remarkable progress has been made in the use of ultrashort laser pulses to manipulate and view quantum dynamics within atoms and molecules. Long-term goals motivating this research include: coherent optical steering of molecular reactions through interfering pathways toward a specific final product; storage and processing of classical and quantum information; and a more complete understanding of me relationship between quantum and classical descriptions of physical phenomena. Rydberg atoms provide particularly attractive systems for exploring problems related to these goals. First, because of the large spatial extent of the Rydberg wavefunction, the system Hamiltonian and quantum-state evolution can be readily manipulated through the application of relatively weak electromagnetic fields [1]. Second, the eigenstate density, associated evolutionary timescales (T* = 2;i/AEj (a.u.)), and dynamical complexity can be continuously tuned with excitation energy [2]. Third, provided the Rydberg electron is attached to a spatially localized ionic core, its response to external electromagnetic fields can be numerically modeled with high accuracy. Such calculations enable important checks of the fidelity of different experimental approaches for creating and probing wavepackets under a variety of experimental conditions.

f

Work supported by the NSF and the AFOSR.

87

88 The techniques associated with the creation and observation of single electron Rydberg wavepackets have evolved rapidly beyond simple demonstration experiments [2]. A variety of methods are now available for manipulating and viewing various aspects of electron dynamics [2-6], constituting a sophisticated toolbox for engineering specific wavepackets to isolate and dissect complex problems and processes. For example, we have explored a number of interesting phenomena related to 3-body, electron-ion recombination as a function of continuum electron energy and distance from the capturing ion [7-9]. In the experiments a well controlled unipolar electric field pulse simulates the impulse delivered to the electron by a third, passing charge. We have also employed wavepacket methods to study electron-electron interactions in a precisely controlled environment [10,11]. Dynamical investigations of wavepackets in 2-electron atoms are intriguing for many reasons. For instance, the configuration interaction between 2-electron channels in atoms is analogous to the coupling that occurs between rotational, vibrational, and electronic modes in molecules. Conveniently, in doubly-excited Rydberg atoms, the number of coupled configurations and, therefore, the system's complexity can be readily tuned by increasing the total excitation energy toward the double ionization threshold. Moreover, at low to intermediate excitation energies, proof-of-principle atomic experiments exploring the feasibility of different schemes for coherently controlling multi-configurational quantum dynamics [12-14] can be accurately simulated using R-matrix based multichannel quantum defect theory (MQDT) [15,16]]. At higher energies, the situation is considerably more complex. Of course, this 3-body Coulomb problem is deceptively complex and has a long history in atomic physics [17]. Motion in large regions of the 2-electron parameter-space is classically chaotic, and the failure of the old quantum theory to accurately treat the problem played a central role in its abandonment in favor of the new theory. The problem still has no general solution in either quantum or semi-classical mechanics, and very near the double-ionization threshold, the enormous density of states makes even approximate quantum calculations extremely difficult. On the experimental side, spectrally resolving individual resonances using frequency domain spectroscopy becomes impossible in the extreme "classical limit" where the electrons have nearly identical binding energies [18,19]. However, coherent short-pulse laser excitation of double Rydberg wavepackets (DRWs) provides direct access to the classical limit, enabling observation and control of highly correlated two-electron dynamics in this previously inaccessible regime.

89

Because the 3-body Coulomb problem has no general solution, a common theoretical procedure has been to consider the stability of particular electron configurations, or modes, at specific energies [17]. In the classical limit, at energies near the double-ionization threshold, this molecular analogue approach becomes particularly difficult due to the diverging number of ways the two electrons can share their total energy and angular momentum. Interestingly, modes that intuitively appear stable (e.g. symmetrical planar orbits) can be quite unstable, while others (e.g. two electrons on the same side of the nucleus) that appear fragile, are remarkably robust [17]. As noted above, electronic wavepackets with specifically tailored probability distributions are now routinely produced in highly-excited single-electron Rydberg atoms [2]. We have extended this methodology and borrowed the basic philosophy of the molecular mode approach to perform the first time-domain investigation of the decay dynamics of DRWs and electron recapture via 'post collision interaction' between double continuum wavepackets [20]. 2. Experiments The DRW experiments are performed in a vacuum chamber with a background pressure, P ~ 10"7 Torr, and use low density, p < 1010 atoms/cm3, gas-phase barium atoms as targets. The target atoms are produced in a thermal atomic beam which originates in a resistively heated oven. The atoms in the beam pass between two parallel, conducting field-plates which serve to define the laser/atom interaction region. Spectrally tailored picosecond laser pulses sequentially excite two Rydberg wavepackets from the Ba ground state. As shown in Fig. 1, the first two laser pulses excite the first electron, ei, creating a 5d5/2n!d radial Rydberg wavepacket. Two additional pulses then launch the Ba+ 5d electron, e2, into a Ba+ n2g wavepacket. Any ions or electrons that are formed in the interaction region via are pushed by a static or pulsed "clearing" field, through a hole in the upper field-plate, toward a micro-channel plate (MCP) detector. The final state-distribution of Rydberg atoms or ions can be monitored using a ramped clearing pulse and state-selective field ionization (SSFI) [1]. 2.1. Bound-State Dynamics Initially, the DRWs created during the sequential laser excitation can be characterized as two distinguishable electrons, ei and e2, that are spatially separated in concentric shells with well-defined radial positions and momenta [2]. In the absence of their mutual Coulomb repulsion, d and e2 would move independently in their respective singly and doubly charged ion potentials.

90

Furthermore, in analogy to classical electrons in Kepler orbits, each would travel periodically between the nucleus and its maximum radius, R] ~ 2ni2 or R2~ n22, with Kepler periods of Xi = 2;mi3 and Tj = itn^/l, respectively. Of course, the electrons are not independent. They interact through their mutual Coulomb repulsion and eventually autoionize to form a free electron and a highly excited ion. We measure, using SSFI, the final distribution of Rydberg ion binding energies as a function of the initial radial positions and momenta of the two electrons. The experimental results are in good agreement with the results of a classical trajectory Monte Carlo (CTMC) simulation, and can be understood using a quantum sudden approximation model that describes the decay and resulting energy distribution of the entire class of radial DRWs [11].

6s:('S„) Figure 1. Schematic diagram of the sequential 4-laser excitation of double Rydberg wavepackets. The inset cartoon depicts the two radial wavepackets soon after the second electron is launched.

Previous frequency domain investigations of double Rydberg atoms have had insufficient resolution to provide any structural or lifetime information for configurations where the radial extents of the two electrons are comparable, i.e for R 2 > Ri/3 or so [18,19]. However, our time-domain experiments enable the study of DRWs even in the extreme case where R2 > Ri. In this situation, ignoring the e r e2 interaction, the wavepackets pass through each other at some critical radius Ro, determined by the delay T, between the launch of the two wavepackets. In our first investigation of DRWs, the delay dependence of die ionic-state distribution was used to infer temporal information regarding the stability and decay dynamics of these fragile systems. Through this measurement, we have developed an intuitive, sudden approximation picture of the time-dependent e-e interactions that govern the decay of all radially localized DRWs. Figure 2 compares the measured delay-dependent autoionization yield percentages for two different DRWs. In both cases, ei is launched with mean

91 principal quantum number ni = 32, Rt = llSnm, and TI = S.Opsec. For DRW1, ea has mean principal quantum number n2 = 70, R2 = 26Qnm, and t2=13psec. In DRW2, e2 is a more tightly bound packet with n2 = 50, R2 = 133nm» and T2=4.8psec. Notably, the signals in Figure 2a have clear delay dependences with period ti, while those in Figure 2b are essentially independent of T. Because any interaction between the two electrons will alter their motion and respective time scales, 11 corresponds to a physically meaningful period only until the first collision! Thus, its conspicuous appearance in Figure 2a indicates that for DRW1, the autoionized election energies are determined by the first e-e collision at or near RQ. The energy distributions in Figure 2a are qualitatively what we would expect from a single collision at RQ: tightly bound Ba+ ions (lower panels in Fig. 2a) and high energy free electrons are produced only when the wavepackets cross with high momentum near die nucleus (T = 0 aid 5 psec). Weakly bound ions (upper panels in Fig. 2a) dominate the signalforRQ-> RJ (T = 2.5 and 7.5 psec), where coherent scattering results in low momentum/energy transfer. Clearly DRW1 is extremely unstable and destroys itself in a fraction of e2*s Kepler period. In contrast, die lack of any delay dependence in Fig. 2b indicates that DRW2 does not autoionize immediately, but rather undergoes multiple collisions prior to electron escape. Multiple interactions homogenize the system so that die initial crossing radius has negligible impact on the final electron energies.

Delay ( p )

Delay (ps)

Figure 2: The panels In (a) and (b) show the percentage of total ions detected at five binding energies (from top to bottom: -130, 470, 495, -230, and -250 cm"1) following the autoionization of DRW1 and DRW2, respectively. The upper scale on each graph indicates the approximate phase of ei's orbit during the first wavepacket crossing, d is near the nucleus at integer multiples of TI, and near its outer turning point, Ri, at half-integer multiples.

92 Somewhat surprisingly, we find that the delay dependence of the finalstate Rydberg ion energy distribution can be quantitatively predicted by considering only the lowest order term in the electron-electron interaction and the sudden change in screening that occurs when the two wavepackets cross. In this approximation, the ei-e2 collision manifests itself as a sudden change in effective nuclear charge seen by the two electrons such that Zi—>2, Z2—»1 and Ej-^Ei-l/Ro = Ei', E2->E2+l/Ro = E2' where E, = -l/2n,2 and Ej = -2/n22 . Instant ionization occurs if and only if E2' > 0, i.e. if the wavepackets cross within a critical radius, Ro < Re = |E2|_1. For DRW1, the maximum possible crossing radius is Ro=Ri < Rc=130 nm, so immediate ionization occurs at the first wavepacket crossing for any initial condition. However, for DRW2 Re = 66 nm, and due to the highly non-linear radial dependence of the electron's velocity, Ro < Re for < 1 psec during each orbit of ei. This time is comparable to the duration of the laser pulse that excites ei, therefore, no signature of immediate ionization is resolved in Fig. 2b. For the instant ionization case, the final-state ion energy distribution can be simulated by projecting the evolving wavepacket, ei, onto the known eigenstates of the Ba+ ion, and the results are in very good agreement with the data and CTMC calculations. For DRW2, e2 remains bound after passing through e] at Ro ~ R] > R^. Some time later, e2 returns to the nucleus, crossing ei along the way. It is most probable ei will again be located near R! during the second collision, and e2 returns the energy it gained during the first interaction back to ei. Thus, there is approximate cycle-averaged energy conservation for the individual electrons. Autoionization does not occur until, on some subsequent orbit, the outward moving e2 crosses ei at a radius < Rj. Since the precise return times for e2 depend critically on the initial and subsequent wavepacket crossings, there is no well-defined final collision time and no time-dependent features in the ion energy distributions are expected. Accordingly we find that the final-state energy distribution for DRW2 can be quantitatively predicted by projecting ej's cycle-averaged spatial probability density onto the eigenstates of the Ba+ potential. The good agreement between the approximate quantum and exact classical calculations, supplemented by additional information on the ionization dynamics from classical simulations, supports our proposition that a gradual diffusion of energy from one electron to the other does not occur. Instead, for this entire class of radially-localized DRWs, the energy transfer required to ionize the atom occurs in a single violent collision.

93

2.2. Continuum Dynamics - PCI in the Time-Domain In a similar set of experiments, the frequencies of the lasers used in the DRW experiments were tuned slightly to the blue to sequentially ionize the two valence electrons from neutral Ba, forming an £id£2g double continuum wavepacket (Ei ~ e2 ~ 20 cm"1) [10]. In this scenario, the Coulomb interaction between the outgoing, radially localized wavepackets can result in the recapture of one of the electrons by the parent ion [10,20]. Note that since e2 moves in the deeper Ba2+ potential, at any given radius its kinetic energy is larger than that of ei and, therefore, the two wavepackets always pass through each other. Although PCI has been studied in detail in the frequency domain, to our knowledge ours was the first direct time domain exploration of this effect. In the experiments, the energy distribution of Rydberg ions formed via this 'post-collision' interaction (PCI) was measured via SSFI as a function of the delay between the ionizing laser pulses. As with autoionization in the DRW experiment, the experimental data and CTMC simulation are in agreement with a quantum sudden approximation that considers only the lowest order (s-wave) change in screening that occurs when the two packets cross at some critical radius, Ro (see Fig. 3). More tightly bound states are produced if the wavepackets cross nearer to the ion core where the electrons have more momentum to exchange.

Ionization Field (V/cm)

Ionization Field (V/cm)

Figure 3: Percentage recapture yield as a function of final-state principal quantum number N at two different delays between the ionization of the two electrons (i.e. two different values of Ro). The lower horizontal axis shows the ionizing field at which Rydberg electrons are liberated.

The success of the sudden approximation is somewhat surprising given that, at this low energy, two non-interacting wavepackets move a considerable distance while overlapped. Moreover, the CTMC calculation predicts that very high-L states are produced via PCI so that the collision is not really in the swave limit. Apparently then, even though the lowest order sudden

94

approximation model accurately predicts final state energy distributions, it must fail to describe the collision details and subsequent electron dynamics. 3. Future Plans We are now attempting to use sub-picosecond unipolar electric field pulses, i.e. half-cycle pulses (HCPs), to directly probe the evolution of DRWs. Specifically, the probability that a HCP produces Ba2+ ions from a DRW should be considerably higher prior to autoionization of the doubly excited atom. Thus, by monitoring the Ba2+ yield as a function of the HCP delay relative to the creation of the DRW, we hope to measure the precise time(s) at which energy is exchanged between two electrons within the same atom. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

T.F. Gallagher, "Rydberg Atoms," 1st Ed. (Cambridge Univ. Press, 1994). R.R. Jones and L.D. Noordam, Adv. in At. Mol. Opt. Phys. 38, 1 (1997). R.R. Jones, Phys. Rev. Lett. 76, 3927 (1996). T.C. Weinacht, J. Ahn, P.H. Bucksbaum, Phys. Rev. Lett. 80, 5508 (1998). R.R. Jones and M.B. Campbell, Phys. Rev. A 61,013403 (1999). T.C. Weinacht, J. Ahn, and P.H. Bucksbaum, Nature 397,233 (1999). T.J. Bensky, M.B. Campbell, R.R. Jones, Phys. Rev. Lett. 81, 3112 (1998). J.G. Zeibel and R.R. Jones, Phys. Rev. Lett. 89, 093204 (2002). J.G. Zeibel and R.R. Jones, Phys. Rev. A 68, 023410 (2003). S.N. Pisharody and R.R. Jones, Phys. Rev. Lett. 91, 203002 (2003). S.N. Pisharody and R.R. Jones, Science 303, 813 (2004). D.W. Schumacher, B.J. Lyons, and T.F. Gallagher, Phys. Rev. Lett. 78, 4359 (1997). R. van Leeuwen, K. Vijayalakshimi, and R.R. Jones, Phys. Rev. A 63, 033403 (2001). S.N. Pisharody and R.R. Jones, Phys. Rev. A 65, 033418 (2002). C.H. Greene and M. Aymar, Phys. Rev. A 44, 1773 (1991). W.E. Cooke and C.L. Cromer, Phys. Rev. A 32, 2725 (1985). For an excellent review see: G. Tanner, K. Richter, and J.-M. Rost, Rev. Mod. Phys. 72,497-544 (2000) and references therein. U. Eichmann, V. Lange, and W. Sandner, Phys. Rev. Lett. 64,274 (1990). R.R. Jones and T.F. Gallagher, Phys. Rev. A 42, 2655 (1990). A. Neihaus, J. Phys. B 10, 1845 (1977).

ANGLE-RESOLVED PHOTOELECTRONS AS A PROBE OF STRONG-FIELD INTERACTIONS* MARC VRAKKING FOM Institute for Atomic and Molecular Physics (AMOLF) Kruislaan 407, 1098 SJ Amsterdam, The Netherlands We present experiments on photoionization in a strong DC electric field and in strong low-frequency radiation fields, emphasizing the importance of the trajectory of the electron and the instantaneous electric field of an intense light source, respectively. Combining these results, the formation of attosecond laser pulses in high-harmonic generation becomes a direct consequence of the physics of strong field ionization. We discuss how two-dimensional photoelectron momentum maps may in the future be a key to the application of attosecond laser pulses in studies of time-dependent electron dynamics.

1. Introduction The recent development of attosecond laser pulses through high-harmonic generation and their characterization using a variety of cross- and autocorrelation techniques' has sparked interest into the question how attosecond laser pulses can be used to study electron dynamics in atoms, molecules and more complex systems. The application of attosecond techniques to these systems poses several important challenges. First of all, the observation of electronic wavepacket motion requires that electronic states are coherently excited with a pulse that is comparable to or shorter than the characteristic timescale of the motion. In many systems of interest this poses a challenge, since the excitation energies of the states of interest are in the UV or VUV range, whereas all attosecond pulses that have been generated and characterized sofar operate in the XUV (extreme ultra-violet) or soft x-ray range. Solutions may be the application of UV/VUV attosecond pulses created via the generation of Raman sidebands2 or the coherent excitation of the electron wavepacket itself via a Raman transition3. A second challenge to the application of attosecond techniques concerns the lack of available spectroscopies that relate the timedependent behaviour of an electron wavepacket to observables that can be measured in the laboratory. Many femtosecond experiments aimed at studying the motion of atomic wavepackets have succeeded because changes in the * This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie (FOM)", which is financially supported by the "Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO)".

95

96

position of the atoms were accompanied by changes in the electronic absorption spectrum of the system4. In the case of electronic wavepackets under investigation by an attosecond laser pulse, no such spectroscopy is available. Since present-day attosecond pulses operate in the XUV/soft x-ray range, the fate of an atom or molecule that is exposed to an attosecond pulse is almost certainly ionization. Therefore, information on time-dependent electron dynamics will almost certainly have to be gleaned from the imprint of this dynamics on the final properties of the photoelectrons (or photo-ions) that are formed in this photoionization event5. The majority of the techniques that have been used to characterize attosecond laser pulses have already made use of this fact1. Two photoelectron spectroscopic techniques have sofar predominantly been used on the basis their high collection efficiencies. In a magnetic bottle spectrometer6 the ionization takes place in a strong, spatially varying magnetic field, that parallelizes the electron trajectories. The photoelectron kinetic energy distribution is obtained by a time-of-flight measurement. In imaging experiments, the ionization takes place in a DC electric field that accelerates the photoelectrons towards a two-dimensional detector where the position of their impact is recorded7. If the time-of-flight is measured with sufficient accuracy, then the three velocity components of the initial electron ejection can immediately be determined, whereas an inverse Abel-transformation is needed if this timing information is lost. The advantage of imaging methods is that the measurement gives both angular and kinetic energy information. Conversely, magnetic bottle spectrometers can be operated with retarding fields, which gives them a somewhat better resolution at high photoelectron kinetic energies. In this paper we present results from a series of experiments involving twodimensional photoelectron imaging. The central theme in these experiments is the behaviour of electrons in strong electric fields. Consequently, the paper can also be read as an introduction on how the formation of attosecond laser pulses is determined by the response of electrons to the strong time-varying electric field of an intense femtosecond laser and the specifics of the trajectories that the electrons follow in the laser field. 2. Photoionization in DC electric fields When an atom is placed in a DC electric field Fdc, ionization is possible as soon as the atom is excited above the saddlepoint in the Coulomb + DC field potential at an energy AEsp = -2VFdc (a.u.). We experimentally investigated the ionization of xenon atoms using a tunable dye laser starting from the metastable 6s[3/2]j=2 state8. The photoelectrons were accelerated towards a twodimensional (2D) detector, consisting of two microchannel plates followed by a phosphorscreen and a camera system that recorded the positions of the electron

97 impact. The image on the detector reflects the 2D velocity distribution of the photoelectrons perpendicular to the detector axis.

^KlHBIBS^iSllPill^^B^^^^^^^H !mmMmmM:^Mm^MM::m^^

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(a)

(b)

Figure I: (a) Four images recorded in a DC field of 170 V/cm with the laser polarization along the detector axis, for different values of the scaled energy 8=Eefeetara/AEsp; (b) Image recorded at Mgh resolution in a DC field of 615 V/cm, with the laser polarization perpendicular to the detector axis, and parallel to the plane of the detector.

In the experiment, all photoelectrons are formed with a well-defined Mnetic energy, since both the initial state energy, the photon energy and the location of the saddlepoint are known with sub-wavenumber accuracy. Nevertheless, the images shown in Figure la reveal a number of rings, as if the photoelecttons are formed with several distinct Mnetic energies. The reason for mis observation is the presence of the DC electric field, which breaks the cylindrical symmetry in the 3D velocity distribution with respect to the polarization axis. Electrons that are emitted in the direction of the detector follow a relatively simple trajectory where they do not approach the parent ion anymore, while electrons emitted away from the detector follow a more complicated trajectory, where they interact one or more times with the parent ion before moving downstream towards the detector. As a result, the radius on the detector where the electrons are detected is a non-trivial function of the photoelectron Mnetic energy and the emission angle with respect to the DC electric field axis, and contains a number of maxima, depending on the photoelectron energy with respect to the saddlepoint9. At energies just above the saddlepoint, most trajectories involve interactions with the parent ion, whereas at higher energies an increasing fraction of the trajectories are direct. A discussion of the images of Figure la in very classical terms does not do justice to the fact that atomic photoionization is in fact a quantum mechanical proces. Similar to the interference between light beams that is observed in Young's double slit experiment, we may expect to see the effects of interference if many different quantum paths exist between the atom and a particular point on the detector. As Figure lb shows, the interference between trajectories is

98 indeed observable , when the experiment is improved by the insertion of a 20fold magnifying lens11 in the flight tube of the imaging spectrometer. The number of interference fringes smoothly increases with the photoelectron energy. A semiclassical analysis shows that the interferences can be understood purely on the basis of path integral arguments12. While the distinction between 'direct' and 'indirect' trajectories and the observation of interferences can be understood on the basis of the photoelectron kinetic energy with respect to the saddlepoint, this is not the only quantity that characterizes the photoelectrons that are emitted. Above the saddlepoint the continuation of the Stark manifold manifests itself in the excitation spectrum of the atom, which shows pronounced modulations as a function of wavelength. When the laser is scanned over these resonances, significant oscillations are observed in the ratio of direct-to-indirect ionization, reflecting the fact that the electronic wavepacket can be preferentially launched on the uphill or downhill side of the potential. No clear differences are however observed in the interference patterns13. In the dipole approximation the initial electron ejection is cylindrically symmetric around the laser polarization axis. Recently we have performed an experiment where non-dipolar effects play a role and where the cylindrical symmetry of the initial electron ejection is broken14. In a 2-photon ionization of xenon the laser wavelength was chosen near a dipole-forbidden quadrupoleallowed transition to the 5d[5/2]J=3 level. This gives the atom two pathways to reach the ionization continuum, namely resonance-enhanced via the 5d[5/2]J=3 level or non-resonant via a dipole-allowed virtual state. The coherent superposition of both pathways leads to a breaking of the symmetry of the electron emission along the propagation direction of the laser. Remarkably, the asymmetry in the 'direct' and 'indirect' channel has the opposite sign. This suggests that close to the resonance the 'indirect' ionization is dominated by electron trajectories where the electron crosses the detector axis a single time. It is interesting to develop the connection between the experiments discussed above and experiments in the optical domain. In strong laser fields, there exist three ionization regimes15, namely (1) multi-photon ionization, (2) tunnel ionization and (3) over-the-barrier ionization. Our results suggest that in over-the-barrier and tunnel-ionization the influence of the electric field on the motion of the electron is of crucial importance. In the strong field laser physics community this has been recognized early on, and has led to the development of the 'strong field approximation' (SFA)16, where the motion of the electron in the continuum is viewed as being completely governed by the laser field, neglecting any residual influence of the Coulomb interaction. Moreover, the experiments suggest that in strong fields careful attention has to be paid to the role of

99 different trajectories that the ionizing electrons can follow. We will return to this point in section 4. 3. Photoionization in low-frequency laser fields Coherent light sources are characterized by a spectral intensity distribution |E(oo)| and a frequency-dependent phase O(co). In first-order perturbation theory, Unear absorption probabilities are given by the overlap between |E(co)| and the optical transition, and are independent of O(co). In non-linear processes excitation probabilities are determined by both |E(cu)| and O(co). If one performs a Taylor expansion 2 3 O(co) = O(coo) + O'((o0) (CQ-O>O) + O"( 0 (see, e.g. Fig. 1). The most interesting one is probably feature (iii): the rise of a peak at e < 0 which becomes red-shifted and splits as the number of atoms N decreases. The single atom case N=l in Fig. 1, analytically given in WKB approximation 8 , marks the asymptotic limit of this peak. Its location at e w — 15GHz can be understood from the single atom curve (Fig. 2, dashed line). The DOS has maxima at the local extrema of the BO curve where its shift is e w — 15GHz. The splitting of the peak for small N resembles an almost symmetric break-away of two curves from the N=l curve with a maximum and a minimum, respectively. A trace of this phenomenon is also visible in the iV=58 case in Fig. 1 near fl=900. 4. Conclusion In summary, a structured or unstructured environment of ground-state atoms unfolds the highly degenerate dynamics of a Rydberg atom in different ways. We are confident that these features can be experimentally probed with ultracold-atomic physics techniques in the future. Acknowledgement I. Liu would like to thank the Deutsche Forschungsgemeinschaft for a travel grant to attend ICPEAC. References 1. 2. 3. 4. 5. 6. 7. 8.

M. D. Lukin et al, Phys. Rev. Lett 87, 37901 (2001). K. Singer et al, Phys. Rev. Lett 93, 163001 (2004). D. Tong et al, Phys. Rev. Lett 93, 63001 (2004). E. Fermi, Nuovo Cimento 11, 157 (1934). C. H. Greene et al, Phys. Rev. Lett 85, 2458 (2000). T. F. O'Malley et al, J. Math. Phys. 2, 491 (1961). I. C. H. Liu and J. M. Rost, EPJD, submitted (2005), physics/0512059. A. Omont, J. Phys. (Paris) 38, 1343 (1977).

SYNCHROTRON-RADIATION-BASED RECOIL ION MOMENTUM SPECTROSCOPY OF LASER COOLED AND TRAPPED CESIUM ATOMS L. H. COUTINHO1*, R. L. CAVASSO-FILHO 1 , M. G. P. HOMEM 1 , D. S. L. FIGUEIRA2, F. C. CRUZ 2 AND A. NAVES DE BRITO 1 ' 3 'National Synchrotron Light Laboratory, LNLS, Box 6192 Campinas, SP 13084-971, Brazil 2 Campinas State University, UNICAMP, Box 6165 Campinas, SP 13083-970, Brazil 3 Brasilia University, UnB, Box 4455 Brasilia, DF 70910-900, Brazil We measured the recoil energy of ions after the ejection of a photoelectron using a time of flight spectrometer, synchrotron radiation as the ionization source and laser cooled Cesium atoms as the target. From the time of flight (TOF) spectra we extracted the asymmetry parameter. We show that the photoelectrons angular distribution for an open shell, one-electron atom with large mass such as Cesium, presents a dramatic dependence on photon energy caused by relativistic effects and interchannel coupling arising from final state configuration mixing. We also present the last measured results of recoil ion momentum spectroscopy for laser cooled and trapped Calcium atoms.

1. Introduction Spectroscopy of atoms and molecules in the UV and X-ray regions has been very much restricted to the analysis of the kinetic energy of the ejected electron and its angular distribution. This is represented by the well-established field of photoelectron spectrometry [1]. However, the high kinetic energy of the ejected electrons places severe restrictions on the angular detection efficiency [2]. The recoil energy of the ions on the other hand is very small, much smaller than their mean thermal energy. Therefore ions are detected but the information of their recoil energy due to the photoelectron ejection is lost. Cold targets are then required for ion recoil momentum detection. Laser cooled and trapped atoms have been employed for this purpose [3,4]. In this work we report the use of cold Cesium and Calcium atoms for photoionization spectroscopy using synchrotron radiation in the little studied low-energy region below 100 eV. At these

* Present address: UFRJ, coutinholh @ yahoo.com.

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RJ

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Brazil;

109 conditions the electrons carry away basically all the excess photon energy and the ions recoil energy is tens of ueV. As the thermal energies for these ions are in the neV range, their complete angular detection over 4n can be achieved. By scanning the synchrotron wavelength and detecting the ions time of flight (see Fig.l), we determined the asymmetry parameter P [5], which is found to undergo rapid changes due to relativistic effects and interchannel coupling [6]. +

p = 2.o(X)

E vector

I

MCP

time-of-flight (ns)

time-of-flight (ns)

Figure 1. Effect of the P parameter on the TOF spectrum. For positive values of (5 (a) two peaks are formed in the TOF spectra while for negative P values (b) only one peak is formed. The asymmetry parameter is obtained by analysis of the peak shape.

2. Experiment We have measured the recoil ion momentum of laser-cooled 133Cs atoms in a magneto-optical trap (MOT), after removal of the 6s electrons. We have also measured the recoil ion momentum of laser-cooled Ca atoms. Both experiments were performed at the Brazilian synchrotron light laboratory, LNLS, in the TGM beamline. A description of the experiment can be found in reference 7. The angular distribution for the electrons is deduced by momentum conservation. 3. Results and conclusions In Fig. 2(a) we present the Total Ion Yield (TIY) of Cesium, which is proportional to the total cross section. The observed peaks are autoionizing resonances. We recorded TOF spectra at several photon energies in the 12 to 35 eV energy range. From these spectra we determined the asymmetry parameter P for the ionization of Cs 6s electrons and the results are presented in Fig. 2(b). The binding energies of interest are: 6s"1 = 3.89 eV; 5p"' (P3/2) = 17.2 eV; 5p"' (P1/2) = 17.6 eV [8], We observe that the P parameter is different from the expected non-relativistic value of 2 not only at the resonances but also at the offresonance regions. At these energies the total cross section is smooth, and the

110 departure from P = 2 would imply the presence of a Cooper minimum caused by relativistic effects. However, this minimum has been calculated to occur at 1.6 eV above the Cs 6s ionization threshold [9], and at an excitation energy above 14 eV P would be close to 2. This new observation is explained by the presence of a second Cooper minimum predicted recently by Altun and Manson [6], which are induced by interchannel coupling. 2.0-

a) Cs 5p

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Figure 2. On the left (a) we present the TTY spectra of laser cooled and trapped Cesium atoms, with the 5p"' ionization threshold marked by a vertical dashed line. On the right (b) we present values for the asymmetry parameter p obtained from time-of-flight spectra taken in the same photon energy region.

Our most recent result for synchrotron-radiation-based recoil ion momentum spectroscopy was conducted on Calcium atoms. In this case we have a closedshell atom with low atomic number, where relativistic effects should not play such as important role as for Cesium. In this case there are however several experimental challenges such as: 1) There is a need to produce a trapping laser beam near 423nm via frequency doubling which introduces instabilities in its frequency locking; 2) a need to heat the sample at more than 400 Celcius to produce an atomic beam, that later must have its velocity reduced enough to allow a part of the atoms to be trapped; 3) a need to use a stronger trapping magnetic field, etc. Despite this we were able to record a TOF spectrum at 30.4 eV, very close to the Ca 3p ionization threshold at 30.8 eV [10]. From the shape and width of the peak we determined the asymmetry parameter for the transition and recoil energy of the ion. We present the experimental and the adjusted TOF spectra in Figure 3. The values of 3.3 x 10-4 eV for the recoil ion energy and 1.3 for the asymmetry parameter were extracted by fitting the recoil ion intensity as a function of the recoil TOF spectrum. This value for P can be compared with the extrapolated value 1.9 ± 0.3 at 31.2 eV taken from the figure 1 in reference 11. Taking into account the statistical variation in the data and the fact that a mixed

Ill contribution from the 4p and 3d electrons that give rise to B closer to zero is present, we can regard the agreement between the two experiments very good.

Time of flight (ns) Figure 3. TOF spectrum for Ca 4s ionization, taken at 30.4 eV. The occurrence of a double peak is the expected sign of a positive P parameter, which was found to be 1.3.

In conclusion, we have reported measurements of the photoionization angular distribution parameter B using synchrotron radiation for laser cooled and trapped cesium and calcium atoms. This novel technique allows precise determination of B outside the resonance region and close to ionization thresholds. Acknowledgments The authors acknowledge the Brazilian agencies FAPESP, CNPq, UNICAMP and LNLS. They would also like to thank the LNLS staff and J. B. Rodrigues from UNICAMP for technical help. References 1. Siegbahn K., Rev. Mod. Phys. 54, 709 (1982). 2. Hemmers O. et al.. Rev. Sci. Instrum. 69, 3809 (1998). 3. Wolf S. and Helm H., Phys. Rev. A 56, 4385 (1997). 4. Wolf S. and Helm H., Phys. Rev. A 62, 3408 (2000). 5. Whitfield S. B. et al, Phys. Rev. Lett. 84, 4818 (2000). 6. Altun Z. and Manson S. T., Phys. Rev. A 61, 030702 (2000). 7. Coutinho L. H. et al., Phys. Rev. Lett. 93, 183001 (2004). 8. Th. Prescher et al., J. Phys. B 19, 1645 (1986). 9. Manson S. T. and Starace A. F., Rev. Mod. Phys. 54, 389 (1982). 10. Bizau J. M. et al., Phys. Rev. Lett. 53, 2083 (1984). U . K . Ueda et al., Phys. Rev. A 48, R863 (1993).

RECONSTRUCTION OF ATTOSECOND PULSE TRAINS* Y. MAIRESSE, P. AGOSTINI, P. BREGER, B. CARRE, A. MERDJI, P. MONCHICOURT, P. SALIERES CEA/DSM/DRECAM/SPAM Centre d'Etudes de Saclay 91191 GifSur Yvette France K. VARJU, E. GUSTAFSSON, P. JOHNSSON, J. MAURITSSON1, T. REMETTER, A. L'HUILLIER Department of Physics Lund Institute of Technology POB 118 SE-221 Lund, Sweden L. J. FRASINSKI The University of Reading, J J Thomson Physical Laboratory, Whiteknights POB 220 Reading RG6 6AF, UK

We show that it is possible to completely reconstruct the intensity profile of the attosecond bursts emitted as a superposition of high harmonics from a series of RABBIT measurements carried out at different infrared intensities. The electric field can be recovered from a measurement of the central harmonic chirp. Timing, chirp and variations of the carrier-to-envelope phase of the attosecond bursts are accessible to the proposed method.

1. High harmonic femtosecond and attosecond chirp Atoms submitted to an intense ultrashort infrared laser pulse emit, twice per laser period, bursts of XUV light [1]. The spectrum of this light consists of the odd harmonics of the fundamental infrared radiation. As well established now, it extends over a large spectral range over which the spectral components are roughly constant (the "plateau"), and dies out in an abrupt "cutoff [2]. Around each maxima of the pump field, i.e. twice per cycle, an electron wavepacket tunnels out into the continuum where it behaves essentially like a free electron. It is accelerated by the fundamental field and, depending on the initial ' This work is partially supported by the 13 LaserLab Europe (RI3-CT-2003-50350), the Marie Curie programs MEIF-CT-2004-009268 and MRTNCT-2003-505138 and the Swedish Science Council. ' Present address: Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA

112

113 conditions, may return to the ion core with which it may recombine while emitting a burst of light. The highest emitted frequency (that of the cutoff) is determined by the sum of the kinetic energy gained in the accelerated motion and the atom ionization potential. This is the essence of the well-known 3-step recollision model of high harmonic generation [3]. The spectrum, composed of only the odd orders for symmetry reasons, has been investigated for many years. Little information can be gained on the temporal profile of a single harmonic order selected by a dispersing device like a grating because of the instrumental time broadening. If a filter like a multilayer mirror is used instead, it is found that the harmonic pulse is somewhat shorter than the pump pulse if the atom ground state is not depleted and much shorter if depletion is significant [4]. (Total depletion indeed stops the harmonic generation, a coherent process which requires part of the initial wavepacket to be in the ground state for the recombination to take place). A quantum description of the atomic dipole, within the strong field approximation, predicts that the nonlinear atomic dipole Fourier component dq has a phase proportional to the quasi-classical action along the wavepacket motion starting and ending at the core [5]. Neglecting the Coulomb potential this quasi-classical action is approximately equal to the ponderomotive energy (the average kinetic energy of the motion) times the total time spent in the continuum T, difference between the instant of the release of the electron and that of its recombination. It follows that this phase is proportional to the intensity and is often termed the "intensity-dependent phase" or "dipole phase" [5]. The solution of the Newton equation for a point charge in the field reveals that, for a given kinetic energy at the recombination time, i.e. for each harmonic order, there are two classes of trajectories: the long ones for which x is close to a full cycle and the short ones for which x is closer to a half-cycle. The intensity is a function of time along the pump pulse. Therefore the phase of a given harmonic is a function of time on the pulse envelope time-scale. The timederivative of the phase is by definition the instantaneous frequency which varies during the pulse. This frequency modulation is called harmonic (or femtosecond) chirp. If the pulse envelope is Gaussian, the chirp will be linear close to the maximum and all the more important as the trajectory is long. Note that a chirp of the fundamental pulse would induce an additional chirp to the harmonics [6]. Besides the femtosecond chirp, recent investigations have uncovered a chirp occurring on a much faster time scale [7]. If, instead of a single harmonic, one now considers a small group of consecutive harmonics, x appears to be orderdependent. This stems from the relationship between the duration of the

114 trajectory and the kinetic energy at the recombination time. More precisely x turns out to be approximately a linear function of the order (or the frequency) with a positive slope for the class of short trajectories and negative for the class of long trajectories. Since T is mainly determined by the recombination time that may be interpreted as a group delay, i.e. the derivative of the phase with respect to frequency, the spectral phase is a quadratic function of the frequency. 2. The new method The reconstruction of a femtosecond pulse with a resolution of a few tens of attosecond is difficult. The RABBIT method [1, 8, 9], working in the frequency domain, allows for a partial reconstruction only of the average attosecond pulse in the train. XSPEDER [10] or CRAB [11] methods are still to be demonstrated on real sources. In the present work we propose a method allowing to completely determining the attosecond pulse train to a constant phase term based on an expansion of the adiabatic phase. The essence of the method [12] relies on a heuristic development of the electric field of the pulse considered in the frequency domain as a sum of consecutive harmonics of orders g, to q/. E(t)= YjAq(t)e-iq,'-i^"

0)

9=9/

where
ar2,J'3,t) represents the radial part of the fully correlated final state. The radial wavefunctions Pfy L,v (ri,r2,rz) are obtained by relaxation of the Schrodinger equation in imaginary time for a three-electron target atom. Care must be taken to properly relax the wavefunction to the correct ground state. The time-dependent close-coupled equations of Eq. (1) are solved using standard numerical methods to obtain a discrete representation of the radial wavefunctions and all operators on a three dimensional lattice. Our specific implementation on massively parallel computers is to partition all the ri, r2 and r$ coordinates over the many processors, so called domain decomposition. At each time step of the solution only those parts of the radial wavefunctions needed to calculate the second derivatives are passed between the processors. The probabilities for double or triple photoionization are obtained by t —¥ oo projection of the radial wavefunction onto fully anti-symmetric spatial and spin functions, within double or triple summations over electron momenta (for double and triple photoionization respectively), including the appropriate angular factors.

134

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u •••»•?.

T ZOO

t — t — • — v-fr-r -•"!•300 Photon Energy (eV)

_l

400

Figure 1. Double photoionization cross section of Li as a function of photon energy. The total double photoionization cross section is compared with experiment3, (b) shows the partial double photoionization cross sections leaving the Li2+ ion in one of three possible final states as shown. (l.Okb = 1.0 x 10 _21 cm 2 ).

The photon double and triple ionization cross section is given by:

1 .4^.

dt

\t—>oo j

(2)

UT.

h,h,h,L,S where I is the intensity of the radiation field with frequency u and V is the total photoionization probability for either double or triple photoionization. A full discussion of our results for the double and triple photoionization of Li and Be has been given4. Here we give two examples of our results, the double and triple photoionization of Li. In Fig. 1 we show the double photoionization cross section for Li. In Fig. 1(a) we compare our total double photoionization cross section with the experimental measurements of Huang et aP. Very good agreement is found with experiment. In Fig. 1(b) we show the partial double photoionization cross section leaving the Li 2 + ion in any one of the Is, 2s, or 2p final states. We note that the Li 2 + ion is most likely to be left in the Is or 2s states, with the probability of being left in the 2s being around 20% higher than that of being left in the Is. In Fig. (2) we show the triple photoionization cross section for Li, and compare it with the experimental measurements of Wehlitz et al1. Our

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Figure 2. TViple photoionization cross section of Li as a function of incident photon energy. We compare our time-dependent close-coupling calculations with experiment1.

calculations which include 51 channels up to and including I = 3 are shown by the solid line. These are in good agreement (within the error bars) for three of the five experimental points. At 225 eV and 320 eV incident photon energy, our calculations are just outside the error bars. In conclusion, we have given a brief overview of the extension of the time-dependent close-coupling method to three-electron systems. Examples were given of calculations of the double and triple photoionization of Li, where good agreement with experiment has been found. Extension of these calculations to studies of Be have also been made 4 . We look forward to extending our calculations to studies of other three-electron systems found in electron-impact double ionization5 and double autoionization problems 6 . References 1. 2. 3. 4.

R. Wehlitz et al, Phys. Rev. Lett. 81, 1813 (1998). J. Colgan et al, Phys. Rev. Lett. 93, 053201 (2004). M. T. Huang et al, Phys. Rev. A 59, 3397 (1999). J. Colgan, M. S. Pindzola and F. Robicheaux, Phys. Rev. A, accepted (2005).

5. M. S. Pindzola et al, Phys. Rev. A 70, 032705 (2004). 6. M. S. Pindzola, F. Robicheaux and J. Colgan, Phys. Rev. A, accepted (2005).

F E W / M A N Y BODY DYNAMICS IN STRONG LASER FIELDS

J. ZANGHELLINI Institue

of Chemistry, Karl-Franzens-University Graz, Austria, E-mail: juergen. zanghellini@uni-graz. at

EU

T. B R A B E C Center for Photonics

Research, University of Ottawa, ON, E-mail: [email protected]

Canada

High harmonic generation in polarizable multi-electron systems is investigated in the framework of multi-configuration time-dependent Hartree-Fock. The harmonic spectra exhibit two cut offs. The first cut off is in agreement with the well established, single active electron cut off law. The second cut off presents a signature of multi-electron dynamics. The strong laser field excites non-linear plasmon oscillations. Electrons that are ionized from one of the multi-plasmon states and recombine to the ground state gain additional energy, thereby creating the second plateau.

When an intense laser pulse is focused onto a noble gas jet, high harmonic generation (HHG) takes place. High harmonic radiation is created in a three step process x. The valence electron is set free by tunnel ionization. In the continuum, the electron is accelerated and follows the quiver motion of the laser field. When the laser field changes sign, the electron is driven back towards the parent ion. Finally, the electron recombines to the ground state upon recollision, and an xuv photon is emitted. The theory of HHG is based on the single-active-electron (SAE) approximation 2 , assuming that only the valence electron interacts with the strong laser field while the residual electron core remains frozen. The valence electron and the core electrons are regarded as uncorrelated. HHG has been performed with noble gas atoms and clusters 3 , and with small molecules 45 ' . All experiments were found to be in agreement with SAE theory. Experimental 6 ' 7,8 and theoretical 9 evidence was found that SAE theories cannot describe optical field ionization of highly polarizable systems, such as large molecules and metallic clusters. Due to the high electron mo-

136

137 bility and polarizability, a factorization into valence and core electrons is no longer valid and the complete, correlated multi-electron (ME) dynamics has to be taken into account. This raises the question as to which extent the SAE approximation is applicable to non-perturbative phenomena in complex materials 10>11. In this article we investigate HHG in highly polarizable molecules by an one-dimensional (ID) multi-configuration time-dependent Hartree-Fock (MCTDHF) analysis. MCTDHF is a recently developed method allowing to account for the electron correlation in a numerically converged manner. Our analysis reveals that in contrast to HHG in noble gases, where the harmonic spectrum exhibits one plateau and cut off, a second cut off is identified, extending far beyond the standard cut off. This second cut off originates from the ME nature of the bound electrons. The strong laser field excites non-linear, collective electron oscillations and populates multiplasmon states that oscillate at a multiple of the plasmon frequency. The second plateau is generated by electrons that ionize from the multi-plasmon states and recombine to the ground state. The energy difference between excited and ground state determines the difference between first and second cut off. 1. The MCTDHF method Here, we demonstrate the general idea of the MCTDHF-ansatz by means of an example, containing two ID particles. For simplicity we will not take spin into consideration, although it is included in the calculation presented below. For an extensive review of the MCTDHF theory and formalism we refer to 12 and references therein. MCTDHF makes the ansatz -

m

*(z» y;*) = —7^ Yl

A

nh (*) \fh (*; *)vj3 (J/; t) - fh (*; t)i Ve{%i - Xj) . Here, Vn = Z/y/xf + a% refers to the nuclear binding potential, Z is the charge state, and an is the shielding parameter of the electron-nucleus interaction. Further, Ve = l/y/(xi — Xj)2 + a2 represents the electron-electron interaction potential with shielding parameter ae. The laser is coupled in velocity gauge and in dipole approximation. Atomic units are used throughout, unless otherwise stated. ID ME simulations tend to overestimate the polarizability. To keep the polarizability at a reasonable level, the ionization potential had to be chosen slightly higher than usual values of complex materials (0.25 — 0.4at.u.). The softening parameter used for the SAE system is an = 1.414, and the parameters to model highly polarizable atoms are an = 0.80, ae = 1.0, and Z = 4. The binding energy of the 4-electron ground state is h = 8.5 at.u. and the successive ionization potentials are given by 0.5, 1.07, 3.09 and 3.93 at.u. The static polarizability is calculated by using the relation a>o = l / £ / Ap(x)xdx, where Ap is the change in electron density caused by the field £. We find a polarizability of a0 = 31 A3, which lies between the polarizability of transition metal atoms and clusters, for example, Nb: oto = 15 A3, Ceo: c*o = 80 A3. Finally, the laser parameters are: center wavelength A = 1000 nm, peak intensity / = 2 x 10 14 W/cm 2 , Gaussian

140 E rc /U p /[arb.u.] 0

0

1

20

2

3

40

4

60

5

80

6

100

O)/(O0 / [arb.u.]

Figure 2. Spectra of the dipole moment squared, | d(u) | 2 , of a highly polarizable (ao = 31 A 3 ), 4-electron model-system, Ip = 0.5 at.u., (thick full line), and corresponding SAE-calculation for the same 7P (thin dashed line). The lower x-axis gives the harmonic order, the upper x-axis gives (E — Ip)/Up with E the harmonic photon energy. The standard cutoff harmonic is at {E — Ip)/Up = 3.17 and is marked with an arrow. Laser parameters: Ao = 1000 nm, peak intensity I — 2 x 10 14 W/cm 2 , FWHM pulse duration r = 47b, optical period To = 3.33 fs, Gaussian envelope.

envelope with FWHM width r = 4Tb, and oscillation period T0 — 3.33 fs. In Fig. 2 the harmonic spectrum is shown for a 4-electron system (full line) and a SAE system (dashed line) with the same HOMO (highest occupied molecular orbital) ionization potential Ip = 0.5 at.u. The cutoff energy E = 7p-|-3.17C/p is in agreement with the standard SAE cutoff law 1,z . Here Up = (£o/2wo)2 = 0.68 at.u. is the ponderomotive energy, £o is the laser peak field strength, and UJQ denotes the laser circular center frequency. The ME spectrum reveals in addition to the regular, first cut off a second one. To identify the origin of the second plateau we have performed a timefrequency analysis of the ME spectrum, depicted in Fig. 3. The dipole moment is truncated by the window function l/(7rT w ) 1 / 4 exp [—t2/(2T%)] with Tw = 0.2Tb and then Fourier transformed. The harmonics corresponding to the first and second plateau are depicted by the thick, dashed, and the thick, full lines, respectively. Surprisingly, the contours of the first and second plateau in Fig. 3 show similar patterns, indicating that the harmonics in both plateaus are generated by the same electron trajectories. The maximum energy in each half cycle occurs at the same return phase for both plateaus. The electron return phase for the ME case is close to the well known SAE cut off trajectory that is born at 163° before and returns at 80° after the pulse

141

electricfield/ [at.u.]

ca/co0 / [arb.u.]

Figure 3. C o n t o u r plot of a time-frequency analysis of t h e 4-electron s p e c t r u m in Fig. 2 (right panel). T h e window-function is a Gaussian pulse w i t h 0.2 optical cycles F W H M d u r a t i o n . C o n t o u r s differ by a factor of 10 3 , decreasing from left t o right. T h e r e t u r n t i m e tT is plotted versus t h e h a r m o n i c frequency normalized t o t h e laser frequency. Here t h e thick dashed line corresponds t o t h e s t a n d a r d cut off, while t h e thick full line represents t h e second cut off. T h e left panel shows t h e corresponding laser electric field. T h e t i m e of birth and t h e t i m e of r e t u r n for a classical electron acquiring t h e m a x i m u m kinetical energy during its excursion in t h e laser field are marked by a dot and a cross, respectively.

maximum * (see left panel in Fig. 3). The (small) difference in the return times arises from the laser induced polarization, which increases the tunneling barrier compared to the SAE case. However, this additional potential decreases rapidly with the distance from the parent system. Thus affecting the electron trajectories only in the vicinity of the nucleus. The second plateau may be explained by the strong laser field bringing the medium into a coherent superposition of ground and excited state. However, single electron excitations can be excluded for the following reasons: (i) The SAE calculation in Fig. 2 does not show a second plateau, (ii) The energy difference between the first and second cut off is larger than the HOMO ionization potential, (iii) The absence of doubly ionized states excludes HHG from a deeper bound electron, (iv) While HHG from a coherent superposition of the ground state and an excited single-electron state does indeed produce two plateaus, it does not result in an over all increase of the standard cutoff law 13, because the HOMO electron is born with the same energy after ionization regardless of its initial state. Careful analysis of the time-dependence of the dipole moment after the laser pulse is switched of reveals the excitation mechanism responsible for the second plateau. The dipole moment exhibits a non-sinusoidal oscillation

142 indicating remaining excitations in the molecule. Moreover, this oscillation decays. The decay of the oscillation is a typical signature of a plasmon oscillations, as due to microscopic collisions the collective motion is eventually destroyed. In contrast to that, the life time of a single-electron excitation is infinite. The decay is not an artifact of the MCTDHF formalism as for increasing numbers of determinates the above statement remains valid. We have determined the plasmon frequency of the ME system by scanning the laser frequency. If laser and plasmon frequency are equal, light absorption is a maximum and the center of charge motion of the electron cloud is 90° out of phase with the laser field. The so denned plasmon frequency matches the frequency of the dipole oscillation. The non-sinusoidal dependence of the oscillation arises from non-linear excitations of multi-plasmon states, quivering at multiples of the plasma frequency, kujp, k = 1,2,3,..., from which HHG can take place. In ME systems the collective excitation energy adds to the harmonic cut off as the collective energy stays in the remaining bound electrons and does not get lost while the valence electron makes its excursion into the continuum. To demonstrate this point we define the ground state energies of the neutral and singly ionized system, EQ ' and EQ , respectively. The energies of the according plasmon states are given by EQ ' +w p and EQ +U)P . Here, we neglect the difference in the plasmon frequencies between the neutral and the singly ionized state, since the difference is of the order of the difference between two adjacent harmonics. As a result in both cases the HOMO potential is given by Ip = E0' — EQ . Although for our ME system the HOMO ionization potential for the plasmon state is slightly smaller, this is a reasonable approximation. In particular, since the difference further decreases for increasing number of electrons and will eventually disappear in real ME system which usually have considerably more than four electrons. There are different pathways by which HHG can take place. Before ionization the system is in its ground state, EQ , remains in the ground state, EQ ', after ionization of the valence electron and returns upon recombination to its initial state. This is the standard HHG situation. The system may also start out in a plasmon state, EQ ' + wp, remains in the plasmon state, EQ ' + wp, after ionization, and returns to its four electron plasmon state upon recombination. For both cases the cut off law is 3.17[/p + [E^ - E03)] = 3.17£/p + Ip since for the latter the plasmon frequency chancels out. However, if ionization starts from the plasmon state,

143 EQ ' + wp, but the electron returns to the ground sate, EQ ', upon recombination, the plasmon energy is converted into harmonic photon energy, extending the cut off, i.e. 3.17UP + Ip + u>p. The multi-plasmon states are (laser) phase looked to the ground state and thus are detectable in a macroscopic system. As the phase difference between ground and excited state is exclusively determined by the laser field, it is therefore the same for each atom. The contributions from individual atoms add up coherently and HHG can take place from the ground as well as from excited states. High harmonic generation (HHG) in complex multi-electron (ME) systems was investigated within the framework of the multi-configuration timedependent Hartree-Fock (MCTDHF) method. MCTDHF is an efficient method to solve the time-dependent Schrodinger equation for few body problems. It is based on approximating the exact wave function by a linear combination of time-dependent Slaterdeterminates. Our analysis of HHG spectra in complex ME system revealed two plateaus. The first cut off agrees with the cut off law of noble gases. The second plateau presents a signature of electron correlation and is due to the non-linear excitation of collective plasmon oscillations. It arises from electrons that are ionized from an excited plasmon state and recombine to the ground state. The plasmon signatures presents a novel tool for the investigation of the non-perturbative multi-electron dynamics in complex materials, a regime that is experimentally very difficult to access otherwise. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

P. Corkum. Phys. Rev. Lett, 71:1994, 1993. J. Krause, K. Schafer, and K. Kulander. Phys. Rev. Lett, 68:3535, 1992. J. Tisch et al. J. Phys. B, 30:L709, 1997. Y. Liang et al. J. Phys. B, 27:5119, 1994. R. de Nalda et al. Phys. Rev. A, 69:031804(R), 2004. M. Lezius et al. J. Chem. Phys., 117:1575, 2002. V. Bhardwaj, P. Corkum, and D. Rayner. Phys. Rev. Lett, 91:203004, 2003. A. Markevitch et al. Phys. Rev. A, 68:011402(R), 2003. M. Kitzler et al. Phys. Rev. A, 70:041401(R), 2004. V. Veniard, R. Taieb, and A. Maquet. Phys. Rev. A, 65:013202, 2001. H. Nguyen, A. Bandrauk, and C. Ullrich. Phys. Rev. A, 69:063415, 2004. J. Caillat et al. Phys. Rev. A, 71:012712, 2005. J. Watson et al. Phys. Rev. A, 53:R1962, 1996.

RESCATTERING-INDUCED EFFECTS FOR ELECTRON-ATOM SCATTERING IN THE PRESENCE OF A CIRCULARLY POLARIZED LASER FIELD

A.V. FLEGEL, M.V. FROLOV, N.L. MANAKOV Voronezh State University, Department of Physics University Square 1, Voronezh, 394006, Russia E-mail: [email protected] ANTHONY F. STARACE University of Nebraska, Department of Physics and Astronomy Brace Lab 116, Lincoln, NE 68588-0111, USA E-mail: [email protected] We analyze the differential cross section {dan/dO) for electron-atom scattering in an intense laser field with absorption of n laser photons. We show that there exist plateau structures in the dependence of don/d£l on n for any polarization state of the laser field, including for the case of circular polarization. Numerical predictions for e — H and e — F scattering and a discussion of plateau features in terms of the rescattering scenario are presented.

The most interesting feature of strong laser-atom interactions is a plateau-like behavior of multiphoton cross sections in their dependence on the number n of absorbed photons. The plateau effects have a one-electron origin and are well-studied for bound-bound [high harmonic generation (HHG)] and bound-free [above threshold ionization (ATI)] transitions of an atomic electron1. Recently, plateau structures have been predicted also for free-free transitions [laser-assisted electron-atom scattering (LAES)]2. For the case of linear laser polarization, the rescattering scenario3 provides a transparent physical explanation for the appearance of plateau structures in HHG and ATI: an intense oscillating laser field returns ionized electrons back to the parent ion, where they either gain an additional energy from the laser field, forming the high-energy plateau in the ATI spectrum, or recombine with the parent ion, emitting high-order harmonic photons. The plateau effects for LAES have a similar interpretation2. With increasing laser ellipticity, plateau structures in HHG and ATI gradually disappear

144

145 and completely vanish for the case of circular polarization. For an initiallybound electron, this fact may be explained in terms of the dipole selection rule, | Am| = 1, for the projection m of an angular momentum / in a circularly polarized field4. For the case of LAES, however, both incoming and scattered electron waves are superpositions of continuum states with different / and m. Hence, for LAES the selection rules do not lead to drastic differences for the cases of linear and circular polarizations and plateau effects in LAES spectra exist even for the case of circular polarization4. To describe electron-atom scattering in the presence of a laser field with the electric vector F(t) = i?Re{eexp(—iu>t)} (e • e* = 1), we generalize our recently developed time-dependent effective range approach for laser detachment of negative ions5. Our approach is based on the formalism of quasienergy states6 and effective range theory7. We assume that the atomic potential vanishes outside a sphere of radius rc and supports a h2K2

weakly-bound state (a negative ion) having an energy EQ = — — and 2me an angular momentum I. The mathematical formulation of the problem is based on the prescribed boundary condition for a scattering state $p{r,t) (with incoming electron momentum p) on a sphere of radius rc («r c £ A, n

;

'

146 where $°(r,t) is the free-electron state in a laser field, and pn/(2me) = En = E + nhw. An is the scattering amplitude, which may be expressed in terms of generalized Bessel functions and Fourier-coefficients of f^m\t). The LAES cross section with absorption/emission of \n\ photons is ddn/dQ. —

(p„/p)\An\2-

Figure 1. Dependence of LAES cross sections on the number n of absorbed photons for forward scattering (pn||p) in the polarization plane of a circularly polarized laser field. Solid lines: exact results; dashed lines: KroU-Watson results. For e — H scattering (thin lines): the incoming electron energy is E = 5.31 eV, the laser intensity is / = 6.34 x 10 11 W/cm 2 , and w = 0.117 eV. For e - F scattering (thick lines): E = 23.4 eV, / = 5.8 x 10 13 W/cm 2 , and u = 0.527 eV.

In Fig. 1 we present numerically-calculated LAES spectra for e — H and e — F scattering for the case of a circularly polarized laser field. To illustrate the rescattering effects, we also plot results of the Kroll-Watson approximation8, in which rescattering is neglected. As follows from a stationary phase analysis of the exact quantum amplitude An4, LAES may be considered classically as a three-step process: (i) the first collisional event (at the moment t — r), resulting in the "transfer" of the electron having non-zero initial velocity to a closed classical trajectory in a laser field; (ii) the propagation along this closed trajectory during the time T; and (iii) the second collisional event (at the moment t). Mathematically, this rescattering scenario is described by the following system of equations4:

147

[p + A ( t - r ) ] 2 = [k(t,r) + A ( t - r ) ] 2 , [(k(t,T)+A(tf

= [pn + A(t)}2,

(2)

where A(t) is the vector potential and k is an "intermediate" electron momentum (corresponding to motion along a closed trajectory) equal to k(t,r) = — i f A(t')dt'. The system (2) has real roots n and U = £(T*). Moreover, the extent of the rescattering plateau (i.e., the maximum value of pn) corresponds to the minimum value of Tj, UITO = 4.086 4 . A distinct feature of rescattering in a circularly polarized laser field (in which case the modulus of the rotating electric vector F(t) is constant: |F(i)| = F/y/2) is that the initial and final kinetic energies of the electron during its route along a closed trajectory are equal and depend only on r (but not on t). Thus, there is no dynamic acceleration of the electron during the second step (unlike for the case of an electron having zero initial velocity in a linearly polarized field, as in the rescattering scenario for HHG and ATI processes): the electron is accelerated at the final (third) step of the rescattering scenario due to the difference between the phases of the laser field at the times t — r and t. This work was supported in part by RFBR Grant 04-02-16350, by the joint Grant VZ-010-0 of the CRDF and the RF Ministry of Education, and by Grant DE-FG03-96ER14646 of the U.S. Department of Energy. AVF and MVF acknowledge support of the "Dynasty" Foundation. References 1. W. Becker, F. Grasbon, R. Kopold, D.B. Milosevic, G.G. Paulus, and H. Walther, Adv. At. Mol. Opt. Phys. 48, 35 (2002). 2. N.L. Manakov, A.F. Starace, A.V. Flegel and M.V. Frolov, Piz. Zh. Eksp. Teor. Fiz. 76, 316 (2002) [JETP Lett. 76, 256 (2002)]. 3. M.Yu. Kuchiev, Piz. Zh. Eksp. Teor. Fiz. 45, 319 (1987) [JETP Lett. 45, 404 (1987)]; K.C. Kulander, K.J. Schafer, and J.L. Krause, Phys. Rev. Lett. 70, 1599 (1993); P.B. Corkum, Phys. Rev. Lett. 71, 1994 (1993). 4. A.V. Flegel, M.V. Frolov, N.L. Manakov, and A.F. Starace, Phys. Lett. A 334, 197 (2005). 5. M.V. Frolov, N.L. Manakov, E.A. Pronin, and A.F. Starace, Phys. Rev. Lett. 91, 053003 (2003). 6. N.L. Manakov, V.D. Ovsiannikov, and L.P. Rapoport, Phys. Rep. 141, 319 (1986). 7. L.D. Landau and E.M. Lifshitz, Quantum Mechanics, 2nd ed. (Oxford, Pergamon, 1978), Sec. 133. 8. N.M. Kroll and K.M. Watson, Phys. Rev. A 8, 804 (1973).

MULTIDIMENSIONAL PHOTOELECTRON SPECTROSCOPY P. LABLANQUIE 1 , F. PENENT 1 , J. PALAUDOUX 1 , L. ANDRIC 1 , T. AOTO 2 , K. ITO 2 , Y. HIKOSAKA 3 , R. FEIFEL 4 AND J.H.D. ELAND 4 /) LCP-MR, CNRS et UPMC, 11, rue P. & M. Curie, 75231 Paris, France 2) Photon Factory, IMSS, KEK, Tsukuba 305-0801, Japan 3) IMS, Okazaki 444-8585, Japan 4) PTCL, Oxford University, Oxford, United Kingdom

Abstract. The implementation of a magnetic bottle spectrometer with synchrotron radiation allows multi dimensional electron spectroscopy, in which all the electrons (2, 3...) ejected in multiple ionization events can be detected in coincidence. We give here the example of (multiple) Auger effect following inner-shell ionization. Application of the technique to Xe and Kr inner-shell ionization allows us to fully disentangle Auger spectra from different sub-shells and also from double Auger decay. All involved energy pathways for the last process are revealed. The dominant decay path proceeds by cascade through intermediate autoionizing states of the doubly charged ion. Weaker processes involving 3 electrons are also observed as excitation of Rydberg series, a process which can be viewed as a precursor of the direct double Auger effect.

1. Introduction One century ago A. Einstein [1], introduced the light quanta (photon) hypothesis from a heuristic point of view and used it to explain the photoelectric effect observed by Lenard [2], and Hertz, which was the precursor of modern photoelectron spectroscopy (PES). Since then, we know that one high energy photon (VUV or X) can also eject more than one electron in a direct or sequential way leading to multiple ionization processes. This provides a lot of information on electron correlations and on properties of matter with, for instance, characteristic Auger spectra (AES) following inner-shell ionization. We present here the results obtained thanks to a new experimental set-up that gives most of the possible information on all processes where two or more electrons are ejected after absorption of a single photon. Capabilities of the new technique include direct spectroscopy of multiply charged ions, determination of branching ratios between double and triple photoionization following inner-shell ionization and identification of the intermediate states and mechanisms involved in the ejection of more than one electron.

148

149 2. Experiments The experiments have been performed at two synchrotron radiation centers: Super ACO in France and Photon Factory (PF) in Japan, using long (-2.5 m) magnetic bottle electron time of flight spectrometers born from Eland's original design [3]. The collision center is at the crossing point between the photon beam (at its focal point ((>«0.5 mm) and the target gas effusing from a needle (O = 0.5 mm). A long solenoid generates a homogenous magnetic field of about 1 mT that guides the electrons (once trajectories have been parallelized) to the detector (chevron micro channel plates MCP, with delay line anode (Roentdek®) in SACO or fluorescent phosphor screen in PF). The diverging magnetic field, generated by a conical shaped permanent magnet (FeNdB), creates the bottleneck of the magnetic bottle in which the electrons trajectories are parallelized after a short distance. The field in this region is about 0.5T and the position of the magnet is adjusted with a XYZ manipulator to optimize the time of flight resolution and the image of the collision center on the detector (by position encoding with the delay line detector or by direct sight through the phosphor screen). A repelling potential is applied to the magnet to push low energy electrons in order to make them arrive to the detector in a finite time (less than ~8/*s), the potential on the needle is also adjusted to achieve the best resolution. The time structure of the synchrotron light in "single" bunch mode (T= 120ns in SACO, T=624ns in PF) allows the determination of the time of flight (TOF) of one electron only modulo [T], but, once a first electron is detected, the TOF of following electrons is no longer limited to one period. The long TOF spectrometer allows good energy resolution down to 10~20 meV for electron energies below 1 eV, very high detection efficiency (> 90% of 4n solid angle) and constant transmission from 0 to 70 eV. The dead time (20 to 150 ns) of the multi-hit detector only forbids detection of electrons with close energies. The electrons TOF was encoded by a time to digital converter (TDC) with a resolution of 250 ps (500 ps in PF). The only information lost is the initial emission angle of the electrons since it is not possible to reconstruct the trajectories of the electrons in this magnetic field configuration due to the size of the interaction region.

3. Experimental results Experimental results have been obtained on Xe(4d"') [4,5], and also Kr(3d"') and Xe(4p_1) inner-shell ionization Coincident detection of photoelectrons with all subsequent Auger electrons offers unprecedented possibilities.

150 The first interest of the method is to completely disentangle, with full determination of branching ratio, complex Auger spectra resulting from the overlap of Auger lines originating from different inner-shells (d5/2,3n)- For sake of simplicity in data analysis, the photon energy was chosen (110 eV for Xe) in order that 4d photoelectrons are faster than all subsequent Auger electrons. The electron detection efficiency (-40%) is determined from the probability of detecting the Auger electrons following the photoelectron. The electron signal filtered to select the photoelectron time of flight for 4dsa.ia sub-shells, is presented in figure 1 after time to energy conversion. The spectra can be directly compared with normal Auger spectra [6], and the separation of N4-OO, and N5-OO lines becomes straightforward and allows determination of the branching ratio between otherwise overlapping peaks.

0

5 10 Auger Kinetic Energy / eV

15

Figure 1: Coincident Xe N-OO Auger spectra filtered against N4 and N5 sub-shells. The gray area corresponds to three electron events after normalization with electron detection efficiency. If the Xe** state lies above the triple ionization threshold it decays by autoionization to Xe3*. Auger peaks numbering is from ref. [6]. The grey area shows scaled three electron coincidences.

The low energy region of the spectrum has not been clearly analyzed in any previous work [6 and ref. therein]. After normalization of the signal where three electrons are detected to the signal where only two are detected, (taking into account the electron detection efficiency), we can see that coincidences between two electrons in this grey region in fig. 1 correspond to aborted coincidences with a third electron. This can result from direct double Auger decay or from

151 cascade Auger decay: the intermediate Xe++ states systematically autoionize when their energy lies above Xe triple ionization threshold. Analysis and filtering of events where three electrons are detected in coincidence allow the identification of pathways for double Auger decay (direct or cascade). Detailed analysis is published elsewhere [5], the prominent decay channel is a cascade Auger decay through two Xe2+ states lying at 66.00 and 67.27eV from Xe ground state, that carry about 30% of the signal for triple ionization. In the absence of theoretical calculations, we interpret these two states as high energy 5s"2 correlation satellite of Xe2+. Although the energy pairs (Ei, E2) give two possibilities for the position of intermediate Xe++ states, the correct energy of the Xe2+ intermediate is unambiguously obtained from the combination of two initial inner-core states 4d'l5/2,3n and five final Xe3+ (4S]/2, 2 D5/2, 2D3/2, 2P3/2, 2Pi/2) states. We observe also three-electron processes with formation of a Xe2+ 5s25p3nl Rydberg series converging towards Xe3+ 2D3/2 threshold, whose members autoionize to Xe3+ *Sia- Such states are precursors of a direct double Auger process that seems to be present in our data, although it is not easy to establish a clear difference between a true continuum and closely spaced discrete states. Similar results have been obtained for Kr 3d inner-shell ionization and force a clear revision by more than leV below of the triple ionization threshold of krypton given in the literature [7]. In this case the available energy to be shared between the 2 Auger electrons is up to about 20 eV and it is possible to produce not only Kr3+ 4p"3 but also Kr3* 4s"'4p"2 states. We have also observed Xe quadruple ionization following 4p inner-shell ionization by detecting 4 electrons in coincidence: the photoelectron and three subsequent Auger electrons. Full analysis of these data will be presented in forthcoming papers and will give a new experimental method for direct spectroscopy of multiply charged ions. Multidimensional photoelectron spectroscopy provides useful high resolution data for further specific experiments (for instance on angular correlations...) since all processes are observed simultaneously and even faint features can be observed thanks to their possible identification in 2 or 3 dimensional maps. References 1. 2. 3. 4. 5. 6. 7.

Einstein, A. Ann. Phys. 17,132 (1905). Lenard, P. Ann. Phys. 8,149 (1902). Eland J. H. D. et al, Phys. Rev. Lett. 90, 053003 (2003). Penent F. et al, J.El.Spect.Rel.Phen, 144, 7 (2005) Penent F. et al, Phys.Rev.Lett,. 95, 083002 (2005) Carroll T.X.et al, J.El.Spect.Rel.Phen., 125, 127 (2002) Sugar J. and Musgrove A., J. Phys. Chem. Ref. Data 20, 859-915 (1991).

FEW PHOTON AND STRONGLY DRIVEN TRANSITIONS IN THE XUV AND BEYOND

P. L A M B R O P O U L O S 1 ' 2 , L. A. A. N I K O L O P O U L O S 3 AND S. I. T H E M E L I S 1 1

Institute for Electronic Structure and Laser, Foundation for Research and Technology - Hellas, P.O. Box 1527, 711 10 Heraklion, Greece 2 Department of Physics, University of Crete, P.O. Box 2208, 710 OS Heraklion, Greece Department of Telecommunication Science and Technology, University of Peloponnese, Tripolis, Greece

In view of recent developments in the production of high intensity and subpicosecond pulse duration, XUV radiation sources, we discuss a number of novel photoabsorption processes that are expected to provide windows into a variety of hitherto unexplored territory of atomic and molecular structure, involving highly excited states embedded in multiple continua.

Recent and ongoing developments on new sources of short wavelengths, XUV and beyond, promise the availability of relatively intense, coherent pulses of radiation of duration around 100 fs. In pondering the type of atomic and molecular processes that will become accessible through such sources, it is perhaps useful and instructive to recall briefly the developments that followed the appearance of the laser in the dawn of the 60's. Immediately after the Ruby laser, the first pulsed laser, became operational, Abella [1] exploited the possibility of very limited but adequate thermal tuning of its wavelength (~ 6940 A), in combination with the coincidental matching of the energy of two such photons to the 6s —• 9d transition in Cesium, to observe this two-photon excitation process; the first experimental observation of a non-linear photoabsorption process. During the same period, second harmonic generation, as well as an observation of twophoton absorption, in crystals, were observed. That is where matters stood for a few years, until the late 60's and early 70's at which time two developments opened the possibilities of a variety of experiments. The Nd:yag laser, considerably more powerful than the Ruby, ushered in the first studies of multiphoton ionization and gas breakdown, with intensities around

152

153 1012 W/cm 2 , which by the mid 70's reached 1015 W/cm 2 . The dye-laser, on the other hand, offered tunability at a much lower range of intensities which was, however, sufficient to open the field of resonant few-photon processes through which new aspects of atomic and molecular physics were explored. With the further development of tunable lasers, as well as the appearance of the excimer laser, delivering significant energy in the UV and pulses of subnanosecond duration, resonantly enhanced multiphoton ionization (REMPI), 3 r d harmonic generation in gases and wave mixing, as well as a variety of related processes, were eventually established as basic tools of atomic and molecular physics. From that point on, developments occurred at a rapid pace, culminating with the TiSa laser, capable of delivering ultrashort pulses down to a few fs and intensities well above 1015 W/cm 2 which have made possible the observation of a number of novel effects, the most relevant to our discussion being high order harmonic generation (HOHG) which produces highly coherent radiation well into the XUV. At the same time, the construction of XUV sources based on the free-electron concept, using high energy electron accelerators, promises to deliver short wavelength radiation well into the hard X-ray regime, of intensity possibly of the order of 1019 W/cm 2 . For the moment, however, it is more realistic to explore ideas for the interaction of atoms with photon energies up to about 200 eV expected to be available within the next few months. Given that the expected intensities in W/cm 2 are of the same order of magnitude as those currently available from short duration, intense sources in the infrared and optical range of wavelength, a few remarks on the relevant typical parameters are useful at this point. A brief summary of such parameters is given below. Let us keep in mind that the most intense source with which most of the non-perturbative phenomena have become accessible is the Ti-Sa laser of wavelength 780 nm i.e. photon energy about 1.59 eV. Since the term intense is also used in the context of the XUV sources, let us examine its meaning in comparison to the parameters below. The quantity that is most meaningful as a criterion of the onset of non-perturbative behaviour, leading to the presence of significant ATI and HOHG, is the ponderomotive potential, representing the cycle-averaged quiver energy of a free electron in the AC field. As a point of calibration, note that at 1064 nm and intensity 1013 W/cm 2 , the ponderomotive energy is about 1 eV, which is very close to the photon energy of 1.16 eV. Thus at intensities 1015 W/cm 2 and wavelength 780 nm (photon energy ~ 1.5 eV), the ponderomotive potential is of the order of about 60 photons.

154 Table 1. Typical laser parameters. - 10 19 W/cm 2

Peak Intensity

10 12

Pulse duration - Things happen on a short time scale

10 - 500 fs

Wavelengths

A 1064

780

620

249 nm

hi/ 1.16 1.59 2.0 5.00 eV -Laser-atom interactions ~ electron-nucleus interaction; I ~ 3.15 x 10 16 W/cm 2 "Intense" is context dependent

-AC Stark shift: important Ponderomotive energy Up = 7/(4u)2) -Pulse shape: important

Note that the ponderomotive potential scales proportionally to the intensity and inversely proportionally to the square of the frequency, while the ratio of the ponderomotive potential to the photon frequency is inversely proportional to the cube of the frequency. Thus for photons of energy of 100 eV and intensity 1015 W/cm 2 , the ponderomotive potential is about 0.01 eV, which is four orders of magnitude smaller than the photon energy. As a result, tunneling, etc. will be of no importance at this combination of intensity and frequency, and that holds true even if the intensity becomes two orders of magnitude larger. What about the pulse duration? Well, even a duration of 5 fs, contains many cycles of radiation with photon energy even 50 eV. And one thing that has become clear is that, surprisingly, if the pulse has duration, say, 10 cycles or more, and insignificant ponderomotive potential (in the sense discussed above) LOPT (Lowest Order Perturbation Theory) is perfectly valid for the treatment of multiphoton transitions. What is not valid, however, is that XUV photons and beyond interact mainly with electrons below the valence shell of atoms. As a consequence, the SAE (Single Active Electron) model that has been so successful in strong- field interactions is no longer valid. We have to deal with a multielectron problem which makes theory more demanding, with the reward that a new landscape of phenomena is now unveiled. Let us examine some of those. TWO-PHOTON DOUBLE IONIZATION OF HELIUM Single-photon double ionization of Helium under short-wavelength radiation is a much studied and well established topic, as is high-order multi-

155 ICfUU

— He++ : direct — He++ : sequential - - He+

le-01 le-02 •3s

c e

I

le-03

-

le-04

-

le-05

-

le-06

-

-

le-07

-

-

i„_ns

1

. A

10 20 30 photoelectron energy (eV)

40

Figure 1. Expected photoelectron energy spectrum from 2-photon double ionization of helium under irradiation by a Gaussian pulse of photon energy 45 eV, peak intensity 10 14 W/cm 2 , and 30 fs duration.

photon double ionization under strong infrared radiation (~ 780 nm) [2-7]. In both cases, it represents a two-step process, in the sense that, for different in each case reasons, the radiation interacts first with one of the electrons which in turn assists in the ejection of the other one. In contrast, radiation of photon energy around 45 eV provides a rather unique case in which direct double ionization, which would take place even if the electrons were non-interacting particles, can be clearly separated from the sequential. This clearest signature [8] of this process is to be found in the photoelectron energy spectrum depicted in the figure below. All electrons of kinetic energy below about 10 eV represent the direct double ionization, which in some sense could be thought of as if each photon were absorbed by one of the electrons. Another, experimentally less demanding signature is to be found in the laser power dependence of the double ion yield, as discussed in detail in [8], in the light of which, related experimental results published most recently in [9] will require further quantitative evaluation. DOUBLE RESONANCE If it were possible to combine an FEL pulse with a pulsed optical laser, another exciting possibility emerges. Excitation of an autoionizing (AI)

156 Formalism 0 Three state model 0 Rotating wave approximation 0 C-C coupling ignored

|b> Strong transition

/

ot>

i

Weak transition fU = U * ( i - — )

H(t) =

»« and g)

a,«

-i(r„+7„) \

$(>1>

Non-Hermitlan(!)

—

2 7tf''

SU -*i

- s2 - §(r k + -,(,)

Effective coupling between a and b (b and a)

Figure 2. Schematic representation of the coupling between the ground, two autoionizing states and the corresponding continua mixed through configuration interaction.

state, in the presence of an optical laser coupling it to another, higher AI state, makes it possible to study the coupling between such states, through the measurement of the resulting AC Stark splitting, as the intensity of the optical laser becomes stronger, and the probing FEL frequency is scanned, across the resonance profile, as depicted schematically in the figure below. A sample calculation with probe and laser coupling intensities Ii=10 10 W/cm 2 and I 2 =10 10 W/cm 2 -10 12 W/cm 2 , respectively, and pulse durations 200 fs, produces the line-shapes shown in Fig. 3 exhibiting a progressively discernible AC Stark splitting with increasing coupling laser intensity. The magnitude of this splitting, for a known coupling laser intensity, provides a direct measure of the matrix element coupling the two autoionizing states, a quantity extremely sensitive to correlation and as a consequence of the accuracy of the theoretical model. Turning this problem around, one could combine these two pulses, introducing a delay between the two, and by probing the signal of ionization from the upper resonance, extract information about the duration and even the temporal shape of the FEL pulse, as discussed most recently in [10]. Doubly excited states is not the only context in which the coupling of highly excited states can be studied in this fashion. Along identical lines, one can consider the coupling of triply excited states (see [12]), or core excited Auger resonances, as illustrated by the predictions in the sequence

157

Is2

ka^

•> 2s2p 'P 0 —^-^

2s3d J D

*lT» is 0,0008•a X 0.0007-

l2=10'2 W/cm2

I 2 =5«lO M W/cin 2

£ 0,0006g 0,0005-

A

« 0.0004' I 0.0003-

'3 § 0,0002i 0,00010,0000-1

a

«!/ra Figure 3. Photoionization yield of the helium atom as a function of the detuning of the probe laser.

of figures below [11]. As a final example of the AC Stark splitting involving two highly excited states, we show in Fig.5 the evolution of the splitting due to the laser coupling of two triply excited (hollow) states in Li [12], as probed through the scanning of the probe laser across the line-shape of the lower resonance. Again, with modest intensities of the coupling laser, a clearly discernible splitting, providing a direct measure of the matrix element between two triply excited states, is obtained. CONCLUDING REMARKS If indeed, as anticipated, FEL sources in the XUV and beyond do deliver intensities of up to 1015 W/cm 2 , or a couple of orders of magnitude more, in the photon energy range up to 200 eV, for the moment, we can look forward to a new phase of multiphoton physics, involving multiple electron excitations, probing of highly excited states, coupled to multiple continua, opening thus new vistas of atomic and molecular processes. Syn-

158

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7,0x10*

£ " 7,0x10*

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• 2 3,0x10* •

• 2 3,0x10*

.N 2.0x10* C O 1,0x10* 0,0.

5

) on the density p, and changes of the density p are caused by ionization due to the electric field £. The model has been refined, e. g. by relaxing the assumption of a homogeneous density [11], replacing the quasi-static dielectric constant by an effective one [12], or allowing for cluster polarization effects in linear polarized pulses [13]. It gives, already in the basic formulation [10], a good qualitative description of the ionization dynamics, at least for clusters of sufficient size, i. e. where the assumption of a plasma is valid. In contrast to that, microscopic approaches can give a quantitative account of the ionization and fragmentation dynamics and, even more important, allow one to study the range of applicability of the phenomenological models and transitions to other ionization regimes. Furthermore, they allow one to investigate laser impact at shorter wavelengths [19,20], which are not accessible by the macroscopic models. The key idea of the microscopic implementation is the division of the ionization process into inner and outer ionization. Here, inner ionization means excitation of bound electrons resulting in so-called quasi-free electrons. These quasi-free electrons are not bound anymore to a particular atom but still to the cluster as a whole, which can provide a sufficiently strong space charge to hold the electrons back. Eventually, these electrons may be further heated until they end up in the continuum, a process we call outer ionization. The dynamics of bound electrons with typical oscillation periods of a few attoseconds are not treated explicitly. Rather, one uses a statistical approach to describe them by means of the occupation number of bound

162 levels which may change after each time step. The rate, i.e., the probability within a certain time-step, for a transition to an excited state, or practically the creation of a quasi-free electron, depends strongly on the laser frequency. A convenient parameter to distinguish different regimes is the Keldysh parameter 7. Originally defined as the ratio between tunneling time and laser period [21], it can be rewritten as 7 = y/AE / (2Epon 1) and non-perturbative tunnel ionization (7 < 1), we list in Table 1 the intensities at which 7 = 1, assuming AE= 1 a. u., for the laser wavelengths discussed below. Table 1. Laser intensities J = 2ui2AE marking the border (Keldysh parameter 7 = 1) between perturbative and non-perturbative ionization for various laser wavelengths A or frequencies u>, respectively. A/nm

(fiw/eV)

//Wcm-2

780 (1.59)

97 (12.7)

3.5 (350)

2.5xl0 1 4

1.5X1016

l.OxlO 19

The classical propagation of the quasi-free electrons is straight forward apart from two aspects: instability of classical particles, due to the Coulomb singularity, and an unfortunate scaling with the particle number n, due to the long-range nature of the Coulomb interaction. To circumvent the first problem one introduces a smoothed Coulomb interaction [15,17,18]. The second problem can be avoided by using hierarchical tree codes [22]. Originally developed for the gravitational n-body problem in cosmology [23], such codes reduce the computational costs from n2 to nlogn. This allows one to tackle clusters with as many as 104 atoms [24]. 3. Intense optical laser pulses In strong optical pulses, with / > 1015 W/cm 2 , atoms lose their electrons by tunneling or through over-the-barrier processes, cf. Table 1. Herefore it is essential, that not only the laser but also the neighbouring ions contribute to the electric field which lowers the barriers. This leads to an rapid inner ionization following the primary ionization events. Firstly seen by RosePetruck and coworkers [14], this process was termed "ionization ignition". Such a cooperative effect may also lead to enhanced ionization, very similar the one observed in diatomic molecules. It has been found for small

163 rare-gas clusters (n < 100), that ionization is favoured at a critical radius, since inner-ionized electrons may directly leave the cluster [17]. This critical radius, being approximately 1.2 times larger than the initial cluster radius, is reached during the cluster expansion, which leads to a characteristic pulse-length dependence of the cluster ionization [17]. For larger clusters (n > 100) the space charge increases rapidly and thus prevents direct ionization events. Instead a plasma is formed which is confined by the potential of the cluster ions. How this electrons are eventually ionized can be understood by looking at the pulse length and cluster size dependence of the final charges of the fragment ions or the amount of energy absorbed by the clusters [24]. This has been systematically calculated with our microscopic approach for Xe„ clusters with n = 135 .. .9093 in pulses with (FWHM) durations T = 2 5 . . . 400 fs, and is shown by the contour plots in Fig. 1. Each row shows the result for pulses of constant fluence, i. e. T x / = const. The average ionic charge q, cf. left column of Fig. 1, has a maximum for small clusters (n « 100) which shifts for increasing fluence from T RJ 200 fs via T = 50 fs to T < 25 fs. The reason for a maximum at a particular pulse length can be explained by a resonance mechanism [18]: The eigenfrequency of the oscillatory motion of the plasma electrons driven by the laser becomes equal to the laser frequency which is connected with an optimal energy absorption [24]. For shorter pulses the partially ionized clusters do not have enough time to expand into resonance, for the longer pulses the resonance has been passed before the pulse maximum. The lower values q for larger sizes n are due to an increased space charge. The absorbed energies E per atom, cf. right column of Fig. 1, show a similar behaviour for the pulse length dependence. However, an opposite trend occurs for the cluster size dependence: Larger clusters absorb more effective energy than smaller ones. This applies at least for longer pulses with T > 100 fs where one observes resonant absorption. It indicates that the heating is due to the whole cluster potential which is much deeper for larger clusters. 4. Clusters in strong short-wavelength laser pulses 4 . 1 . VUV

regime

Pushed by the Hamburg experiment [25], there have been several theoretical attempts [20,26] to understand the surprisingly high charge states measured for clusters irradiated by VUV-FEL light with A = 97 nm at

164 average ionic charge q

energy per atom E [keV]

1.4

100 pulse length T [fs

5

18

TT

100 pulse length T [fs]

500

Figure 1. Contour plots of the final average charge q of the fragment ions (left column) and the absorbed energy E per atom (right column) as a function of pulse length T and cluster size n. Each row shows the result for pulses of constant fluence, i. e. T x / = const. The fluence decreases from one row to the next one (top to bottom) by a factor of 5. At the right side we specified the intensity I corresponding to a pulse of length T = 100 fs.

165 I = 7 x 10 13 W/cm 2 . Single-photon ionization, the dominating process at such low intensities (cf. Table 1), is sufficient to ionize a separate atom but not electrons from a cluster, which are more deeply bound by the cluster's space charge. However, ionization into the quasi-continuum of the cluster is possible due to the lowering of the barriers [20]. Since this applies not only for the second electron of the atoms but for all electrons of the upper shell, atoms are rapidly eight-fold inner-ionized and a plasma is formed. Due to its high density, this plasma is effectively heated by inverse bremsstrahlung and an average charge per atom of about 1.5 is achieved [20]. The higher charged ions, seen in the experiment [25], are those from the surface. There, the electric field from the positively charged cluster points towards the center and attracts electrons. The quiver motion at this laser frequency is far too small to distribute the electrons and equalize the ionic charges.

4.2. X-ray

regime

The dynamics of clusters in strong X-ray laser pulses is much less studied and understood. The main reason is the lack of experimental data, which will be available only if the planned X-FEL machines, at DESY in Hamburg [27], at the LCLS in Stanford [28] or at BESSY in Berlin [29], will start operating in the next years. For short-wavelength laser impact, ionization proceeds fundamentally different compared to the situations discussed above. Despite the high intensities the laser-atom interaction is of non-relativistic and perturbative nature, cf. Table 1. Ionization starts from the inside because photoionization cross sections at X-ray wavelengths are considerably higher for the inner shells than for the valence shells [30]. Typically, the inverse rates are with 1 . . . 10 fs much smaller than the pulse length of about 100 fs. Hence, multiple single-photon ionization is possible, in particular because the inner-shell holes created by photo-ionization are refilled by Auger-like processes. The Auger decay is only weakly dependent on the atomic charge state and occurs fast, typical times are 0.2... 5 fs [31]. Due to this almost instantaneous refilling of the inner shells they can be ionized many times during the pulse and thus the atoms can be efficiently "pumped dry". This occurs "inside-out" and is the exact opposite to the ionization mechanism in the wavelength regimes discussed before. We studied small argon clusters (n= 13, 55) in a 100 fs laser pulse with A = 3.5nm at intensities / = 10 1 4 ... 1018 W/cm 2 . At a first glance sur-

166 prisingly, we found suppression of ionization for the clusters compared to isolated atoms in the same pulse of intense X-ray radiation [19,32]. This behaviour is in striking contrast to that of rare-gas clusters in intense optical lasers. Two effects are responsible for the difference: Firstly, the high positive space charge of the cluster hinders electron emission since the space charge is not compensated by a large quiver motion. Secondly, delocalization of electrons in the cluster reduces photoionization as well as autoionization drastically. Both effects are more important for the larger clusters investigated and the relative weight of both effects depends on field strength and cluster size. Our findings indicate that in general the coupling of energy from the laser light to matter is less effective at high frequencies. This has important consequences for X-FEL imaging applications since it implies a higher damage threshold.

Acknowledgments We gratefully acknowledge many helpful discussions with Christian Siedschlag, Md. Ranaul Islam and Ionut Georgescu. References [1] E. M. Snyder, D. A. Card, D. E. Folmer, and Jr A. W. Castleman, Phys. Rev. Lett. 77, 3347 (1996). [2] T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, G. Hays, and K. B. Wharton, Nature 398, 489 (1999). [3] J. Zweiback, T. Ditmire, and M. D. Perry, Phys. Rev. A 59, R3166 (1999). [4] L. Koller, M. Schumacher, J. Kohn, S. Teuber, J. Tiggesbaumker, and K. H. Meiwes-Broer, Phys. Rev. Lett. 82, 3786 (1999). [5] E. Springate, N. Hay, J. W. G. Tisch, M. B. Mason, T. Ditmire, J. P. Marangos, and M. H. R. Hutchinson, Phys. Rev. A 61, 044101 (2000). [6] V. Kumarappan, M. Krishnamurthy, and D. Mathur, Phys. Rev. Lett. 87, 085005 (2001). [7] K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, Phys. Rev. Lett. 90, 023401 (2003). [8] E. Springate, S. A. Aseyev, S. Zamith, and M. J. J. Vrakking, Phys. Rev. A 68, 053201 (2003). [9] T. Doppner, Th. Fennel, Th. Diederich, J. Tiggesbaumker, and K. H. Meiwes-Broer, Phys. Rev. Lett. 94, 013401 (2005). [10] T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry, Phys. Rev. A 53, 3379 (1996). [11] H. M. Milchberg, S. J. McNaught, and E. Parra, Phys. Rev. E 64, 056402 (2001). [12] J. Liu, R. Li, P. Zhu, Z. Xu, and J. Liu, Phys. Rev. A 64, 033426 (2001).

167 [13] V. Kumarappan, M. Krishnamurthy, and D. Mathur, Phys. Rev. A 66, 033203 (2002). [14] C. Rose-Petruck, K. J. Schafer, K. R. Wilson, and C. P. J. Barty, Phys. Rev. A 55, 1182 (1997). [15] I. Last and J. Jortner, Phys. Rev. A 60, 2215 (1999). [16] K. Ishikawa and T. Blenski, Phys. Rev. A 62, 063204 (2000). [17] Ch. Siedschlag and J. M. Rost, Phys. Rev. Lett. 89, 173401 (2002). [18] U. Saalmann and J. M. Rost, Phys. Rev. Lett. 91, 223401 (2003). [19] U. Saalmann and J. M. Rost, Phys. Rev. Lett. 89, 143401 (2002). [20] Ch. Siedschlag and J. M. Rost, Phys. Rev. Lett. 93, 043402 (2004). [21] L. V. Keldysh, Sov. Phys. JEPT 20, 1307 (1965). [22] S. Pfalzner and P. Gibbon, Many-body tree methods in physics. Cambridge University Press 1996. [23] J. E. Barnes and P. Hut, Nature 324, 446 (1986). [24] U. Saalmann, J. Mod. Opt. 53, 173 (2006). [25] H. Wabnitz, L. Bittner, A. R. B. de Castro, R. Dohrmann, P. Gurtler, T. Laarmann, W. Laasch, J. Schulz, A. Swiderski, K. von Haeften, T. Moller, B. Faatz, A. Fateev, J. Feldhaus, Ch. Gerth, U. Hahn, E. Saldin, E. Schneidmiller, K. Sytchev, K. Tiedtke, R. Treusch, and M. Yurkov, Nature (London) 420, 482 (2002). [26] R. Santra and C. H. Greene, Phys. Rev. Lett. 91, 233401 (2003). [27] G. Materlik and T. Tschentscher (eds.) TESLA Technical Design Report volume V: The X-ray free electron laser. DESY Hamburg 2001; see also h t t p : / / x f e l . d e s y . d e . [28] J. Arthur, Rev. Sci. Instrum. 73, 1393 (2002); see also http://www-ssrl.slac.stanford.edu/lcls. [29] D. Kramer, E. Jaeschke, and W. Eberhardt (eds.) Technical Design Report BESSY Berlin 2004; see also http://www.bessy.de/fel. [30] M. Ya. Amusia, Atomic photoeffect. Plenum Press New York 1990. [31] A. G. Kochur, V. L. Sukhorukov, A. J. Dudenko, and Ph. V. Demekhin, J. Phys. B 28, 387 (1995). [32] U. Saalmann, Interaction of strong X-ray laser pulses with small argon clusters. In B. Piraux (ed.), Electron and photon impact ionization and related topics 2004. Institute of Physics Conference Series vol. 183, p. 165, Bristol and Philadelphia 2004.

ON THE SECOND ORDER AUTOCORRELATION OF AN XUV ATTOSECOND PULSE TRAIN E. P. BENIS 1 , L. A. A. NIKOLOPOULOS 2 , P. TZALLAS 1 , D.CHARALAMBIDIS 1 ' 3 , K. WITTE 4 , AND G. D. TSAKIRIS 4 'Foundation for Research and Technology - Hellas, Institute of Electronic Structure ALaser, PO Box 1527, GR-711 lOHeraklion (Crete), Greece 2

Department of Telecommunication Sciences and Technology, Univ.

ofPeloponnisos,

GR-22100, Greece 3

Dept. ofPhysics.UniversityofCrete,

P.O. Box2208,

GR-71003Heraklion(Crete)

Greece 4

Max-Planck-Institut fur Quantenoptik, D-85748 Garching, Germany.

Temporal widths of an attosecond (asec) XUV radiation pulse train, formed by the superposition of higher order harmonics of a Ti:Sapph laser, have been recently determined utilizing a 21*1 order autocorrelation measurement of the XUV radiation field. The measured mean width of the attosecond train bursts is discussed in terms of the spectral phases of the individual harmonics, as well as in terms of the spatially modulated temporal width of the radiation and is found in reasonable agreement with the expected attosecond burst duration.

The superposition of harmonics of a femtosecond (fsec) laser beam may form a train of pulses with duration in the attosecond (asec) regime [1] or even isolated as pulses [2]. Since this extreme temporal localization of light has been demonstrated in the laboratory, its rigorous characterization became a challenging problem that has set off intense experimental and theoretical efforts. Among them, the one targeting the extension of well established methods of optical fsec metrology to the XUV asec regime resulted to the demonstration of a second order autocorrelation (AC) measurement of an asec pulse train [3] formed by the superposition of five harmonics. In this experiment, the measured pulse duration was found to be substantially longer than the Fourier transform limited (FTL) duration, in contrast to the findings of other characterization approaches that have resulted in durations much closer to their FTL values [2] for several sets of superpositions of five harmonics. Although the harmonics of the two different approaches are not of the same order, this discrepancy has raised important questions as to its origin. As a first step to investigate the discrepancy, the artificial broadening due to the spectral and temporal response of the two-XUV-photon ionization of He, acting as the non-linear detector [4] for the 2nd order AC measurement, has been assessed through ab initio calculations. The time-dependent Schrodinger

168

169 equation of helium in the XUV pulse has been solved numerically. The energy resolved photoelectron spectrum has been calculated and compared to that of a detector having a perfectly flat spectral response for FTL pulses. The deviation from the flat response is of the order of 30%, having no practical consequences in measuring temporal profiles. In addition, interferometric 2nd order AC traces for a collinear geometry have been calculated for various wavelengths and then compared to the 2nd order interferometric AC trace of a detector with rigorously instantaneous response. The comparison shows that for all harmonics far from resonance the two AC traces are almost identical, a case that is fulfilled for the 790 nm wavelength used in the experiment [5]. The measured mean pulse duration was then examined on the basis of the harmonic phases resulting from the atomic response in the generation process. Following the classical three-step model [6], the emission times t«. [7] associated with each harmonic were estimated at the experimental driving field peak intensity. Using these emission times, the experimental harmonic amplitude ratios, a mean harmonic generation nonlinearity of 6, and a 2nd order extrapolated phase for the 7th harmonic, asec bursts have been reconstructed. The reason for using an extrapolated phase value for the 7th harmonic is that it is below the ionization threshold of the generating atom and thus no phase information can be extracted from the rescattering model. A 2nd order interferometric AC trace of the reconstructed pulse showed pulse duration of 595 asec [5], a value which largely departs from the FTL value of 315 asec. Moreover, the emission times t^, as a function of the harmonic order, q, exhibit an extended almost linear part with a slope (2Ate)/Aq = 50-10 M /1 (I in W/cm2) [7], the time shifts Ate being the difference between the emission times te of two subsequent harmonics. The strong dependence of the harmonic phases on the intensity of the driving field causes some additional broadening of the measured AC peaks, due to the spatiotemporal laser intensity variation, leading to a spatiotemporal modulation of the duration of the asec bursts. The largest contribution of this effect is from the radial intensity distribution of the laser, due to the increase of the generating surface with increasing radius. In Fig. 1 the XUV pulse intensity is plotted as a function of the generating radial segment. The intensities were corrected for the geometrical factor expressed by the product of the generating area and the Gaussian beam distribution, i.e., TcAr^expt-r2). It is clearly seen that the main contribution to the pulse width is not coming from the neighboring area around the peak intensity but rather from an area around the value of 0.22 w0, where w0 is the beam waist. Thus, the pulse duration may be well underestimated if only the peak intensity is taken into account. Note that the further the XUV generation happens from the beam axis the broader it is, not only due to the dependence of the harmonic phases on

170 the intensity of the driving field but also due to the decrease of the number of the superimposed harmonics as the cutoff shifts to lower energies. This is exactly the case of the structure seen in Fig. 1 around the radius of 0,54 w0, where the 13th harmonic was eliminated due to energy considerations, and the pulse was broadened abruptly.

Fig. 1. Intensity distribution of asec bursts generated along the radial segments of a Gaussian beam.

So far, the expected radial distribution of the asec burst duration at the generation plane was described. In the experiment [3], this plane is imaged by the bisected mirror into the autocorrelator interaction region, thus effectively preserving the spatial phase distribution characteristics. The spatially integrating autocorrelator detector "sees" the sum of the radial autocorrelation ion signals. Thus, the sum of the autocorrelation traces of the set of pulses generated at radial, segments shown in Fig. 1, resulted in burst durations of-680 asec9 that is an increase of 15% compared to the peak intensity estimation. Due to the uncertainty in the phase of the 7th harmonic the above estimated durations have a large uncertainty with a lowest limit of 550 asec in the averaged trace. The above estimations indicate that the measured pulse duration of (780&80) asec is close to the expected XUV pulse duration. They also indicate that the duration of the asec pulses is sensitive to the exact driving intensity and thus they exhibit spatiotemporally modulated duration. The later is more pronounced the lower the driving intensity is because of the 1/1 dependence of A^. This modulation leads to an increased measured duration than the duration

171 at the peak intensity when the measurement is through a 2nd order AC. In contrast, in approaches that measure spatiotemporally averaged spectral phases, like those using XUV-IR cross-correlation [7], the same effect may result in reduced phase difference between subsequent harmonics and therefore, to an underestimation of the burst duration. Acknowledgement This work was conducted at the Ultraviolet Laser Facility (ULF) operating at FORTH-IESL (contract no. HPRI-CT-2001-00139) in partial support by the European Community's Human Potential Programme under contract MRTNCT-2003-505138 (XTRA) and MIRG-CT-2004-506583 (CHARA). References 1. T. W. Hansch, Opt. Comm. 80, 71 (1990); N. A. Papadogiannis et al., Phys. Rev. Lett. 83,4289 (1999), P. M. Paul et. al., Science 292,1689 (2001). 2. P. Christov et. al., Rev. Mod. Phys. 72, 545, (2000); M. Hentschel et. al., Nature 414, 509-513 (2001); R. Kienberger et. al., Science 297, 1144 (2002); R. Kienberger et. al., Nature, 427, 817, (2004). 3. P. Tzallas et. al., Nature 426, 267 (2003); P. Tzallas et. al., J. Mod. Opt. 52,321(2005). 4. N.A. Papadogiannis et. al., Phys. Rev. Lett. 90, 133902 (2003); N.A. Papadogiannis et. al., Appl. Phys. B76, 721 (2003). 5. L.A.A. Nikolopoulos et. al., Phys. Rev. Lett. 94, 113905 (2005). 6. P. B. Corkum Phys. Rev. Lett. 71, 1995 (1993); M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994). 7. Y. Mairesse et. al., Science 302, 1540 (2003).

EVIDENCE FOR RESCATTERING IN MOLECULAR DISSOCIATION I D WILLIAMS, J MCKENNA, M SURESH, B SRIGENGAN Department of Physics, Queen's University Belfast, Belfast BT7 INN, UK E M L ENGLISH, S L STEBBINGS, W A BRYAN, W R NEWELL Dept. of Physics and Astronomy, University College London, London WC1E 6BT, UK I C E TURCU CLF, CCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX 11 OQX, UK Dissociation of the singly ionized C0 2 + ion has been investigated in an intense ultrafast (55 fs) laser field, by employing an intensity selective scan technique and comparing the signals from linearly and circularly polarized pulses. Non-sequential contributions have been observed unambiguously for the first time, highlighting the role of rescattering in the dissociative process.

1. Introduction The interaction of matter with intense femtosecond pulses of light is a topic of considerable current interest, due to both the very short interaction times involved and to the inherent electric field achieving values comparable to atomic fields giving rise to highly non-linear processes1. One such process involves the rescattering of an ionized electron from its ionic core, as it is retarded and re-accelerated periodically in a linearly polarized laser field. Electron impact excitation or double ionization may follow if the scattering energy is above the inelastic threshold. This process, expounded by Corkum2, explained the so-called non-sequential (NS) enhancement observed in the double ionization of inert gases at laser intensities where sequential ionization was predicted to be orders of magnitude less3. Manipulation of the rescattering electron 'pulse' to act as a probe of nuclear motion between electron returns has been the emphasis of recent landmark experiments4. With sub laser-cycle (attosecond) resolution, rescattering events have been used to 'clock' the molecular dynamics. High kinetic energy (> 4 eV) proton and deuteron peaks, observed following strong field ionization of H2 and

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173 D2 respectively, have been interpreted as being due to dissociation of unstable H2+ and D2+ ions excited by electron rescattering to the au state. However this analysis has been questioned, with subsequent experimental5 and theoretical6 studies suggesting that the excited H2+ and D2+ ions are readily further field ionized, with the higher energy peaks arising from double ionization. It is against this backdrop that we present unambiguous evidence for the rescattering enhanced dissociation of a molecular ion. 2. Experimental Technique The experimental arrangement has been described in detail elsewhere7. Briefly, the 790 nm Ti:Sapphire laser system produced 55 fs pulses, with an energy of 22 mJ per pulse at a repetition rate of 10 Hz. The 22 mm diameter laser beam was focused into the interaction region by a 25 cm focal length spherical lens, mounted on a high precision translation stage, to give a peak focal intensity of 6 x 1016 Wcm"2. The target gas was C0 2 and product ions were extracted into a high resolution time-of-flight mass spectrometer. Instead of the traditional focal intensity variation method, the optical arrangement employed the less conventional intensity selective scan (ISS) approach8,9. There are two distinct advantages to this method. At low intensity where ionization rates are inherently low, the Gaussian expansion of the focal volume heightens the sensitivity to production rate. Moreover, as extraction is from a well-defined intensity region of the focus, intensity-dependent features are not masked by spatial averaging over the entire volume. It is well known that rescattering diminishes with increasing ellipticity of polarization due to the greater transverse momentum spread of the wavepacket. Thus differences in signal between linearly and circularly polarized pulses provide an indication of rescattering effects. In the present study this method has been used to observe rescattering events from a C0 2 + ionic core over a range of intensities in the tunnelling regime. However for the NS differences to be apparent it is vitally important that the sequential rates for the two elliptical extremes are exactly matched. This has been achieved by using an input pulse energy for linearly polarized pulses 0.65 that for circularly polarized pulses; a full description of this matching has appeared elsewhere10. 3. Results and Discussion Displayed in Fig. 1(a) is the net production of C0 2 + ions following field ionization of neutral C0 2 molecules. The ion yield (linear - SL, circular - Sc), obtained through charge integration over the relevant time-of-flight window, is

174 plotted on an arbitrary scale with the peak circular yield normalized to 1.0. Figures 1(b) and 1(c) are plotted relative to this scale. The characteristic shape of the ISS spectrum is a convolution of decreasing intensity (on-axis Lorentzian profile) and increasing volume (radial Gaussian expansion) as one scans away from the central position (see for example Ref. 9). The single ionization of both atomic and molecular targets is in general well described by the single active electron approximation. Using the ratio of 0.65 as described earlier, the linear and circular field ionization signals should be equal. The observation in Figure 1(a) of a reduction in the linear yield with respect to the circular (SL < Sc) is indicative of second order effects producing a loss mechanism in the observed SL yield. There are two possible pathways leading to a reduction in the C0 2 + yield; the first being dissociation, via either of the channels C0 2 + -» CO+ + O or C0 2 + -» CO + 0 + , the second being further ionization to produce C022+. Here we concentrate solely on the dissociative processes, observed by detecting the respective CO+ and 0 + yields. On-axis Intensity (X1011 Wcm"2)

Z Position (mm)

Figure 1: ISS signal measured as a function of focusing lens position, with respect to spectrometer axis, for linear (solid grey) and circular (dashed black) polarizations for production of (a) C0 2 + , (b) CO* and (c) 0 + . The C0 2 + circular signal is normalized to one whilst the remaining graphs are plotted on a relative scale.

It is important to note that the CO+ and 0 + ions are peaked at zero momentum i.e. there is little dissociation energy imparted to the fragments as they break apart. This ensures the full collection of all the product ions independent of the orientation angle of the C0 2 + molecule with respect to the detection axis. This was confirmed by monitoring the yield of the dissociation

175 products as the direction of the linear polarization vector relative to the detector axis was rotated. A direct comparison of the yields produced from linear and circular polarizations could therefore be made. Figures 1(b) and 1(c) both exhibit a clear enhancement in the dissociation of CCV ions with linear polarization over the intensity range 9 x 1013 - 1 x 1015 Wcm"2. The enhancement is reminiscent of the 'shoulder' observed in the NS double ionization of C0 2 observed using an intensity variation method11. A feature of rescattering, the increase of SL over Sc only occurs at intensities below the saturation intensity for the field dissociation of CCV. Analogous to the mechanism for double ionization, the returning electron wavepacket scatters off the parent CCV ion, but rather than promoting a further electron to an ionizing state, the electron-impact process excites the molecular ion to a dissociative potential. 4. Conclusion By means of the Intensity Selective Scan technique, and comparing results of linear and circular polarized pulses in C0 2 , it has been demonstrated that rescattering enhanced dissociation can occur for molecules in intense, femtosecond laser fields. Acknowledgements The experiments were undertaken using the ASTRA laser at the Rutherford Appleton Laboratory and with the financial support of EPSRC (UK). JMK acknowledges funding from DEL, MS from IRCEP at QUB and EE and SS from EPSRC. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

A. D. Bandrauk, Molecules in Laser Fields (Marcel Dekker, NY 1994). P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993). B. Walker et al., Phys. Rev. Lett. 73, 1227 (1994). H. Niikura et al., Nature 417, 917 (2002); ibid 421, 826 (2003). A. S. Alnaseref al., Phys. Rev. Lett. 91, 163002 (2003). X. M. Tong et al., Phys. Rev. Lett. 91, 233203 (2003). W. A. Bryan etal., J. Phys. B 33, 745 (2000). P. Hansen et al, Phys. Rev. A 54, R2559 (1996). A. A. A. El-Zein etal., Phys. Scripta T92, 119 (2001). M. Suresh et al., Nucl. Inst, and Methods B, 235, 216 (2005). C. Cornaggia and P. Hering, Phys. Rev. A 62, 023403 (2000).

PHOTOIONIZING IONS U S I N G S Y N C H R O T R O N RADIATION*

RONALD PHANEUF* Department of Physics, University of Nevada, Reno, NV 89557-0058, USA E-mail: phaneuf@unr. edu

Intense beams of extreme ultraviolet and soft x-ray radiation from third-generation synchrotron radiation facilities have enabled absolute measurements of photoionization cross sections for ions at high spectral resolution. Recent merged-beams measurements made at the Advanced Light Source with atomic and molecular ions probe their internal electronic structure in unprecedented detail, and provide evidence for the collective behavior of photo-excited valence electrons in fullerene ions.

1. Introduction Interactions of photons with ions dominate the properties of ionized plasmas that occur in interstellar clouds 1 and laboratory plasmas 2 . Recently, new windows on the cosmos have been opened by orbiting x-ray observatories such as CHANDRA 3 and XMM-Newton 4 . The merging of intense beams of monochromatized undulator radiation from synchrotron light sources with ion beams presents new possibilities for the detailed experimental study of photon-ion interactions 5 . Such experiments provide quantitative data at high spectral resolution, permitting detailed tests of ab-initio theoretical calculations of the electronic structure and photon dynamics of ionized matter. ""This work was supported by the Chemical Sciences, Geosciences and Biosciences Division of the U.S. Department of Energy under grant number DE-FG02-03ER15424. t T h e author gratefully acknowledges the contributions of many collaborators: A. Miiller, S. Schippers, A.L.D. Kilcoyne, A.S. Schlachter, J.D. Bozek, C. Cisneros, I. Alvarez, G. Hinojosa, S.W.J. Scully, A.M. Covington, A. Aguilar, M.F. Gharaibeh, E.D. Emmons, B.M. McLaughlin, S. N. Nahar, H.S. Chakraborty, M.E. Madjet and J. M. Rost.

176

177

Intertable Tuning

Bending

Figure 1. Merged ion-photon-beam endstation installed on undulator beamline 10.0 of the Advanced Light Source.

2. Photoion Spectroscopy with Merged Beams A schematic diagram of the experimental setup 6 at the Advanced Light Source is presented in Figure 1. Ions are produced in the discharge of a 10GHz electron-cyclotron-resonance (ECR) ion source, accelerated by 6 kV and electrostatically focused to form a highly collimated beam. A beam of synchrotron radiation from the undulator is dispersed by a sphericalgrating monochromator, whose spectral resolving power E/AE may be varied between approximately 1,000 and 30,000 by adjustable entrance and exit slits. Three interchangeable gratings cover the photon energy range from 17 eV to 340 eV. A spherical electrostatic deflector merges the ion beam onto the axis of the highly collimated photon beam. Product ions in the beam whose charge has increased due to photoionization are magnetically separated from the primary ion and photon beams and counted by a single-particle detector with near-unit efficiency. A spectrum is accumulated by recording the yield of photoions as the energy of the photon beam is stepped. The photon flux, which can be as high as 5 x 10 13 photons/s, is measured by a calibrated Si photodiode. The central interaction region consists of an insulated cylinder of accurately known length (29.4 cm) to which an electric potential may be applied to energy-label the product ions created within. A mechanical chopper wheel in the photon beam permits subtraction of background produced by stripping collisions of ions with residual gas in the ultra-high vacuum system. Three two-dimensional slit scanners measure spatial intensity profiles of the beams within the interaction region, permitting absolute cross sections to be determined from

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the measurements. The ECR ion source facilitates the production of multiply charged ion beams, making possible systematic studies along isoelectronic or isonuclear sequences. A broad spectrum of electronic configurations is accessible, permitting a fine-tuning of the role of electron-electron interactions and of giant resonance phenomena in photoionization of positive ions. Interchanging ion sources permits the endstation to be used as well to study multiple photodetachment of negative ions 7 . 3. Photoionization of Atomic Ions Mechanisms leading to the photoionization of atomic ions may be broadly classified as direct or indirect. Direct photoionization is a non-resonant process whereby an electron is ejected to the continuum by absorption of a photon having an energy greater than its binding energy. This channel is often referred to as the photoionization continuuum or background because it has a cross section that varies monotonically with photon energy. Indirect photoionization is a resonant process resulting from a discrete transition to an intermediate multiply excited state that is unbound and subsequently decays by autoionization. The resonance width is a measure of the lifetime of the intermediate state. The direct and indirect channels may interfere, giving rise to asymmetric resonance line shapes in the photoionization cross section 8 . A well-known complication in experiments with ion beams is the population of metastable states whose lifetimes are comparable to or exceed their flight times in the apparatus. 3.1. Nitrogen

Isoelectronic

Sequence

A recent example of a systematic study is photoionization of the nitrogen isoelectronic sequence 9 ' 10 . In addition to the 4 S ground state, the longlived 2 P and 2 D metastable states of N-like ions are significantly populated in ion beams. While this enriches the information content of the experiments, it complicates the interpretation of resonance structure as well as the determination of absolute cross sections for each initial state. A comparison of absolute measurements for 0 + , F 2 + and Ne 3 + at photon energies below their respective ground-state ionization thresholds is presented in Fig. 2. The initial-state fractions were determined from ion-beam attenuation measurements for 0 + in N2, whereas for F 2 + and Ne 3 + they were estimated from comparisions of the measured steps in the photon yield at the thresholds with theory for direct photoionization. The resonances in

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Fig. 2 correspond to Rydberg series of 2p-nd excitations originating from the 2 P and 2 D metastable states. An inter-comparison of these Rydberg series, and also of series for 2s-np excitations from the ground states of the three N-like ions and of atomic nitrogen 11 facilitated a quantum-defect analysis and systematic characterization of the behavior of the excited orbitals with nuclear charge along the isoelectronic sequence 10 . -i

f

1

1

1

1

1

1

1

1

1

1

1

1

.

1

1

1—rr

Photon Energy (eV) Figure 2. Absolute photoionization measurements for the N-like ions 0 + , F 2 + and N e 3 + in the threshold energy regions of the 4 S ground state and the 2 P and 2 D metastable states 9 ' 1 0 . T h e photon energy axes have been shifted and scaled to align their respective ionization thresholds (indicated by vertical lines).

3.2. Time-Reversal Resonance

Symmetry

and Truncation

of a

Giant

Since photoionization and electron-ion recombination are time-reversed processes, their cross sections are related on a state-to-state basis by the principle of detailed balance. Electron-ion recombination has been studied in detail at heavy-ion storage rings, providing a basis for comparison with in-

180

dependent measurements of photoionization cross sections. Since indirect or resonant photoionization is the analog of dielectronic recombination, the same intermediate autoionizing states may be populated by both processes. An example is photoionization of T i 3 + and dielectronic recombination of T i 4 + , which are compared in Figure 3. The recombination experiment 12 indicated an anomalously large cross section at relative energies approaching zero, suggesting the existence of a giant 3p-3d dipole resonance very close to the ionization threshold of T i 3 + . This was subsequently verified by a photoionization measurement that showed the predicted broad resonance to overlap and to be truncated by the ionization threshold 13 .

43.0

43.5

44.0

44.5

45.0

Photon Energy (eV) Figure 3. Comparison of photoionization measurement for T i 3 + (points) with prediction via detailed balance from measurements of dielectronic recombination of e + T i 4 + (solid curve) 1 3 . The dashed curve is a Fano-Voigt profile fit to the giant 3p-3d resonance that is truncated by the ionization threshold.

4. Photoionization of Fullerene Ions The size, structure and symmetry of Ceo place its properties and behavior intermediate between those of a free molecule and a solid. Ceo is known to support a surface plasmon excitation whereby the 240 delocalized L-shell electrons undergo a collective oscillation about the spherical cage formed by the positive ion core 14 . This dipolar plasmon produces a giant resonance in

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photoabsorption of Ceo near 20 eV that may result in photoionization 15,16 . At photon energies above 280 eV, localized molecular excitation of the Kshell of Ceo occurs 17 and may also lead to photoionization. Because of their stability, quantitative measurements of photoionization of fullerene ions is possible. 2+ Absolute cross sections were measured for photoionization of Cg"0, C,60 18 and C|Q" ions over the photon energy range 18-70 eV . They are compared with previous results 15,16,19 for neutral Ceo in Fig. 4. The giant dipole resonance near 20 eV is evident in each case. The data for photoionization of Ceo ions indicate a second broad resonance near 40 eV that is also evident in the data of Reinkoster et al.19 for neutral Ceo~

i i

r^

.-•/•\ 1000 -

Cq+ + hv -> C(q+1)+ + e" 60

60

o o

"-*—•

CD

CO CO CO

2

100

£ 03 N

q=0, Hertel et al. • q=0, Yoo et al. • q=0, Reinkoster et al. o q=1\ • q=2 f Scully et al.

'c o o o

q=3j 10 10

20

30

40

50

60

70

Photon Energy (eV) Figure 4. Absolute cross-section measurements for photoionization of Cg0, C 6 Q and CgJ ions18. Measurements for neutral C60 are indicated for comparison 15 ' 16 ' 19 .

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Figure 5 indicates a fit of two Lorentzian profiles to the experimental data for Cg"0- On the basis of calculations using time-dependent densityfunctional theory, the additional feature centered near 40 eV is attributed to a volume plasmon oscillation that can be photo-excited because of the special fullerene geometry of a hollow spherical shell 18 .

20

30

40

50

60

70

Photon Energy (eV) Figure 5. Lorentzian curve fits to the experimental data for photoionization of Cg 0 , indicating the presence of two broad resonances attributed to surface and volume plasmon excitations.

At photon energies exceeding 280 eV, K-shell electrons in fullerenes may be excited, leading to ionization and/or fragmentation. Absolute photoionization cross sections for Cg"0 and Cy"0 ions at photon energies in the range 280-311 eV differ significantly from those at lower photon energies in that they are distinctly molecular in character, indicating localized rather than collective electron excitation. Analysis of the resonance structure in this energy range permitted a precise determination of the HOMO-LUMO energy separations in CQ~0 and Cy"0 molecular ions.

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References 1. E.B. Jenkins, W.R. Oegerle, C. Gry, J. Vallerga, K.R. Sembach, R.L. Shelton, R. Ferlet, A. Vidal-Madjar, D.G. York, J.L. Linsky, K.C. Roth, A.K. Dupree and J. Edelstein, Astrophys. J. Lett. 538 L81 (2000). 2. D.H. Cohen, J.J. MacFarlane, J.E. Bailey and D.A. Liedahl, Rev. Sci. Instrum. 74, 1962 (2003). 3. N.A. Levenson, J.R. Graham and J.L. Walters, Astrophys. J. 576, 798 (2002). 4. M. Gudel, M. Audard, K. Briggs, F. Haberl, H. Magee, A. Maggio, R. Mewe, R. Pallavicini and J. Pye, Astron. Astrophys. 365, L336 (2001). 5. J. B. West, J. Phys B: At. Mol. Opt. Phys. 34, R45 (2001); Rad. Phys. Chem. 70, 275 (2004). 6. A.M. Covington, A. Aguilar, I.R. Covington, M.F. Gharaibeh, G. Hinojosa, C.A. Shirley, R.A. Phaneuf, I. Alvarez, C. Cisneros, I. Domfnguez-Lopez, M.M. Sant'Anna, A.S. Schlachter, B.M. McLaughlin and A. Dalgarno, Phys. Rev. A 66 062710 (2002). 7. R.C. Bilodeau, J.D. Bozek, A. Aguilar, G.D. Ackerman, G. Turi and N. Berrah, Phys. Rev. Lett. 93, 193001 (2004). 8. U. Fano and J.W. Cooper, Phys. Rev. 137, A1364 (1965). 9. A. Aguilar, A.M. Covington, G. Hinojosa, R.A. Phaneuf, I. Alvarez, C. Cisneros, J.D. Bozek, I. Dominguez, M.M. Sant'Anna, A.S. Schlachter, S.N. Nahar and B.M. McLaughlin, Astrophys. J.: Suppl. Ser. 146, 467 (2003). 10. A. Aguilar, E.D. Emmons, M.F. Gharaibeh, A.M. Covington, J.D. Bozek, G. Ackerman, S. Canton, B. Rude, A.S. Schlachter, G. Hinojosa, I. Alvarez, C. Cisneros, B.M. McLaughlin and R.A. Phaneuf. J. Phys. B: At. Mol. Opt. Phys. 38, 343 (2005). 11. S.J. Schlaphorst, S.B. Whitfield, H.P. Saha, C D . Caldwell and Y. Azuma, Phys. Rev. A 47, 3007 (1993). 12. S. Schippers, T. Bartsch, C. Brandau, G. Gwinner, J. Linkemann, A. Muller, A.A. Saghiri and A. Wolf, J. Phys. B: At. Mol. Opt. Phys. 31, 4873 (1998). 13. S. Schippers, A. Muller, R.A. Phaneuf, T. van Zoest, I. Alvarez, C. Cisneros, E.D. Emmons, M.F. Gharaibeh, G. Hinojosa, A.S. Schlachter and S.W.J. Scully, J. Phys. B: At. Mol. Opt. Phys. 37, L209 (2004). 14. G.F. Bertsch, A. Bulgac, T. Tomanek and Y. Wang, Phys. Rev. Lett. 67, 2690 (1991). 15. I.V. Hertel, H. Steger, J. de Vries, B. Weisser, C. Menzel, B. Kamke and W. Kamke, Phys. Rev. Lett. 68, 784 (1992). 16. R. K. Yoo, B. Ruscic and J. Berkowitz, J. Chem. Phys. 96 911 (1992). 17. S. Krummacher, M Bierman, M. Neeb, A. Liebsch and W. Eberhardt, Phys. Rev. B 50, 13031 (1994). 18. S.W.J. Scully, E.D. Emmons, M.F. Gharaibeh, R.A. Phaneuf, A.L.D. Kilcoyne, A.S. Schlachter, S. Schippers, A. Muller, H.S. Chakraborty, M.E. Madjet and J.M. Rost, Phys. Rev. Lett. 94, 065503 (2005). 19. A. Reinkoster, S. Korika, G. Priimper, J. Viefhaus, K. Godenhusen, O Schwarzkopf, M. Mast and U. Becker, J. Phys. B: At. Mol. Opt. Phys. 37, 2135 (2004).

PHOTO DOUBLE IONIZATION OF FIXED IN SPACE DEUTERIUM MOLECULES THORSTEN WEBER, REINHARD DORNER, ACHIM CZASCH, OTTMAR JAGUTZKI, HORST SCHMIDT BOCKING, ALKIS MULLER, VOLKER MERGEL Institutfiir Kernphysik, Universitat Frankfurt, Frankfurt a.M., D-60438, GERMANY MIKE PRIOR, TIMUR OSIPOV, SEBASTIAN DAVEAU, ELI ROTENBERG, GEORGE MEIGS Lawrence Berkeley National Laboratory, Berkeley, CA-94720, USA LEW COCKE Dept. of Physics, Kansas State University, Manhattan, KS-66506, USA ALLEN LANDERS 206 Allison Laboratory, Auburn University, AL-36849 5311, USA ANATOLI KHEIFETS Research School of Physical Sciences and Engineering, Australian National University, Canberra A CT 0200, A USTRALIA JIM FEAGIN Dept. of Physics, California State University-Fullerton, Fullerton, CA-92834, USA RICARDO DIEZ MUINO DIPCand UFMCentro Mixto CSIC-UPV/EHU, 20 018Donostia-San Sebastian, SPAIN In the following we present the kinematically complete study of the four-body fragmentation of the D2 molecule following absorption of a single photon. For equal energy sharing of the two electrons and a photon energy of 75.5 eV, we observed the relaxation of one of the selection rules valid for He photo double ionization and a strong dependence of the electron angular distribution on the orientation of the molecular axis in the coplanar geometry. This effect is reproduced by a model in which a pair of photo ionization amplitudes is introduced for the light polarization parallel and perpendicular to the molecular axis. The results in a non-coplanar geometry reveal that the correlated motion of the electrons is strongly dependent on the inter-nuclear separation in the molecular ground state at the instant of photon absorption.

184

185 1. Introduction The simultaneous ejection of two electrons by the absorption of a single photon (Photo Double Ionization or PDI) is a paradigm in the study of the dynamics of electron-electron correlation. However, only the simplest process of this kind, i.e. PDI of helium, is substantially well understood (see [1]). A more intricate PDI process is the photo fragmentation of the H2 (or D2) molecule. Here the rapid departure of the two photoelectrons is followed by the Coulomb explosion of the two bare nuclei, and their relative momentum defines the molecular alignment, a reference axis essential to fully describe the process. As in He, one expects important effects from electron-electron repulsion, and selection rules, but also from additional electron-nuclei interactions, and the final state molecular symmetry. How do these combine to yield the four-body final state? To help elucidate these issues, we report the coincident measurement of the momenta of both nuclei and both electrons from the single photon induced fragmentation of the deuterium molecule. We point out the similarities and differences with PDI in He. The momenta, i.e. the set of vectors, of all fragments of an atom or molecule break-up were measured in coincidence with high precision using state-ofthe-art imaging and timing techniques (COLTRIMS: [2], [3]). In brief, the 2bunch mode photon beam at beam-line 7.013 of the Advanced Light Source at LBNL, intersected a supersonic molecular beam of D2 inside the momentum spectrometer (D2 has higher target density than a comparable H2 jet and yields data with fewer random coincidences from background H 2 0). The particles were guided by electric and magnetic fields onto two position sensitive channel plate detectors that registered multiple hits on rectangular and hexagonal delayline anodes (see [4]). 1.1. Coplanar Geometry: All particles and the polarization vector are in one mutual plane Pioneering experiments on the PDI ([5], [6], [7], [8], [9], [10]) revealed surprising similarity of the electron angular distributions for He and D2. For He, at energies up to 100 eV above threshold, these angular distributions (Fully Differential Cross Sections - FDCS) are governed by the final state repulsion of the two electrons and selection rules resulting from the 'P° symmetry of the final two-electron state [1]. On the basis of the Born Oppenheimer Approximation Feagin ([11], [12]) introduced a helium-like model with two complex symmetrized amplitudes, gz and g n , for the PDI of randomly orientated D2 which well described previous measurements [8].

186 But despite the similarity of the PDI of He and H2 some selection rules that exclude certain escape geometries are relaxed for H2 ([11], [13]). Primarily, this relaxation stems from loss of a fixed angular momentum for the photoelectron pair; i.e. the electronic continuum wave function does not have pure P symmetry. The molecular ground state contains high angular momentum components and electron scattering by the nuclei during escape can mix angular momenta. In helium, for equal energy electrons, the cross section is zero on a cone 62 = 180° - 0i, where 0!i2 are the polar angles of electrons 1 and 2 with respect to the polarization axis (see selection rule F in fig. 1 and [1]).

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Figure 1. Illustration of the selection rules: The dots show the FDCS for the PDI of helium at 24 eV above threshold for equal energy sharing (E,/(E,+E2) = 0.5 ± 0.1). The polarization axis is horizontal. The first electron is fixed at 6, = 55° ± 12° (red arrow). For equal energies, the twoelectron states with 'P° symmetry (final state in the PDI of He) have a node for e2 =180° - 6i indicated by the cone (selection rule F), where 6i,2 are the polar angles of electron 1 and 2 with respect to the polarization axis. The dashed straight (red) line indicates the forbidden back-to-back emission (selection rule C). The dashed line represents a Gaussian fit function (AOn = 99.5° ± 1.5°).

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Figure 2 shows the FDCS for D2 at different molecular orientations, and, for comparison, results for helium. The helium results (figure 2d) display the well known structure of two lobes separated by the area at 02 = 180° - 0i (forbidden by selection rule F). This is indicated by the vertical dashed line equivalent to the cone shown in fig. 1 (see also fig. 11 in Ref. [3] and fig. 2 in Ref. [14]). As predicted by Walter and Briggs (selection rules H and I in [13]), the nodal cone, and hence the He-like FDCS, is also observed for D2 with its molecular axis parallel or perpendicular to the polarization of light where only one amplitude fs (not shown here) or fn (figure 2c) contribute to the PDI. For arbitrary orientation of the molecule, the cone fills up due to interference of the fj and fn amplitudes; this is weighted by the factor cos 0R • sin 0R and hence is strongest at 0R = 45°. The coplanar geometry where the electron momenta, molecular and polarization axes are in the same plane displays in more detail the influence of the molecular axis orientation on the photoelectron angular distributions as is shown figure 3 for equal energy sharing. The measurements in panel (3a) are integrated

187 over all molecular orientations. The solid line (in 3a) shows the spherically averaged FDCS calculated using Eq. (6) of Feagin [11]. To evaluate the amplitudes fj and fn, we used a single-center expansion model of the H2 ground state [15], and a convergent close-coupling (CCC) expansion of the final twoelectron state in the field of a point-like charge Z = 2 [16]. For comparison, the interference-free FDCS calculated with fj = fn (open triangles) is shown. The interference of f% and fn causes the main lobe in the spherically averaged FDCS for D2 which is slightly shifted backwards, i.e. here the two electrons repel each other more strongly than in the case of helium. Figure 2. A density plot of the angular distribution of the second electron when the first electron is detected at 8i - 55° ± 12° (circled cross). The patterns show the PDI of D2 (a-c) at 75.5 eV and He (d) at 103 eV photon energy (sum electron energy 24 eV), equal energies (Ei/(E,+E2) •= 0.5 ± 0.1) and linearly polarized light. Horizontal axis: polar angle 62 of electron 2 with respect to the polarization axis, vertical axis: difference between the azimuthal angles of the two electron AiJ^. The back-to-back emission is at the full dot on the A ^ = 180° line. The dashed vertical line is the nodal cone 92 = 180° -Q\= 125°. The color scale is linear in the count rate, (a) D2 molecule 8R - 45°± 11°, i.e. a mixture of £ and ft transition (integrated over AeR), (b) D2 integrated over all molecular orientations, (c) 9R - 90°± 11°, i.e. n transition (integrated over A(J>OR). (d) Helium.




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Figure 3. Schematic representation of an experimental molecular double-slit experiment with combined electron and fragment ion detection. The experiments were performed behind soft-X-ray beamlines of BESSY in Berlin and HASYLAB in Hamburg. The molecular double-slit has two setting possibilities described by (g) and (u) as shown in Fig. 2. Depending on the setting, one receives characteristic angular pattern which correspond to fringes and anti-fringes in Young's double-slit experiment.

197 periment. With soft x-rays to destabilise the innermost, and thus most strongly localised, electrons of nitrogen from the molecule, one can follow their movement in the molecular frame of reference using electron-ion coincidence detection. In addition, the experiment prove something that has long been doubted: a disruption of the inversion symmetry of this molecule leads to a partial loss of coherence through the introduction of two different heavy isotopes, in this case N-14 and N-15. The electrons begin to localise partially on one of the two, now distinguishable, atoms. This is equivalent to partially marking one of the two slits in Young's double slit experiment. It provides partial "which way" information, because the marking gives information about which path the electron took. The experiments were carried out at the synchrotron radiation laboratories HASYLAB at DESY in Hamburg and BESSY in Berlin. The measurements employed a multi-detector array for combined, coincident electron and ion detection behind undulator beam lines, which deliver soft x-rays with high intensity and spectral resolution (Fig. 3). References 1. A. Einstein, Ann. Phys. 17, 132 (1905); English translation in The World of the Atom, edited by H.A. Boorse and L. Motz (Basic Books, New York, 1966). 2. N. Bohr, Nature 121, 580 (1928). 3. R.P. Crease, Physics World Sep. 2002; http://physicsweb.Org/articles/world/15/9/2 4. M.O. Scully, B.-G. Englert and H. Walther, Nature 351, 111 (1991). 5. S.P. Walborn, M.O. Terra Cunha, S. Padua, and C.H. Monken, American Scientist 91, 336 (2003). 6. S. Diirr, T. Nonn and G. Rempe, Nature 395, 33 (1998). 7. L. Hackermiiller, K. Hornberger, B. Brezger, A. Zeilinger and M. Arndt, Nature 427, 711 (2004). 8. D. Rolles, M. Braune, S. Cvejanovic, O. Gefiner, R. Hentges, S. Korica, B. Langer, T. Lischke, G. Priimper, A. Reinkoster, J. Viefhaus, B. Zimmermann, V. McKoy and U. Becker, Nature 437, 711 (Sep. 2005). 9. B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996). 10. M. Arndt, Nature Physics 1, 19 (Oct. 2005).

EXPERIMENTAL OBERSERVATION OF INTERATOMIC COULOMBIC DECAY IN NEON DIMERS* T. JAHNKE 1 , A. CZASCH 1 , M. SCHOFFLER 1 , S. SCHOSSLER 1 , A. KNAPP 1 , M. KASZ 1 , J. TITZE 1 , C. WIMMER 1 , K. KREIDI 1 , R. E. GRISENTI 1 , A. STAUDTE 1 , O. JAGUTZKI 1 , U. HERGENHAHN 2 , H. SCHMIDT-BOCKING 1 , AND R. DORNER 1 'insitutfiir Kernphysik, JWG Universitat, Max-von-Laue-Str. 1, Frankfurt/M, Germany Max-Planck-lnstitut fiir Plasmaphysik, EURATOM association, Boltzmannstr. 2, Garching, Germany The spectral lines of photons emitted from excited atoms, ions and molecules have been used ever since their discovery as a fingerprint of the particle's electronic structure. In 1925 Pierre Auger [1] discovered that, in competition to the emission of these characteristic photons, excited atoms can release their energy by emission of one of their electrons in a process commonly known as "Auger decay". Seven years ago, Cederbaum et al. [2] predicted a third, additional decay mechanism termed Interatomic Coulombic Decay (ICD). According to calculations this novel effect often becomes the dominant decay channel, once the excited atom is placed in an environment of other atoms. In that case the deexcitation energy is transferred to a neighboring atom, which releases it by emission of its most weakly bound electron. Here we report on an experimental observation of this interatomic coulomb decay in 2s ionized neon-dimers. The decay is unambiguously identified by detecting the energy of two Ne* fragments and the ICD electron in coincidence, yielding a clean experimental spectral distribution of the ICD electrons.

1. Introduction Electronically excited states of atoms, ions and molecules are of key importance for many technical applications. They also played and still play a major role in the development of quantum theory. Electronically excited matter is found for example in stellar plasmas or fluorescence tubes. Here, the excited states relax by emission of a photon, which carries information on the decaying system, and can be used in light sources. For more highly excited states, emission of an electron instead of a photon is a competing decay mechanism. This route is called Auger decay [1]. Here, one electron from a higher electronic level fills the hole in a more tightly bound orbital, while the excess energy leads to * This work is supported by BESSY II, DFG.

198

199 emission of a second electron. The properties of Auger and fluoresence decay are mainly determined by the atom or molecule which has been initially excited. Interaction with the environment is known to cause distortions such as broadening of spectral lines, but was for long not expected to principally alter the decay routes. In pioneering theoretical work Cederbaum and coworkers have shown that this text book perspective is not the full story [2]. Their calculations predict that if the excited atom or molecule is put in close neighborhood of other particles, a fundamentally new decay mechanism, interatomic coulomb decay (ICD), may emerge. The excited species can transfer its energy in an extremely efficient way to a neighboring particle which then releases that energy by emission of one of its own outer shell electrons. ICD is different from the Auger decay since firstly the electron does not emerge from the excited particle but from its neighbor and secondly this emission is not mediated by the overlap of the participating wavefunctions but rather by an energy transfer via a virtual photon. A reason why this fundamental effect has not been discovered along with Auger and radiative decay is that ICD electrons are of low energy, in the order of a few electron volts (eV), and emerge from weakly bonded systems, such as van der Waals clusters or hydrogen bonded liquids. In this kind of environment there are always plenty of slow secondary electrons which experimentally mask the ICD electrons, leaving the decay mechanism concealed. A surplus of such low energy electrons at photon energies above the neon 2s ionization threshold has recently been reported in an experiment on large neon clusters [3]. This has been interpreted as an evidence for the existence of ICD. A clean prototype system for which ICD has been calculated and which we chose for our investigation is the neon dimer Ne2- In this exotic but exhilarating species two neon atoms are bound by the van der Waals force with an energy of 3 meV at an internuclear distance of 3.4 A [4]. In neon (Z=10) the Is, 2s and 2p shells are filled. If an electron is removed from the 2s shell, Auger decay in a single , isolated neon atom is energetically prohibited: The energy gained in a transition of an electron from a 2p orbital to the 2s shell, 26.84 eV, is not sufficient to enable the most loosely bound electron to escape from the singly charged neon ion (noted as Ne+). In contrast to that, ICD is energetically allowed, since the amount of energy is sufficient to emit one electron from a neighboring neutral neon atom with an ionization potential of only 21.6 eV. The ICD process in the neon dimer, and the sequence of events which allowed its separation from the background of secondary electrons is shown in Figure 1. At first a 2s electron from a Ne2 is removed by absorption of a photon

200

(Fig. l.top). After that the Ne2+ (2s1) dimer cation undergoes IC-decay (Fig. 1,middle), leading to a second free electron and two adjacent singly charged Ne+ ions repelling each other. Consequently the ions are emitted back-to-back with a kinetic energy release (KER) corresponding to the internuclear distance at the instant of the ICD (Fig. l.bottom). The energy difference between the Ne2+(2s"') initial state and the final three-body state at asymptotically large distance of the two Ne+ ions is predicted as 5.3 eV [5]. This amount of energy will be distributed to the kinetic energy of the ICD electron and the KER of the Ne+ ion pair. Therefore a unique fingerprint of ICD is the coincident three particle detection of two ions, which are emitted back-to-back, and one electron, with the further constraint that the sum of all kinetic energies has to add up to a constant. Therefore measuring the three particles' energy sharing and the backto-back emission of the two Ne+ ions reveals the existence of ICD.

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Figure 1. The investigated process. A 2s electron is removed from one atom of the dimer by means of photoionization. A 2p electron drops into the vacancy. The energy that is released by that transition is transferred to the neighboring atom, ejecting a 2p electron from that atom. Then the dimer fragments in a Coulomb-explosion.

201

2. Experimental Setup The experiment has been performed at beamline U125/1-PGM of the BESSY synchrotron radiation facility in Berlin in single bunch operation using the COLTRIMS (COLd Target Recoil Ion Momentum Spectroscopy) technique (see Figure 2) [6,7]. The neon dimers have been produced by expanding neon gas at room temperature through a 30 fim diameter nozzle at a stagnation pressure of 25 bar. The dimer fraction in the beam has been measured by means of time-of-flight mass spectrometry after 2p photoionization to be about >0.5%. For the experiment a photon energy of 58.8$ eV, sufficient for ionization of the 2p and 2s levels but below the double ionization potential of atomic neon has been chosen [8]. Ions and electrons created in the interaction volume are guided by a combination of parallel electric and magnetic fields (5.5 V/cm and 6.9 Gauss, respectively) towards two position and time sensitive channel plate detectors [9]. The length of the ion arm of the spectrometer was Sr=30 mm, the electron arm employs McLaren-timefocusing with a field free drifttube (Sd=120 mm) following an acceleration region with a length of se=67 mm. The guiding fields and geometry of the spectrometer yield a 47t acceptance solid angle for electrons with an energy of up to 12 eV and Ne+ ions up to 4 eV. For each event, in which two ions and at least one electron were detected the positions and times-of-flight of all particles have been recorded for offline-analysis. From these data all three components of the vector momenta of each particle are obtained. ion detector

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exp[-i^-(/).r ] A~(t). [ik + v] = 0.3: all ATI peaks predicted by CV2 were smaller than TDSE ones, while TDSE presented a new set of secondary peaks that were unexplained by the CV2 theory. In fact, due to energy conservation, the main ATI peaks were found at the energies: Ep = £j + pa

(7)

where p is the number of absorbed photons. In the considered case, the ponderomotive energy U„=F02/4o)2 is negligible because of both the low laser intensity, and the high photon frequency. Further, it was noticed that the positions of the secondary peaks follow a similar rule: E

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where s > 0 and n > 1 are integers. This suggests that the secondary peaks may be traced back to the absorption of s photon(s) from excited states n= 2, 3... This may be physically understood by realizing that a short laser pulse has a broad spectrum, thus making possible to populate a wide range of atomic excited states through the absorption of a single photon. It is worth insisting on the fact that this intermediate transition may occur even though the laser frequency a is not in tune. Hence, improving the theory CV2 implies taking into account a pathway through intermediate bound states. A simple way to do it consists in a different choice for the trial wave function j ; + ( P,t ) . Since the first Bora approximation reproduces very well the non-resonant background of the whole spectrum, even very far from the ionization threshold, it is natural to propose:

*, + (F,O=5»)M'.4 are wiped out by the overwhelming contribution of the background. 3.2. Influence of the photon energy Let us now consider a pulse composed of 20 cycles with different values of a. To remain clearly in the perturbation regime, we keep the same laser intensity, , MCV2- and PJJ for four i.e., Fo=0.01. In Fig. 2, we compare P CV2fi values of a below the ionization potential (0.25 < co =0.35, there is a perfect agreement between MCV2 and TDSE. As expected, CV2 does not agree with the latter. Further, secondary peaks appear as shoulders of principal peaks when they are not well resolved.

212

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Now, for co = 0.25, both MCV2 and CV2 underestimate the height of the principal peaks as given by TDSE. However, MCV2 appears much better than CV2 and the two secondary peaks which show up above the background are well reproduced by MCV2 . The first and second secondary peaks are the signature of one and two-photon absorption from the excited state «=2, respectively. Since the bound energy of the state «=2 is - 0.125, i.e., half the value of co, the secondary peaks stand out above the background at equal distances of the neighboring principal peaks. As to the small discrepancy between the heights of MCV2 and TDSE principal peaks, it might be traced back to the contribution from intermediate Rydberg states that are almost at resonance of a two-photon absorption for co=0.25. Indeed, such a contribution is not taken into account in the present model because the coefficients b (- (t) in (10) can only describe one-photon absorption. Finally, the analysis of the positions of secondary peaks for the different values of co confirms that their origin is the above-mentioned two-step process. For co=0.35, the first secondary peak due to the level n=2 is a shoulder on the right wing of the first principal peak (direct two-photon absorption). Further, two secondary peaks, attributed to a one- and two-photon absorption from the intermediate level n=3, loom up at the expected place to the right of the first and second principal peaks, respectively. For co=0.45, the only resolved secondary peak is located to the left of the first principal peak at a place that permits to ascribe it to the intermediate level n=2. It appears also as a shoulder in the left wing of the second principal peak. Scrutinizing the case co=0.40 reveals that the first secondary peak is larger than the first principal peak. It is attested by both its position, and the position

213 and height of the principal peak as predicted by CV2 . Thus, the first principal peak manifests itself as a shoulder in the right wing of the secondary peak. Actually, the energy separation between the two peaks is 0.05 a.u.. Indeed, this case corresponds to an almost resonance situation (which would occur for #=0.375 a.u.). Further, the shape of the first peak shows a large width, visible on the left wing. The shape is characteristic of single photon ionization as given by the first Born approximation. It is without doubt the signature of the first step leading to a secondary peak (here, the excitation of the level n=2). 4. Conclusions We have shown that substituting the genuine initial state for a new bound state, which corresponds to an evolution of the initial state under the influence of the laser field, permits to reproduce accurately the ionization process for photon energies smaller than the ionization potential. In the present theory MCV2 , the new initial state is made of the genuine initial state plus a limited number of bound intermediate states, whose coefficients are given, with the correct phase, by the amplitude of the first Born approximation. Acknowledgments VDR acknowledges support by the Universidad de Buenos Aires, CONICET, CELIA-Universite Bordeaux 1 and by ECOS/CONICYT, Grant No. C03E01. References 1. A. Einstein, Ann. Phys. 4, 132 (1905). 2. For a review see: P. Agostini and G. Petite, Contemp. Phys. 29, 57 (1988). 3. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, Phys. Rev. Lett. 59, 1092 (1987). 4. M. P. de Boer and H. G. Muller, Phys. Rev. Lett. 68, 2747 (1992). 5. R. R. Freeman and P. H. Bucksbaum, J. Phys. B 24, 325 (1991). 6. J. H. Eberly and J. Javanainen, Phys. Rev. Lett. 60, 1346 (1988). 7. J. Wassaf, V. Veniard, R. Taieb and A. Maquet, Phys. Rev. A 67, 053405 (2003). 8. E. Cormier and P. Lambropoulos, J. Phys B. 30, 77 (1997). 9. G. Duchateau, E. Cormier and R. Gayet, Phys. Rev. A 66, 023412 (2002) 10. G. Duchateau, E. Cormier, H. Bachau and R. Gayet, J. Mod. Optics 50, 331 (2003). 11. V.D. Rodriguez, E. Cormier and R. Gayet, Phys. Rev. A 69 053402 (2004). 12. Yu N. Demkov, Variational Principles in the Theory of Collisions, (Pergamon Press, Oxford 1963). 13. A. Bouhal et ah, Phys. Rev. A 58, 389 (1998).

MOLECULAR FRAME PHOTOEMISSION IN PHOTOIONIZATION OF H2 AND D2 : THE ROLE OF DISSOCIATION ON AUTOIONIZATION OF THE Qi AND Q2 DOUBLY EXCITED STATES D. DOWEK, M. LEBECH AND J.C. HOUVER Laboratoire des Collisions Atomiques et Moleculaires, CNRS-Universite Paris-Sud (UMR 8625, FR LUMAT), Bat. 351. Universite Paris Sud, F-91405 Orsay Cedex, France Dissociative photoionization (DPI) of H2 and D2 in presence of resonant excitation of the Qi'Z+„(l) and Q2'n„(l) doubly excited states has been studied by combining the (VH+/D+> V„ 8) vector correlation method and the use of linearly or circularly polarized synchrotron radiation at 28.5 eV, and 32.5 eV. The \(x, ft, #,) molecular frame photoelectron angular distributions (MFPADs) are reported for the dominant DPI processes identified, and compared for the two isotopes. They provide a sensitive probe of the molecular photoionization dynamics when resonant and non-resonant ionisation channels interfere. In particular, the forward-backward emission anisotropics observed when autoionization takes place at intermediate internuclear distances, indicating a breaking the g-u symmetry, as well as the circular dichroism characterizing electron emission in the molecular frame, should provide a sensitive test of the theoretical description of these processes.

1. Introduction Dissociative photoionization (DPI) of the H2 molecule involving the Qi(2pau,nlA) and Q2(2pnu,nlA) ( n > l ) doubly excited Rydberg series [1] converging to the H2+(2pau) and H2+(2p7t u) ionic states, has been the subject of several experimental studies based on the kinetic energy distribution (KED) of the H+ fragments [see e.g. 2,3,4]. These neutral states are all repulsive and can either autoionize to the H2+(lsOg) and H2+(2pou) ionic states, or dissociate into neutral fragments [5]. In particular it was inferred that autoionization (AI) of the Qi'Z+u(l) lowest state of the Qi(2pc„,nlA) series and Q2,rIu(l) lowest state of the Q2(2p7TT,,nlA) series plays a major role for the production of fast H + fragments in the 25-30 eV and 30-35 eV photon energy range, respectively. Since ionization and dissociation occur on a very short time scale, the coupling of both continua requires a quantum treatment of both electron and ion motion [6]. Most of the features observed in the KEDs, including H2/D2 isotope effects, are well predicted by the recent theoretical studies of Sanchez and Martin [7],

214

215 who demonstrated the importance of interference effects between resonant and non-resonant DPI channels. In order to get more insight into the photoionization (PI) dynamics of H2/D2 in presence of the Q i ' S ^ l ) and Q 2 l n u (l) autoionizing states, we have used the (VA+, Ve, e) vector correlation method to measure the generalized I(x, 6a 0J molecular frame photoelectron angular distributions (MFPADs), where x represents any orientation of the molecular axis AB with respect to the polarization axis e, and (0„ #,) the electron emission direction in the MF frame [8], for each identified DPI process AB + hv-» A+ + B + e. The sensitivity of the molecular frame photoemission observables has been demonstrated in several studies in the recent years [8,9]. The selected photon energies at hv = 28.5 eV and 32.5 eV correspond to the resonant excitation of the Q / E ^ l ) and Q2'n u (l) doubly excited states, and the experiments have been performed for the two isotopic molecules D2 and H2. Here we present some results for a study of DPI of D2, where the (VD+, Ve, 6) vector correlation method is combined with the use of circularly polarized light providing the conditions of a complete experiment [10], and compare them with those reported in a first paper, referred to as paper I, where the MFPADs for the DPI processes of H2 induced by linearly polarized synchrotron radiation (P) were measured at the same photon energies [Lafosse et al, 2003, ref.l 1], The isotope effects are pointed out, which can bring new insight into the characterization of the coupling between the nuclei and electronic movement, in particular the u-g symmetry breaking in the molecular frame photoemission [12]. A detailed discussion of the previous work by other authors on DPI of D2 and H2 is included in paper I. We note that I(0J MFPADs have been reported for a molecule oriented parallel or perpendicular to linearly polarized light for direct ionisation of H2 into the H2+(lsOg) ground state and higher H2+ (2R gu ) excited states at selected energies [13], and that results for the investigation of DPI of H2 and D2 induced by linearly polarized light in the energy region of interest in this paper using the COLTRIMS method [14] at the Advanced Light Source were also discussed recently [15]. 2. Experimental method The (VA+, Ve, e) vector correlation method consists of measuring for each DPI event the three components of the VA+ ion fragment and V e photoelectron nascent velocity vectors, deduced from the arrival time and position of both particles in a double velocity spectrometer described in detail previously [16]. For these experiments, the interaction region was defined at the intersection of a supersonic molecular beam [17] and the polarized light beam delivered by SU5

216 undulator-based VUV beamline [18] at Super-ACO (LURE, Orsay), operated in the two-bunch mode. Using the Stokes parameters (sonify***) the circular polarization rate s$/sQ of the light was higher than 0.95. Ions and electrons were extracted from the interaction region by a dc electric field E whose magnitude* here 100V/cms ensures a 4 M collection of both particles for the studied processes, and guided to the two delay-line position sensitive detectors (Roentdek) through an intermediate region where focusing lens sets are set to control the trajectories [16]. The main resolution limitation here was due to the St« 0.5-0.8 ns time width of the light pulse of Super-ACO. 3.

(EH+/D+9 Ee)

ion-electron kinetic energy correlation diagrams

The (EA+9 Ee) ion-electron kinetic energy correlation diagram (KECD) is the bidimensional histogram of the (A+s e) coincident events distributed as a function of the EA+ and Ee ion and electron kinetic energies, derived from the magnitude of the ¥4+ and Ve velocities in the (VA+, V e , i) vector correlation analysis.

Figure 1. KECDs of the coincident events (D+, e) (hv - 28.5 eV) (a), (H*. e) (hv - 28.5 eV) (b) and (D+, e) (hv = 32.5 eV) (c); the extraction fields of lOOV/cm ensures a 4ft collection of electrons and ions withfiH+< 8 eV and E« < 8 eV; the straight line of slope -2 corresponds to the ground state dissociation limit L; the intensity scale runs from blank (lowest intensity) to black (highest intensity) in linear scale as shown, the contour lines are spaced by 10% of the maximum value. The two regions separated by the vertical solid line are on a different intensity scale (xlO).

Figure 1 displays the KECDs obtained for DPI of D2 and H2 at the photon excitation energy hv = 28.5 eV (Fig.l(a,b), and for DPI of D2 at 32.5 eV (Fig. 1(c)), respectively. Each peak in the KECD corresponds to a specific DPI

217 process which can be identified by its reaction pathway. Process Si provides an example of direct ionisation (DI) which takes place in the FC region prior to dissociation of the molecular ion: at 28.5 eV, the electron energy Ee = 10 eV identifies population of the H2+/D2+(2X+g) ground state ionic state and EH+ = 0-1 eV identifies the dissociation limit, here the H+ + H(ls) lowest limit labelled (L) in Fig.l. This limit is the only one opened for the two reported photon energies. Direct ionisation into the H2+/D2+(2I+U) first excited state is on the contrary characterized by the production of very low energy photoelectrons, since the DI threshold in the Franck-Condon (FC) region is about 29 eV, and quite energetic H+ ions, i.e. a peak lying at the other end of the (L) dissociation limit in the KECD. For the main DPI processes at the resonant energies, the characteristics are different since the autoionization lifetime of the QilZ+u(l) and Q 2 'n u (l) Rydberg states and the dissociation time of the order of few femtoseconds are of comparable magnitude, and ionisation may occur during the course of dissociation. The main structure producing energetic D+ ions in the (ED+, Ee) KECD, labelled S2 in Fig. 1(a) for a photon energy hv = 28.5 eV, corresponds to a continuous ridge elongated along the L dissociation limit. The intensity distribution of the (D+,e) coincident events shows a maximum probability for the production of D+ ions with ED+= 1.5-3 eV, corresponding to photoelectrons of E e = 5-8eV energy. The position of S2 along (L) in the (ED+, Ee) KECD is shifted towards lower EEH- energies as compared to the corresponding ridge S2 in the (EH+, Ee) KECD Figure 1(b). However we assign unambiguously this process to the same reaction, i.e. excitation of the Qi'Z+u(l) lowest state of the Qi(2pau,nlX) series autoionizing into the dissociative continuum of the H2+/D2+(2Z+g) (eq.l, H label is used), based on the angular analysis presented in the next section. H2(X'l+g) + hv -> H2(Q,'Z+U(1)) -> H2+(2£+g) + e -> H+ + H(ls) + e (1) The shift of the position of the peak along (L) suggests that AI of the D2(Qi1E+,,(l)) state takes place preferentially at smaller internuclear distances, than does the F^Qi'S^O)) state, leading to a different kinetic energy sharing between the photoelectron and the heavy fragments. This observation is consistent with a similar AI lifetime for both states, but a different fragmentation velocity, slower for D2 than for H2. The situation is different for the photon energy hv = 32.5 eV, since the (ED+, Ee) KECD looks very similar to the (EH+, Ee) KECD at the same energy (Fig. 1(c)). Two peaks labeled S3 and S4 are identified along the L dissociation limit corresponding to the production of 2.5 < EH+/D+ < 5 eV and 5 < E

218 H+/D+ ^ 7.2 eV energetic fragments, respectively, and to E6 = 7 eV and Ee ~ 1 eV photoelectron energies at the maximum of each structure. Accordingly, we tentatively assigned S4 and S3 to the excitation of the Q 2 'n u (l) state, autoionizing preferentially into the H2+/D2+(2£+u, 2pou) state (eq.2) at short internuclear distance leading to the higher ion fragment energy component (S4), and into the H2+/D2+(2£+g) state (eq.3) at larger distances (S3). H2(X'Z+g) + hv -> H2(Q2'nu(l)) -> H2+(2S+U) + e -> H+ + H(ls) + e (2) H2(X'Z+g) + hv -> H2(Q2'nu(l)) -> H2+(2Z+g) + e -> H+ + H(ls) + e (3) However, despite the similar characteristics of the KECDs, the angular analysis presented below for the processes S4 and S3 reveals significant differences between the PI reactions for D2 and H2. We already note at this level that the PD+ asymmetry parameter amounts to pD+ = -0.25 ±0.1 for peak S4 (PH+ = +0.25) and to Pt>+ = 0.5 ± 0.1 for peak S3 (PH+ •= -0.1), respectively. As was found for PI of H2 at this photon energy, S4 and S3 cannot be assigned only to the reactions in eq. (2) and (3), since the pio„ parameter would be about -1, but also involve the contribution of other reactions, which are not identical for D2 and H2. The results at 28.5 eV and 32.5 eV indicate that AI of the Q,'Z+U(1) state into the ionic ground state (2Z+g) (eq.l), still accessible in the FC region at 32.5 eV, which contributes to peak S4 in PI of H2, now contributes to peak S3 in PI of D2. The other contribution to peak S4 in PI of D2 is attributed to DI into the D2+(2S+U) first excited state, for which the p\on parameter was estimated to be of the order of 0.6 [3]. In the next section we present some results of the angular analysis for each process, conveniently selected in the KECD at each photon energy. 4. Molecular frame photoelectron angular distributions (MFPADs) 4.1. Theory of measurement The spatial analysis of the (VA+, Ve, e) correlation provides for each (A+, e) coincident event three angles (i) the polar angle x between the VA+ vector and a fixed laboratory frame polarization axis which identifies the molecular orientation at the instant of PI (due to the strong repulsive character of the molecular states involved in DPI of D2 and H2, the axial approximation is valid here) (ii) the polar angle 6e between the VA+ and V e vectors, and (iii) the angle ,' (cosj) sin (*) (4) in the frame of the dipole approximation. The four P^icostf) Legendre polynomials are known analytical functions of the x polar angle, and the MF azimuthal dependence involves simple functions, therefore, a three angle fit of the /+i Of, 6e, fa) measured distribution provides the five FLN(0e) functions. These functions contain the complete information about the PI process, leading to the magnitude and phases of the transition amplitudes [10]. Knowing the .FLN functions, the same information can be presented in the form of the MFPADs for four specific orientations of the molecule, namely the l(0e, $,) MFPAD for a molecule aligned perpendicular to the propagation axis k of circularly polarized light, or for a molecule aligned parallel, perpendicular, or at the magic angle with respect to the linear polarization axis P. These MFPADs are obtained by inserting the x = 90° value in eq. (4), or the x = 0°, X = 54.7° and x - 90° values in eq.(5) valid for linearly polarized light, respectively [8]. They correspond to a well defined orientation in space, and are obtained with the best statistics since all the events acquired for a given process are used for each orientation. / Or. &e. 4>e) = FM (0e) + F J O W /VCcos^) + F2l(0e) P2X (coS/ir) cos (&) + F12 (8J P22 (cos/) cos (2(/>J (5) The MFPADs characterizing DPI of D2 discussed here are derived from a single experiment performed with circularly polarized light. 4.2. MFPADs at hv= 28.5 eV The process S2 at this photon energy corresponds to AI of the Qi'X+u(l) Rydberg state according to eq.(l). The values of the pD+ « 1.8 ± 0.1, attesting of the parallel character of the X—»£ excitation process, and pe = 0.6 ± 0.1 asymmetry parameters are identical to those found for DPI of H2 at the same energy. The MFPAD for the molecule oriented parallel to the polarization axis of linearly polarized light (not shown) shows a dominant per,, orbital shape. The I{0a) = Foo(0e) + F2O(0J MFPAD is deduced from the Fm and F20 functions, which are the only meaningful functions in this case. The result of the partial wave analysis of I(0a) using a Legendre polynomial expansion h(0e) = A0 (1 + S/ 2/max A; P/(cos0e)) shows a /= 2 major contribution. The AX value amounts to 15%, characterizing a molecular frame forward-backward

220

(MF-FW-BW) electron emission anisotropy, which favors electron emission in the direction of the D+ ionic fragment, comparable to that found for the same process in DPI of H2. This anisotropy indicates a u-g symmetry breaking, which can only occur if ionisation takes place at intermediate internuclear distance. 4.3. MFPADs at hv= 32.5 eV The five FLN functions characterizing the D2 DPI S4 process are displayed in Fig.2 (a). The measured F\\ function reveals the existence of a molecular frame circular dichroism (CD) of the order of 0.15 at maximum; this value, although smaller than those previously found for homonuclear [19] and heteronuclear [10,20] molecules in valence shell and inner shell PI reactions, is remarkable since for PI of a lsa orbital one does not expect CD [21]; the origin of the measured Fn function may then be looked for in the electronic correlation resulting in the doubly excited state. The other measured FLN functions are used to build up the selected MFPADs for the D2 DPI S4 process, displayed in Fig.2 (b-d). The MFPAD for a molecule oriented perpendicular to the polarization axis P (S'4) displayed in Fig.2(b), very similar for both isotopes and close to a dng orbital, strongly supports the assignment of the S'4 perpendicular transition component of peak S4 to AI of the Ch'n^l) Rydberg state according to eq. (2). For this process we plot in Fig.2 (e-f) the cut of the 1(90°, da #,) MFPAD in the plane (#>=0° and 180°), and the I(K& 3p, 3d —> ep). SCK processes are very fast due to the large overlap of the contributing wave functions. This results in particular in the large linewidth of the 3p absorption spectra (see e.g. [2]). However, for the high spin states this SCK process is spin forbidden and is possible only by small admixtures of low spin states. In table 2 the theoretical average linewidth of the high-spin states calculated in a SCA and for a calculation including final ionic state configura-

228

Table 1. Possible spins of the 3p and 3d electrons in cobalt. The 4s 2 spins are not shown in the table, because they will always couple to S — 0. There is only one type of high spin configuration but two different types of low spin configurations, where either one 3d or 3p spin is changed.

high spin low spin low spin'

-i

I

|

70

I

Spin 3p f 1 T

State 3p 5 3d 7 4s 2 5 £ 3p 5 3d 7 4s 2 3 L 3p 5 3d 7 4s 2 3 L /

I

i

I

|

I

75

i

i

i

r~
3p decay. Thus, an Auger decay is only possible by small admixtures of low spin character

229 Table 2. Typical average values for the calculated linewidth for the high and low spin states of the 3p hole states of the 3d electrons in a SCA and a CI calculation. All linewidths are given in units ofeV. SCA CI SCA CI

high low

Sc 3•10"a 4•10-2 0.2 0.9

Ti 1•10"3 0.2 0.3 3

V 4-10"3 0.2 1 7

Cr 2•IO"" 3•10"5 5 10

Mn 3•10-a 6•10~2 3 11

Fe 7•10"3 0.1 5 10

Co 5-10"2 0.1 5 10

Ni 0.2 0.2 3 6

to the high spin wavefunctions due to the spin-orbit interaction. The high spin linewidth is increasing for Co and Ni. Here the SCK channel opens also for the high spin states, due to the subsequent filling of the 3d subshell. For the low spin states also an increase of the linewidth is observed from Sc to Cr. The low spin linewidth in the case of the later 3d metals is almost constant. The linewidths of both the low- and high-spin states increase, when FISCI is included in the calculations, which has already been mentioned by Borne et al. for Cr [7]. The linewidth increases up to two orders of magnitude for the high spin states, because already a small admixture of low-spin state character opens the SCK decay channel. The effect is smaller for the low spin states. However, also here the increase is in the order of a factor of 2 for the elements from Cr to Ni and up to 10 for Ti and V. The strong broadening of the low-spin states as compared to the highspin states has been shown to dominate the 3p photoemission spectra of almost all 3d transition metals. Only for Cu and Sc the situation is slightly different. For Cu the 3d subshell is filled, therefore the SCK decay is possible for all states resulting in only two broad photolines. For Sc only a CosterKronig decay is possible, because Sc has only one 3d electron. The broadening of the low-spin states has already been studied theoretically in the condensed phase for several 3d transition metal compounds by Kotani and coworkers [11-13]. However, in these calculations the decay of the high spin states has not been taken into account, because in solids the lifetime of these states is strongly influenced by the interaction of one atom with the surrounding ligands. This can be understood as a generalized CI with the ligands resulting in a larger linewidth as compared to the free atoms. In figure 4 for manganese the atomic data is compared to the data of some compounds and Mn metal. The atomic data is very similar to the compound data, due to the localized 3d electrons, which is also observed in the 2p photoemission spectra of several 3d metal compounds [14-17].

230

i iIiiii| iiii| iiii| iiii| iiii 20

15

10

5

0

-5

I i i | i i i i | i i i i | i i i i | TTi i | i ~n T* 20

15

10

5

0

-5

Relative binding energy (eV) Figure 4. 3p photoemission of free Mn a t o m s , c o m p o u n d s a n d m e t a l in comparison. T h e c o m p o u n d s show a similar fine s t r u c t u r e due t o t h e localized 3d electrons. T h e c o m p o u n d d a t a is t a k e n from reference [11]. T h e M n m e t a l d a t a [7] is interpreted in t e r m s of a single electron model, where only t h e 3p spin orbit splitting plays a role.

However, for metals a different interpretation is usually used. The 3p-3d exchange interaction is assumed to be much smaller than the 3p spin-orbit interaction, because the 3p hole can be screened efficiently in the metal. Nevertheless, recent results on the electronic structure of a 3p hole state obtained by x-ray emission spectroscopy (XES) are interpreted in terms of low spin and high spin states as in the free atom [18]. To study the transition of the exchange splitting and the possible influence of screening free, small, mass selected 3d transition metal cluster will be the ideal system. Nevertheless, photoemission experiments on these systems have not been feasibly, due to the low photon flux even from modern third generation synchrotron radiation sources. Such experiments will be possible for the first time at the VUV-free electron laser (FEL) at Hasylab/DESY [19]. 4. Conclusions The presented experimental 3p photoelectron spectra are found to agree in general quite well with the theoretical spectra calculated in a single configuration approximation. This allows a consistent interpretation of the electronic structure of the 3p core hole state. The huge 3p-3d exchange interaction in the order of 20 eV split the electronic structure into low-spin and high-spin states. Whereas for the low spin states a linewidth in the range from 2-10 eV due to the SCK decay of the 3p hole is found, the high spin states have a much smaller linewidth typically below 0.2 eV. The origin of this large difference is the spin dependent decay of the 3p hole, because

231 for the high spin states the SCK decay is forbidden. In particular the lifetime of the core hole states is strongly influenced by correlation effects, because already small admixtures can open further decay channels. Acknowledgments I would like to thank the groups of P. Zimmermann from the TU Berlin and B. Sonntag from the University of Hamburg. In particular I have to thank K. Tiedtke, K. Godehusen, T. Richter and Ph. Wernet for numerous beamtimes. Finally the excellent support of the BESSY staff should be acknowledged. References 1. S. Whitfield, R. Wehlitz, and M. Martins, Rad. Phys. Chem. 70, 3 (2004). 2. B. Sonntag and P. Zimmermann, Rep. Prog. Phys. pp. 911-987 (1992). 3. S. Whitfield, M. Krause, P. van der Meulen, and C. Caldwell, Phys. Rev. A 50, 1269 (1994). 4. K. Ross and B. Sonntag, Rev. Sci. Instr. 66, 4409 (1995). 5. R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, Los Angeles, London, 1981). 6. M. Martins, K. Godehusen, T. Richter, and P. Zimmermann, in X-ray and inner-shell processes (AIP Press, New York, 2003), vol. 652 of AIP Conf. Proc, pp. 153-158. 7. A. von dem Borne, R. L. Johnson, B. Sonntag, M. Talkenberg, A. Verweyen, P. Wernet, J. Schulz, K. Tiedtke, C. Gerth, B. Obst, et al, Phys. Rev. A 62, 052703 (2000). 8. K. Tiedtke, C. Gerth, M. Martins, and P. Zimmermann, Phys. Rev. A 64, 022705 (2001). 9. K. Tiedtke, C. Gerth, B. Kannegiefier, B. Obst, P. Zimmermann, M. Martins, and A. Tutay, Phys. Rev. A 63, 3008 (1999). 10. K. Tiedtke, C. Gerth, M. Martins, B. Obst, and P. Zimmermann, J. Phys. B 33, L755 (2000). 11. M. Taguchi, T. Uozume, and A. Kotani, J. Phys. Soc. Jpn. 66, 247 (1997). 12. Y. Tezuka, S. Shin, Takayuki, and A. Kotani, J. Phys. Soc. Jpn. 66, 3153 (1997). 13. K. Okada and A. Kotani, J. Phys. Soc. Jpn. 61, 4619 (1992).

232

14. T. Richter, K. Godehusen, M. Martins, T. Wolff, and P. Zimmermann, Phys. Rev. Lett. 93, 023002 (2004). 15. K. Godehusen, T. Richter, P. Zimmermann, and M. Martins, Phys. Rev. Lett. 88, 217601 (2002). 16. P. Wernet, B. Sonntag, M. Martins, P. Glatzel, B. Obst, and P. Zimmermann, Phys. Rev. A 63, R050702 (2001). 17. P. Wernet, J. Schulz, B. Sonntag, K. Godehusen, P. Zimmermann, M. Martins, C.Bethke, and F. Hillebrecht, Phys. Rev. B 62, 14331 (2000). 18. J. Rueff, M. Krisch, Y. Cai, A. Kaprolat, M. Hanfiand, M. . Lorenzen, C. Masciovecchio, R. Verbeni, and F. Sette, Phys. Rev. B 60, 14510 (1999). 19. V. Ayvazyan, N. Baboi, I. Bohnet, R. Brinkmann, M. Castellano, P. Castro, L. Catani, S. Choroba, A. Cianchi, M. Dohlus, et al, Phys. Rev. Lett. 88, 104802 (2002).

COLLISIONS INVOLVING ELECTRONS

SPIN-RESOLVED COLLISIONS OF ELECTRONS WITH ATOMS AND MOLECULES G. FRIEDRICH HANNE Physikalisches Institut, Universitat MUnster, Wilhelm-Klemm-Str. 10, 48149 Miinster, Germany, E-mail: [email protected]

Abstract. Sophisticated experimental methods to study electron collisions with atoms and molecules include spin-resolved measurements of cross sections, (e,2e) coincidences or optical methods (integrated Stokes parameters, electron-photon coincidences). Sources of polarized electrons with a polarization of P > 0.5 and currents of up to several uA have been developed with which such investigations can be performed successfully. Spin effects in elastic and inelastic collisions of electrons with atomic targets can be explored on the most fundamental level in such experiments. In this talk some recent work on spin-resolved electron scattering from complex atoms and molecules is reviewed with the main emphasis on recent results for spin exchange effects for simple target molecules such as H2, Nj and 0 2 , results for spin up-down asymmetries with Cs and Rb targets and results for electron-photon coincidences from Hg atoms.

Introduction The organizers have asked me to cover the subject of my talk in an educational way for an audience of which the larger part will not be fully familiar with the latest developments in our field. Therefore I will start with some general remarks. Why should we perform electron scattering experiments? Measured absolute cross sections should be provided for practical purposes such as modeling gas discharges and for a direct comparison with theoretical data. A detailed understanding of various phenomena on the most fundamental level is provided by measuring and calculating spin asymmetries and correlation parameters which enables one to determine magnitudes and relative phases of the scattering amplitudes. However, there was some doubt, that such detailed investigations are useful. In 1983 the late Callaway and McDowell [1] grumbled: «One purpose of this Comment is to remind our colleagues, both theorists and experimentalists, that while it is of great interest to measure or calculate such esoteric parameters as spin-flip ratios, differential cross sections and orientation and alignment parameters, we are still unable to give a satisfactory answer to the simple question "What is the absolute value of the cross section for ... at a specified energy?" We find that the uncertainties are of the order of 20% at some energies for the simplest cases, of at least a factor of two in other apparently simple cases, while in many cases there is no reliable information at all.» That this criticism was too fundamental has been demonstrated e. g. by Bray and Stelbovic [2,3], who showed how close-coupling approaches have to be

235

236

implemented to converge. They found out that such criticized esoteric parameters could be described adequately only if target continuum states are included in the expansion to get a proper description of charge-cloud polarization effects! With these "convergent close-coupling" (CCC) approaches the various cross sections for simple one-electron targets are accurately described. The nature of spin effects In the following I will discuss the nature of the basic spin effects that influence collisions of electrons with atoms and molecules. We can distinguish the following mechanisms. Direct observation of exchange In a conventional scattering experiment, in which unpolarized electrons are scattered by unpolarized atoms, it is impossible to decide whether the scattered electron came from the incident electron beam (direct scattering) or was initially part of the target (exchange scattering), because the electrons cannot be distinguished in such an experiment. The situation is different, however, if polarized electrons are scattered from targets with an open shell before or after scattering. As an example, Fig. 1 gives a simple picture of the process in which the spin of an unbound electron is changed by exchange with a target electron of opposite spin direction (no spin-orbit interaction!). The polarization P' of the scattered electrons is then different from the initial polarization P. Although the target quantum number My must change in that process, the multiplicity 25 + 1 is retained and thus the example shown in Fig. 1 is applicable to elastic collisions of electrons from a target with 5 = 1 (triplet state) such as 02(X 3 £/).

ms = -l/2

+

S=l,Ms = +l

=>

S'=l,Af s =0

+

m s =l/2

Fig. 1: Simple picture of a spin exchange process for electron scattering from spin-1 targets

A recent experimental example for such a measurement is shown in Fig. 2 [4]. Older results have been confirmed and it can be seen that theory is in fair but not perfect agreement with the experimental results. Another example of a direct observation of exchange are measurements where polarized electrons (polarization Pe, t or i) are scattered from polarized atoms (PA, ft or U) and the spin antiparallel-parallel asymmetry CT(TU) + g(llt) - (T(tfl) - (T(IU) = A ex a(TU) +CT(w)+ o(tiO + a(w)

p e

p A

(1)

237

is measured. A nonzero Aex is also a direct observation of exchange. Such experiments were performed, e. g. for elastic scattering with polarized Na [5] and Cs [6] atoms and for (e,2e) experiments with polarized Li atoms [7]. 1.0

0.9

-rfM] 1 ++

0.8

0.7 20

• Hegemann 1993 a Hollkotter 2005 Woesteetat 1996

.

.

T .

40 60 80 100 Scattering angle (deg)

120

Fig. 2: Results for E = 10 eV [4] of the spin exchange parameter P'lP for elastic collisions between polarized electrons and 0 2 molecules.

Continuum spin-orbit interaction A simple picture of this phenomenon is shown in Fig. 3 (left). The magnetic moment \is of the electron moving with velocity v in the electric field E of the nucleus experiences a magnetic interaction -(\is-B() that depends on its relative orientation to the magnetic field vector B( ~ (v x E)lc2 perpendicular to the scattering plane. This results e.g. in an up-down (or left-right) scattering asymmetry of electrons that are initially polarized perpendicular to the scattering plane. As the spin-orbit interaction is small, significant asymmetries are, in general, observed only where the differential cross section has a deep minimum. Interference between exchange and spin-orbit effects For complex atoms and molecules exchange and spin-orbit effects may act simultaneously. A particularly interesting effect is observed if the orbital angular momentum L > 0 of a target with unsaturated spin 5 > 0 is involved in the collision in the initial and/or the final state. The scattering cross section may be different for left- and right-oriented target orbitals, i. e. there is, in general, a preferred orientation (L) of the orbital angular momentum vector of the target electrons perpendicular to the scattering plane during the collision. If we select a certain fine-structure level with quantum number J, the spin of the target is coupled to that preferential orbital orientation, and thus the spin (5) of the target is also oriented as indicated in Fig. 3 for a state with £,= 1,5=1/2 and J = 1/2.

Fig. 3: Simple picture of spin-orbit effects. Left: Continuum spin-orbit interaction. Right: Simple picture of target orientation effect for L = 1, S = 1/2 and 7=1/2

238

Excitation by direct and exchange scattering is possible, if we perform the scattering with continuum electrons of that preferred spin direction whilst for excitation with electrons of opposite spin direction exchange is suppressed, and, therefore, the cross section is different. With other words, there is a spin updown asymmetry or a left-right asymmetry if that mechanism is involved. The two mechanisms illustrated in Fig. 3 have quite different origins: The continuum spin-orbit interaction probes the target field near the nucleus whereas the orientation effect is dominated by the interaction of the continuum electron with the valence electron(s) of the target. Nevertheless they give rise to similar phenomena. If they can act simultaneously in heavy targets, they will interfere and it is, in general, not possible to distinguish these two mechanisms. For inelastic collisions one can, however, compare different scattering channels. For example, the spin up-down asymmetry for the excitation from a s state to a pia state should be of opposite sign and twice as large as that for excitation of the pm orbital if only the target orientation effect (Fig. 3, right) is important: SA (1/2) = -2-^(3/2).

(2)

A (theoretical) example shown in Fig. 4 may illustrate this effect [8]. In (e,2e) collisions in Xe or Ar (ionization of 5p or 2p electrons) it was found that the target coupling effect leading to Eq. (1) is the dominating spin effect [9-11] 0.3 0.2

-

0.1

y f

0 -0.1 -0.2

\

*****

.'x / V 0

30

10

90 8 Idtgl

120

ISO

180

Fig. 4: Spin polarization after electron-impact excitation of the 2p orbital of H-atoms with unpolarized electrons at E = 50 eV [8]. In that paper it was stated: »These calculations were carried out in 1971. At that time the significance of the non-zero polarizations were not appreciated, and a programming error was suspected. No such programming error could be found, and the results were put aside with puzzlement. Understanding of the result came only after the appearance of the work ... at Munster.« This is a nice illustration of Fano's remark about spin-orbit coupling [12]: »A weak force with conspicuous effects«

Electron dichroism The transmission of longitudinally polarized electrons through a target of chiral molecules may depend on the helicity of the electrons by a spin-dependent interaction in conjunction with the chiral structure of the molecule. This effect is called electron dichroism. From the transmitted beam intensities l(P) and I(-P) for electron polarization P parallel and antiparallel to the beam axis we can determine a transmission asymmetry

239

A = i(p)-n-p)

(3)

As I will not further review these type of experiments (for a progress see [13]) I will mention that there are tiny but measurable effects, if the chiral molecule contains at least one atom as complex as Br [14-16]. An example is shown in Fig. 5. S-bromo camphor R-bromo camphor

-2 1 2

3

4 5 6 Energy (eV)

7

8

Fig. 5: Results for electron dichroism in bromo camphor [16]

Review of selected experiments Spin asymmetries in electron-atom scattering Various spin effects can be explored by experiments with polarized electrons (polarization Pe, t or i) that are scattered from polarized atoms (P&, ft or U). Three independent asymmetries can be calculated from the four different cross sections, a(tft), a (VI), a(tJJ) and a(M), which are obtained for the different relative orientations of the spins perpendicular to the scattering plane. In addition to the exchange asymmetry (1) we get: a(n) + o(n)- v = 0) transition in N2. The observed transition is that of the 337 nm laser transition of the N2 laser. To our surprise we find almost zero circular polarization of this line [23]. This behavior is not understood. Interestingly such a circular polarization has been observed in singlet-triplet excitations [24] and for dissociative excitation of H2 molecules [24,25] where the fluorescence from the H2 molecule and from the Balmer-a line is even averaged over different excitation channels. Green et al [24], whose results are also shown in Fig. 9 (right), anticipated that it is the coupling between rotation and the strongly coupled total electronic angular momentum (Hund's case a) that smears out the initial spin orientation transferred to the N2 molecule. However angular momentum is conserved and thus an orientation cannot completely vanish. The reason for the different behavior of H2 and N2 targets is still to be discussed.

242

12 13 14 15 16

24 25 26 27 28

Energy (eV)

Energy (eV)

Fig. 9: Results for the integrated Stokes parameter in He and N2 [23] and H2 [24]

Electron-photon coincidences with Hg atoms If we detect scattered electrons and emitted photons in coincidence, we select those excited atoms that have scattered the electrons into a particular direction. With this method measurements of the Stokes parameters (Fig. 8) of the VUV Hg transition 6s6p lPi -> 6s2 lS0 (185 nm) have been carried out [26], The 6s6p states in Hg must be described in the intermediate coupling scheme: ^(6'P,) = aV^Pi) 3

3

+ PVFU(63P1) 1

¥(6 P,) = a ^ ( 6 P . ) - P¥ U (6 P 1 )

a«0.985

(5)

Theoretical models generally predict an almost "coherent" population of the 6s6p lPi state for an impact energy of 15eV at scattering angles 9 < 30°, due to the dominant singlet character of the wave function and negligible spin effects. This leads to a degree of polarization />,„, = 1 for that transition in contrast to findings of Murray et al [27] who observed P^ » 0.6 and less for this transition using a laser-assisted stepwise technique. Accounting for depolarization of the emitted radiation due to hyperfine coupling we should obtain 0.84 < />,„,< 0.95., Our recent results for 15 eV [26], shown in Fig. 10 confirm the theoretical prediction [28]. No significant loss of coherence is observed and spin effects are obviously absent for excitation of the 6 lP\ state at 9 < 40° . These results show that even at 15 eV impact energy, the influence of the triplet part of me wave function is almost negligible for the excitation at small scattering angles. That strong spin effects in other systems may be observed even at small scattering angles is also illustrated in Fig. 10 for excitation for the Hg 6s6p 3/>i state where the spin resolved circular polarization P3 is studied [29]. Conclusions The use of polarized electrons allows one to probe collisions of electrons with atoms and molecules in great detail, particularly in conjunction with coincidence techniques. These methods can help to study separately reaction channels over which the average is usually performed, to study the influence of the weak spin-

243

orbit interaction, and to disentangle it from exchange and the Coulomb interaction by which it is usually masked. A detailed understanding of these processes is achieved by a close cooperation between experimentalists and theorists which is documented by an increasing number of common papers in recent years.

0.2

°' 0

0.2 • spin up spin down unpolarized 30

60

90 120

°'°0

30

60

\ /, ' / y 90 120

" ' 0

30

60

90

120

Scattering angle (deg)

Fig. 10: Total light polarization P tot and circular polarization Pi for electron-impact excitation of 6p orbitals in Hg. Left and middle: excitation of 6s6p '?! at 15 eV [26, 28]. Right: excitation of 6s6p 'fi state at 8 eV [29].

Acknowledgements. The author would like to thank his co-workers in Munster and his colleagues at various places for their fruitful cooperation, and he is indebted to the Deutsche Forschungsgemeinschaft for support of his scientific work presented here. References [1] J. Callaway and M.R.C. McDowell, Comm. At. Mol. Phys. XIII (1983) 19 [2] I. Bray and A.T. Stelbovics, Phys. Rev. A 46, (1992) 6995 [3] I. Bray , Phys. Rev. A 49 (1994) Rl [4] I. Holtkotter and G.F. Hanne, XTV ICPEAC, Rosario, Argentina, Book of Abstracts (2005) Tu050 [5] S.R. Lorentz, R.E. Scholten, J.J. McClelland, M.H. Kelley and R.J. Celotta, Phys. Rev. A 47 (1993) 3000 [6] G. Baum, N. Pavlovic, B. Roth, K. Bartschat, Y. Fang and I Bray, Phys. Rev. A 66 (2002) 022705 [7] M. Streun, G. Baum, W. Blask, J. Rasch, I. Bray, D. V. Fursa, S. Jones, D.H. Madison, H.R.J. Walters and C.T. Whelan, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 4401 [8] W.N. Shelton, J. Phys. B: At. Mol. Phys. 19 (1986) L257 [9] A. Dorn, A. Elliott, X. Guo, J. Hum, J. Lower, S. Mazevet. I.E. McCarthy, Y. Shen and E. Weigold, J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 4097

244

[10] C. Mette, T. Simon, C. Herring, G.F. Hanne, and D.H. Madison, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 4689-4700 [11] M. Kampp, S. Kawano, P.J.P. Roche, J. Rasch, D.H. Madison, H.R.J. Walters, and C.T. Whelan, EPJ D 29 (2004) 17 [12] U. Fano, Comments At. Mol. Phys. II (1970) 30 [13] A.H Zimnol, T. Meyer, V. Hamelbeck and G.F. Hanne, XIV ICPEAC, Rosario, Argentina, Book of Abstracts (2005) Tu049 [14] S. Mayer and J. Kessler, Phys. Rev. Lett. 74 (1995) 4803 [15] K.W. Trantham, M. E. Johnston and T. Gay, J. Phys. B: At. Mol. Opt. Phys. 28 (1995) L543 [16] C. Nolting, S. Mayer and J. Kessler, J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 5491 [17] G. Baum, S. Forster, N. Pavlovic, B. Roth, K. Bartschat and I. Bray, Phys. Rev. A 70 (2004) 012707 [18] W.E. Guinea, G.F. Hanne, M.R. Went, M.L. Daniell, M. A. Stevenson, K. Bartschat, D. Payne, W.R. MacGillivray and B. Lohmann' J. Phys. B: At. Mol. Opt. Phys. 38 (2005) submitted. [19] D. Payne, B. Krueger and K. Bartschat, J. Phys. B: At. Mol. Opt. Phys. 38 (2005) submitted. [20] M. Uhrig, A. Beck, J. Goeke, F. Eschen, M. Sohn, G.F. Hanne, K. Jost and J. Kessler, Rev. Sci. Instr. 60 (1989) 872-878 [21] T.J. Gay, J.E. Furst, K.W. Trantham, and W.M.K.P. Wijayaratna, Phys. Rev. A 53 (1996) [22] D.H. Yu, P. A. Hayes, J.E. Furst, and J.F. Williams, Rev. Lett. 78 (1997) 073201 [23] C. Herring, G. Aussendorf and G. F. Hanne (2001) unpublished results [24] A.S. Green, G.A. Gallup, M. A. Rosenberg and T. Gay, Phys. Rev. Lett. 92 (2004)093201 [25] J F. Williams and D. H. Yu, Phys. Rev. Lett. 93 (2004) 073201 [26] F. Jiittemann, G. AuBendorf, A. Tepe and G.F. Hanne, XTV ICPEAC, Rosario, Argentina, Book of Abstracts (2005) We044 [27] A. J. Murray, R. Pascual, W.R. MacGillivray and M.C. Standage, J. Phys. B: At. Mol. Opt. Phys. 25 (1992) 1915 [28] K. Bartschat and R. Srivastava, private communication (2004) [29] C. Herting, G.F. Hanne, K Bartschat. A.N. Grum-Grzhimailo, K Muktavat, R. Srivastava and A.D. Stauffer, J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 4439

CALCULATION OF IONIZATION A N D EXCITATION PROCESSES U S I N G T H E C O N V E R G E N T CLOSE-COUPLING M E T H O D

DMITRY V FURS A, IGOR BRAY AND ANDRIS T STELBOVICS Centre for Atomic, Molecular and Surface Physics, Division of Science and Engineering, Murdoch University, Perth 6150, Australia

A brief review of recent CCC results for electron scattering from zinc and ytterbium atoms is presented. In the study of ionization processes we demonstrate that the close-coupling approach is capable to obtain very accurate results for the most difficult e-He equal energy sharing kinematics. Similarly good agreement was found for e-Ca ionization except for energies close to ionization threshold.

1. Introduction Convergent close-coupling (CCC) method was first introduced for study of electron scattering from light atoms, hydrogen 1 and helium 2 . Here the CCC method together with growing number of other advanced computational technique, such as R-matrix with pseudo-states method 3 , time dependent techniques 4,5 , the exterior complex scaling method 6 ' 7 have achieved remarkable agreement between themselves and experiment. The next challenge is to apply these theoretical methods to heavy atoms where an adequate description of electron-electron correlations in the target wave functions is more difficult and relativistic effects become apparent. In this Report we present some recent results of the CCC method applied to the heavy atoms zinc and ytterbium. These atoms are also attracting interest from applications, for example zinc is considered as a replacement for mercury in high-pressure discharge lamps 8 and ytterbium is actively used in Bose-Einstein condensation studies 9 . We also present our recent results for electron-impact ionization processes involving helium and calcium atoms and present results for the most challenging equal energy sharing kinematics.

245

246

1.1. CCC theory The details of the CCC method for scattering from quasi two-electron atoms have been given by Fursa and Bray 2 and for CCC approach to ionization by Bray and Fursa 10 . Here we give a brief overview specific to electron-impact excitation of zinc and ytterbium atoms and electron-calcium ionization. For all atoms considered in this Report we use a model of two active electrons above an inert Hartree-Fock core. The set of single-electron orbitals is obtained by diagonalization of the corresponding one-electron ion Hamiltonian (Zn + for example) in a Sturmian type (Larguerre) basis. These orbitals are used further to perform configuration-interaction calculations for two active electrons and obtain a set of target wave functions. In order to model the effect of inert shells more accurately we use one- and two-electron polarization potentials. An important parameter of such potentials is static dipole polarazability of the corresponding ion core (Zn + + ) which has values of 3.26, 2.6, and 28.0 a.u. for calcium, zinc, and ytterbium respectively. The obtained set of square integrable target states {0 n }, n = 1,...,N are used to expand the total electron-atom wave function:

|*i+)> - A\4+)) * A £ |<M(n|W+)>-

(1)

n=l

The set of close-coupling equations for the T-matrix is then set up and solved in momentum space

(k^lTlfck,) = <M,V | %k,> + S / ^ ^ i ' ^ ^ ] ^ n—1

(2) Scattering amplitudes for elastic scattering and excitation of bound states are defined simply as: / / i ( k / ) = (k/0/|T|0iki>l

(3)

while for ionization the amplitude is defined as:

fi(qf,kf) where qf

= (^-^/XM/ITI&k,),

(4)

is a continuum eigenstate of HT.

HT\q{-f))=ef\qif))

(5)

with ef < kj/2. For ef = kj/2 = E/2 we use 2/ i (-0-
20eV (e.g. [10]). 2. Experiment The experimental results were obtained with a high-resolution electron scattering apparatus [8] involving two-stage hemispherical analyzers. The incident beam possesses an energy width (full width at half maximum) of 9meV. The energy loss peaks have a width of 14meV, permitting the resolution of all four Ne(2p53s) levels. Measurements were taken at three positions of the analyzer (45°, 90°, 135°) relative to the incident beam direction. Around these three (geometrical) angles, the scattering angle was varied in smaller steps by using a magnetic angle changer [11] of special design [12], thus covering scattering angles from 0° to 180°. The analyzer response function was determined over the energy range of interest (0 - 3 eV above threshold) through studies of elastic electron-helium scattering, for which the absolute angle-differential cross sections are accurately known over the range 0 — 19 eV [13]. Absolute cross sections for neon were measured by comparison to the known cross sections for helium by using the relative flow method [14]. The uncertainties of the absolute inelastic cross sections are about ±20% for energies more than 0.2 eV above each threshold. At lower energies, the response function becomes increasingly uncertain and the error bars increase gradually, reaching ±50% very near threshold. 3. Theory The numerical calculations performed for the present work are based upon the semi-relativistic B-spline il-matrix (BSRM) approach described in [2,3]. Details of this particular method and references to earlier work can be found in these papers, as well as in the progress report by Zatsarinny and Bartschat contained in this volume [15]. 4. Results and discussion Figure 1 displays the experimental cross sections for Ne(2p53s) excitation, obtained at the scattering angle 45°, in comparison with the B-spline /{-matrix results. The threshold peaks observed in all four inelastic channels are followed by an overall increase of the cross sections, on which sharp resonances are superimposed, similar to those observed in previous measurements of the total yield for production of metastable Ne(2p53s)3P2,o

263

atoms [5,6,7]. In the excitation functions for the three 3P2,i,o states, a prominent Wigner downward cusp is observed at the threshold (18.383 eV) for excitation of the lowest Ne(2p53p) level with 3Si symmetry (solid bar in Fig. 1). This cusp is not visible in the Ne(2p53s)1Pi excitation function. The resonance structure associated with the Ne(2p53p) levels (18.3 - 19 eV) is similar in the cross sections for the three triplet levels (2p53s)3P2,i,o, but rather different in that for the singlet level (2p 5 3s) 1 Pi. In particular, the sharp Feshbach resonance, attached to the highest level of the Ne(2p53p) configuration with xSo symmetry (dashed bar in Fig. 1) is clearly present in the 3P2,i,o cross sections but not visible (within the error bars) in that for the 1 Pi level. The theoretical cross sections are in very good overall agreement with the experimental results — in shape, propensity trends, and absolute size. Some deviations are observed very close to threshold, but these may partly be due to increased uncertainties in the experimental data. .

40302010-

1111111II11II11111111111 ip 9=45"

Experiment 3

'S„

[

"E 3

2

3p SS,

p

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1

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:

p,

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S5 o 10

; if—,-^VJ"-

0"l I l" |"ll""M"|"i'|"|"|"i"|"7|"lll"Tl"|"|"|"li"|"i 19.0 19.5 16.5 17.0 17.0 17.5 17.5 18.0 18.0 18.5 18.5 19.0 INCIDENT ELECTRON ENERGY [eV]

Figure 1.

16.5 17.0 17.5 18.0 18.5 19.0 19.5 INCIDENT ELECTRON ENERGY [eVJ

Absolute cross sections for Ne(2p53s) excitation at # = 45°.

At the scattering angle of 135° (not shown), threshold peaks were again observed in all four inelastic channels, but now followed by a nearly constant cross section and a weaker downward cusp for excitation of the (2p53s)3P2,i,o states, prominent peaks for the triplet of resonances between 18.5 — 18.7 eV, and only weak resonance structure near 18.96 eV. The cross section for (2p53s)1Pi excitation, on the other hand, decreases after the

264 threshold peak, shows an upward Wigner cusp at the (2p 5 3p) 3 Pi threshold, a window resonance structure in the range 18.5 — 18.7 eV, and a peak for the Feshbach resonance near 18.96 eV. All these features are again fully reproduced theoretically. When the measured and theoretical cross sections are superimposed, astounding agreement is indeed observed, except in the size of the threshold peak for excitation of the (2p 5 3s) 1 Pi state. Excitation functions were also measured at scattering angles of 90° and 180°. Again, very good agreement was observed between the measured and calculated excitation cross sections, both with regard to shape and absolute size. In addition, the angular distributions for all four Ne(2p 5 3s) excitation channels were measured from 0° to 180° on a narrow angular grid at an incident energy of 18 eV, showing semi-quantitative agreement with theory. All these results will be presented in detail elsewhere. Note that the experimental and theoretical cross sections were obtained without prior knowledge of the respective other results. We conclude that the B-spline iJ-matrix method is a powerful tool to predict integral and angle-differential electron-impact excitation cross sections of light atoms near threshold — a particularly interesting range for many applications. This work has been supported by the European Science Foundation (EIPAM Network), by the Swiss National Science Foundation, by the Deutsche Forschungsgemeinschaft, and by the US National Science Foundation. KF and HH thank T. H. Hoffmann for helpful cooperation. References

[1 L. G. Christophorou, J. K. Olthoff, Adv. At. Mol. Opt. Phys. 44 (2000) 59 [2 O. Zatsarinny, K. Bartschat, J. Phys. B 37 (2004) 2173 [3 O. Zatsarinny, K. Bartschat, J. Phys. B 37 (2004) 4693

K

O. Zatsarinny, K. Bartschat, Phys. Rev. A 71 (2005) 022716

[S. S. J. Buckman, C. W. Clark, Rev. Mod. Phys. 66 (1994) 539

[6 S. J. Buckman, P. Hammond, G. C. King, F. H. Read, J. Phys. B 16 (1983) 4219

[7] J. Bommels, K. Franz, T. H. Hoffmann, A. Gopalan, O. Zatsarinny, K. Bartschat, M.-W. Ruf, H. Hotop, Phys. Rev. A 71 (2005) 012704

[8] M. Allan, J. Phys. B 25 (1992) 1559 [9] J. M. Phillips, J. Phys. B 15 (1982) 4259 [io: M. A. Khakoo et al., J. Phys. B 37 (2004) 247 in F. H. Read, J. M. Channing, Rev. Sci. Instrum. 67 (1996) 2372 [12: M. Allan, J. Phys. B 33 (2000) L215 [13 R. K. Nesbet, Phys. Rev. A 20 (1979) 58 [14; J. C. Nickel, C. Mott, I. Kanik, D. C. McCollum, J. Phys. B 21 (1988) 1867 th [15 O. Zatsarinny, K. Bartschat, Progress Report, 24 Int. Conf. on Photonic, Electronic and Atomic Collisions, Rosario, Argentina, July 2005

STUDIES OF QED AND NUCLEAR SIZE EFFECTS WITH HIGHLY CHARGED IONS IN AN EBIT

J. R. C R E S P O L O P E Z - U R R U T I A , J. BRAUN, G. BRENNER, H. BRUHNS, A. J. GONZALEZ MARTINEZ, A. L A P I E R R E , V. MIRONOV, R. SORIA ORTS, H. TAWARA, M. TRINCZEK, AND J. ULLRICH Max-Planck-Institute for Nuclear Physics Saupfercheckweg 1 D-69117 Heidelberg, Germany E-mail: [email protected] A. A R T E M Y E V t , J. H. SCOFIELD*, I. I. T U P I T S Y N t 'St. Petersburg State University, St. Petersburg 198504, Russia ^Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Highly charged ions can be conveniently produced and stored at the Heidelberg electron beam ion trap. Various experiments have been undertaken to exploit the strong scaling of QED effects and nuclear size contributions with the ion charge. Instrumental developments in our group have led to an increased spectroscopic precision. Wavelengths of forbidden transitions in the visible have been measured with sub-ppm accuracy, and their Zeeman splitting has been resolved, thus allowing a direct determination of g-factors, and even the measurement of isotopic recoil effects with relativistic bound electrons. Experiments on the lifetime of metastable levels has yielded results sensitive to hitherto unmeasurable QED contributions of the order of 0.5%, such as that arising from the electron anomalous magnetic moment. In the mid-Z region, measurements of the Lyman-c*i (H-like CI) and l s 2 p 1 P i —»ls2 'So transitions (He-like Ar) have been performed with an accuracy better than 10 ppm. Finally, in the dielectronic resonances of very heavy ions, such as Hg 7 8 + - 7 5 +, where QED contributions are in the order of 160 eV, excitation energies of several tens of keV have been determined within a few eV absolute uncertainties, and quantum interference effects studied with state selectivity, allowing a detailed comparison with different predictions.

1. Precision studies with electron beam ion traps An electron beam ion trap (EBIT) is an ideal device for precision spectroscopy of highly charged ions (HCI), as the experience from several groups has shown in recent years. The EBIT at the Max-Planck-Institute for Nuclear Physics in Heidelberg1 produces and confines HCI by means of a mo-

265

266

noenergetic electron beam compressed by an intense magnetic field. The ions are prepared in well defined charge states, trapped in a small volume under UHV conditions, and their electronic excitation can be tuned, modified and switched on an off easily. Spectroscopic access to the trapped ions enables high resolution measurements and lifetime studies; extracted ions can be used for collision physics studies. Here we present recent results obtained with this device, showing how newer developments have allowed us to become very sensitive to QED contributions and nuclear size effects in a wide range of energies.

2. Observation of isotopic shifts in Zeeman-splitted forbidden transitions in Ar XIV and Ar XV Magnetic dipole (Ml) transitions in highly charged ions (HCI) are of great interest to obtain essential information on astrophysical and tokamak plasmas2. However, various spectroscopic techniques used so far in experimental studies of such plasmas could not provide a direct observation of the Zeeman splitting because of excessive line broadening caused by the thermal motion of the ions. By a judicious choice of the operation parameters, namely low electron current (20-50 mA), low axial trapping voltage (nominally 0-10 V) and strong magnetic field (6.82 T) the ion temperature, and thus the Doppler width of the emitted lines was significantly reduced. This made a direct observation of the Zeeman splitting in B-like (Ar 13+ ) and Be-like (Ar 14+ ) argon ions with an accuracy of better than 0.5 ppm at 441 nm possible. For the 2s22p 2 Pi/ 2 - 2 P3/2 Ar 13+ Ml transition, six Zeeman components were resolved (see Figure 1). Their polarization was also investigated. For Ml transitions, the central components (AM=0) are polarized perpendicularly to the field, hence the AM=0 transitions are cr-components and the AM=±1 are 7r-components, in contrast to the case of the El transitions. Tens of individually calibrated spectra were acquired with a grating spectrometer, achieving excellent statistics. We have remeasured the central wavelength, obtaining A = 441.2558(1) nm, in good agreement with previous measurements3. Through the measured line splitting we determined the gj of the upper (J=3/2) and lower (J=l/2) level of the 2s22p state as well. The results of g3/2 = 1.331(1) and p 1 / 2 = 0.655(3) can be compared with theoretical predictions of 1.331665 and 0.664492, respectively. Isotopic shifts could also be measured with this setup; the results for the wavelength and the isotopic shifts are compared in Table 1 with cal-

267

- l — ' — i — • — i — ' — i — • — r

a- components

%

m'*

100

- components

_

-

t/1

| §200 o

n ii

50

-

"trff 441.0 441.1 441.2 441.3 441.4 441.5

441.0 441.1 441.2 441.3 441.4 441.5

X (nm)

A, (nm)

Figure 1. Single spectrum of the Ml line viewed perpendicularly to the magnetic field. (a) AM=0 , (b) A M = ± l .

Table 1. Wavelengths of the A r 1 3 + , 1 4 + Ml lines and their isotope shifts ( 4 0 Ar/ 3 6 Ar) (in nm).

Ion Ar"4+

Wavelength Theory Experiment 441.16(27) 441.2556(2) 594.24(30) 594.3879(2)

Isotope shifts Theory Experiment 0.00126 0.00125(7) 0.00136 0.0012(1)

culations including second-order Coulomb interaction and Breit-Coulomb interaction, frequency-dependent Breit interaction in lowest order as well as the Lamb shift. A large-scale configuration interaction Dirac-Fock (CIDF) method was used. Here, the largest theoretical uncertainties, which are mainly due to the treatment of electronic correlation and QED corrections, disappear when comparing the two isotopes, revealing the small contribution of the mass shift. In this way, it was possible to observe how the relativistic dynamics of relativistic bound electrons induces isotopic shifts, which up to very recently could not even be predicted properly due to difficult treatment of many-electron relativistic recoil effects.

268

3. High accuracy lifetime measurement of the Ar XIV ls 2 2s 2 2p 2 P £ / 2 metastable level Accurate measurements of atomic transition energies and excited-state lifetimes, besides being important for the diagnostics of tenuous plasmas, are of interest due to their sensitivity to quantum electro-dynamic (QED) effects. Lifetimes reveal non-averaged information on the magnitude of the expansion coefficients in an individual basis of the atomic wavefunction and, hence investigate a widely unexplored facet of current atomic theories. Unfortunately, accurate lifetime measurements still remain an serious experimental challenge due to the difficulty of reaching a high statistical significance allowing to understand, control and model the time evolution of the ion (or atom) population under observation. The Heidelberg EBIT offers the possibility to significantly circumvent these problems thanks to its trapping efficiency, large trap volume and light collection solid angle. The lifetime of the metastable ls22s22p 2Pl/2 l e v e l of boronlike Ar XIV was measured4 by monitoring its temporal decay to its 2 P°/ 2 ground state through the aforementioned Ml transition at 441 nm. The decay was followed for a duration up to 100 times longer than the lifetime to understand and exclude possible systematics effects. Achieving a 0.1% accuracy level, this result of 9.573(4)(5) ms (stat)(syst) is 17 times more precise than a previous one 9.70(15) ms 5 and the most accurate ever performed in multiply charged ions. The experimental accuracy had been, up to now, always insufficient for a verification of the theoretical treatments of relativistic correlation and QED effects in high-precision atomic theories. As seen in Figure 2, the result shows a discrepancy of about 3a with the most recent theoretical predictions corrected by the accurate experimental 2 P°/ 2 - 2 P3/2 transition wavelength and the previously (in almost all cases) neglected contribution of the free electron anomalous magnetic moment (EAMM). 4. High precision x-ray spectroscopy of hydrogenic and helium—like argon ions In order to overcome many of the current difficulties found in the absolute calibration of x-ray spectrometers, a novel method not using any collimation has been implemented in the HD-EBIT flat crystal x-ray spectrometer6,7 making it more suitable for experiments at low x-ray fluxes and eliminating numerous sources of systematic error. The central point of the technique is to measure and monitor the exact position on the crystal where the monoenergetic x-rays are reflected in dependence of the mea-

269

MCDF

MCBP

C-S

ODFS

SS'98

RQDO

MCDF LL-EBIT

Theoretical and experimental method Figure 2. Theoretical lifetimes with and without EAMM corrections compared with experimental results.

sured crystal angle instead of defining it through collimation. Two light beams projected onto the Bragg crystal are used as fiducials for this purpose. Unlike the x-rays, which have to fulfill Bragg's law, light is reflected by the crystal surface under any angle, and a rotation results in a shift of the x-ray reflection position with respect to the fiducials' reflection positions on the crystal. Consequently, the position at which the CCD camera detects the x-rays moves in relation to the light fiducials. The three relative positions yield full information about the reflection position of the x-ray line on the crystal and therefore very accurate Bragg angle measurements. By using this technique, the transition ls2p x Pi —•Is2 1So of He-like argon Ar16+(commonly referred to as w-line) has been measured at the HD-EBIT with respect to the Lyman-ai transition of H-like argon, which is known to a precision of 5ppm 8 . About 50 x-ray exposures at the expected Bragg angles (with small deviations to actively change the reflection position on the crystal) of the Lyman-Q! and w transition have been acquired, all of them preceded and followed by a visible light exposure. For each of these sets of spectra the relative position of the x-ray line to the fiducials was obtained and plotted over the corresponding measured crystal angle. From this plot the difference of Bragg angles of the two lines was extracted. With this angular difference and the literature value of the Lyman-a i transition energy, the result for the w transition energy

270

is 3139.538(21) eV, in good agreement with the best available experimental result of 3139.552(37) eV9. In this way, a precision of 7ppm for the w and z transitions in helium-like argon, and of 9 ppm for the Lyman-ai transition in H-like Cl 16+ was reached using the Ar 17+ Lyman-«i transition as reference. This result is in excellent agreement with the theoretical prediction. The Dirac energy for the Cl 16+ Lyman-ai transition is 2963.310eV. The total Lamb shift of —0.947 eV10 includes a contribution from the vacuum polarisation of 0.068 eV . Since the uncertainties of previous measurements of this transition were 100 meV or larger, the present measurement is the first one sensitive to resolving the vacuum polarisation contribution in Hlike Cl 16+ and achieves a sensitivity to the total Lamb shift on a level of better than 3 %. The precision reached in the Ar 16+ w transition energy measurement corresponds to 1.9% of the one-electron QED contribution to the ground state binding energy, and it even probes the two-electron QED contribution at a level of 22 %. In the case of the z line, the one-electron QED contribution to the excited 3 5i state can also be resolved. Currently, the setup is being modified in order to perform absolute wavelength measurements and completely eliminate the need for reference lines, aiming at a precision approaching 1 ppm or better. Energy (eV) 3145 T

3140 '

1

3135 •

1

3130 '

1

3125 '

1

Wavelength (mA) Figure 3. The Ar 1 6 + w transition at 3140 eV.

3120 •

r

271 700 600 500 400 300

W c

o O

200

1 70 60 50 40 30 45

46

47

48

49

50

51

52

53

54

Electron beam energy (keV) Figure 4. Projection of the Be-like DR resonances on the in the KL1/2L1/2 (left) and KL!/ 2 L3/2 (right) region. Small contributions of Li-like and B-like resonances can be seen at higher electron energies.

5. Quantum interference and fine structure splitting in the photorecombination of (Hg 7 8 + - " T 5 + )ions Heavy HCI allow one to test in detail QED contributions in strong fields, as well as finite nuclear size effects, since these effects scale tremendously with high powers of the ions' nuclear charge Z\ e.g., the calculated QED contributions to the energy of the Is electron in mercury ions are about 160 eV, and nuclear size effects are of the order of 50 eV. In this experiment, while scanning the electron beam energy of the EBIT, the energies of the photons emitted due to photorecombination are recorded event by event and displayed versus the beam energy in two-dimensional plots. Distinct structures in radiative recombination (RR) and dielectronic recombination (DR) processes appear in the plots. Here, the excitation energies of the KLL DR resonances of mercury ions ranging from He-like Hg 78+ to B-like Hg 75+ are determined within a few eV at 50 keV using a temperature-stabilized high precision voltage divider. The fine structure splitting between states with different total angular momentum J are even more accurately extracted by measuring voltage differences. The splitting between the states [(ls2s22p!/2)o2p3/2]3/2 a n d [ls2s 2 (2p 1 / 2 ) 2 ]i/2 of Be-like ions in the initial

272 state was determined and compared with different calculations 1 2 1 1 . Small, yet significant discrepancies were found for the absolute excitation energies of the Li-, Be- and B-like ions, while the He-like results showed excellent agreement with theory. Additionally, by projecting narrow slices of the RR bands containing photon events arising mostly from a single charge state onto the electron beam energy axis (see Figure 4) we are able to study the photorecombiantion process for well-resolved electronic states of that individual charge state. The observed resonance curves were fitted with asymmetric Fano line profiles caused by the interference between DR and RR recombination channels 13 , yielding state-resolved Fano-factors.

References 1. J. R. Crespo Lopez-Urrutia, A. Dorn, R. Moshammer, and J. Ullrich, Phys. Scr. T80, 502 (1999) 2. U. Feldman, J. F. Seely, N. R. Sheeley, S. Suckewer, and A. M. Title, J. Appl. Phys. 56, 2341 (1984) 3. I. N. Draganic, J. R. Crespo Lopez-Urrutia, R. Dubois, S. Fritsche, V. M. Shabaev, R. Soria Orts, I. I. Tupitsyn, Y. Zou, and J. Ullrich, Phys. Rev. Lett. 91, 183001 (2003) 4. A. Lapierre, U. D. Jentschura, J. R. Crespo Lopez-Urrutia, J. Braun, G. Brenner, H. Bruhns, D. Fischer, A. J. Gonzalez Martinez, Z. Harman, W. R. Johnson, C. H. Keitel, V. Mironov, C. J. Osborne, G. Sikler, R. Soria Orts, H. Tawara, I. I. Tupitsyn, J. Ullrich, and A. Volotka, accepted in Phys. Rev. Lett. (2005) 5. E. Trabert, P. Beiersdorfer, S. B. Utter, G. V. Brown, H. Chen, C. L. Harris, P. A. Neill, D. W. Savin, and A. J. Smith, Astrophys. J. 541, 506 (2000) 6. J. Braun, Diploma thesis, 2003, MPI-K Heidelberg 7. J. Braun, H. Bruhns, M. Trinczek, J. R. Crespo Lopez-Urrutia, and J. Ullrich, Rev. Sci. Instrum.76, 073105 (2005) 8. H. F. Beyer, R. D. Deslattes, F. Folkmann, R. B. LaVilla, J. Phys. B: At. Mol. Phys. 18, 207 (1985) 9. R. D. Deslattes, H. F. Beyer, F. Folkmann, J. Phys. B: At. Mol. Phys. 17, L689-L694 (1984) 10. A. N. Artemyev, V. M. Shabaev, V. A. Yerokhin, G. Plunien and G. Soff, Phys. Rev. A 71, 062104 (2005) 11. J. H. Scofield, Phys. Rev. A 40, 3054 (1989) 12. A. Artemyev, V. M. Shabaev, M. M. Sysak, V. A. Yerokhin, T. Beier, G. Plunien and G. Soff, Phys. Rev. A 67, 062506 (2003) 13. A. J. Gonzalez Martinez, J. R. Crespo Lopez-Urrutia, J. Braun, G. Brenner, H. Bruhns, A. Lapierre, V. Mironov, R. Soria Orts, H. Tawara, M. Trinczek, and J. Ullrich, Phys. Rev. Lett. 94, 203201 (2005)

RECOMBINATION OF ASTROPHYSICALLY RELEVANT IONS: BE-LIKE C, N, AND O

M. F O G L E Physics Division Oak Ridge National Laboratory Oak Ridge, Tennessee, USA 37831-6372 E-mail: [email protected] R. SCHUCH Department of Physics AlbaNova University Center Stockholm, Sweden SE106 91 N. R. BADNELL Department of Physics University of Strathclyde Glasgow, UK G4 ONG S. D. LOCH, SH. A. ABDEL-NABY, AND M. S. PINDZOLA Department of Physics Auburn University Auburn, Alabama, USA 36849 P. GLANS Department

of Engineering, Physics, and Mid-Sweden University Sundsvall, Sweden SE851 70

Mathematics

The absolute recombination rate coefficients for Be-like C, N, and O were measured using the CRYRING storage ring. The AUTOSTRUCTURE code was used to account for field ionization effects in the experiment and to estimate the ion beam metastable fraction. The resulting hybrid rate coefficients were convoluted with Maxwellian temperature distributions ranging for 10 2 -10 7 K to produce plasma recombination rate coefficients for initial ground state Be-like ions. The resulting plasma rate coefficients are compared to those prominent in the literature and published in databases. A sizable effect from trielectronic recombination is noted for the case of 0 4 + .

273

274 1. Introduction Aside from H and He, C, N, and O represent almost 75% of the total elemental abundance of the universe. Observation lines from these elements are ubiquitous and commonly used for plasma diagnostics, e.g., determining electron temperature or ionization charge balance, yet unsolved discrepancies remain. As an example, the elemental abundance determination of planetary nebulae are common determined via two methods: one using collisionally excited lines and another using optical recombination lines. The typical phenomenon observed is that the abundances derived from collisionally excited lines are up to 20 times less than those derived from optical recombination lines (Kaler 1981, Kholtygin & Feklistova 1992, Liu 2002). The collisionally excited lines are easily observed given the transpicuous nature of the surrounding plasma, however, optical recombination lines can experience a large opacity resulting in poor signal-to-noise in spectroscopic measurements. As detector technology progresses, this problem is receiving more attention and it is necessary to have the best rate coefficients available, in determining the ionization balance and elemental abundance, in order to remove poor atomic data from the list of explanations for the observations. There have only been a few single-pass experiments of the Be-like C, N, and O ions (Dittner et al. 1987, Badnell et al. 1991). These experiments provided a great insight as to the complexity of models required, e.g., core fine structure interactions, field induced enhancements, etc., yet the resolutions and energy ranges covered were not sufficient to produce a reliable and accurate plasma rate coefficient. Another difficulty is the presence of the 2s2p 3 P metastable state. The 2s2p 3 Po state has a long lifetime; estimated at 10 10 s for C 2 + by Laughlin (1980). The metastable content of a typical electron-impact ionization type source could be > 50% and, with such a long lifetime, it becomes inconceivable to store the ions long enough for them to decay to the XS ground state. Without a means to quantify the metastable content, it would be difficult to establish an absolute rate coefficient. Of particular importance are the low temperature dielectronic recombination (DR.) rate coefficients. The ions in the plasma of a planetary nebula are produced mainly by photoionization from the central star. This typically occurs at relatively low electron temperatures in the plasma, hence, it is important to have recombination rate coefficients that apply to this low temperature region. The previously mentioned experiments did not

275

provide a detailed measurement of the low energy DR resonances just a few eV above the threshold. This low energy region can have many strong resonances which can drastically impact the rate coefficient and thus the ionization equilibrium derived from these rate coefficients. The ability of atomic structure codes, commonly used to model DR rate coefficients, can become limited in this low energy region due, e.g., to correlation effects and LS-coupling limitations. Discrepancies of up to a factor of 10 exist between the various literature values for the DR rate coefficients of some ions leading to the required benchmarking by experiments. We have used the CRYRING storage ring to measure the rate coefficients of Be-like C, N, and 0. The electron cooler coupled to CRYRING is capable of center-of-mass (CM) energies down to approximately 100 /xeV. The AUTOSTRUCTURE code (Badnell 1986) was used to evaluate level energies, Auger, and radiative rates necessary to theoretically determine DR rate coefficients. This code has been commonly used in the past along with storage ring data. The AUTOSTRUCTURE code is compared to the experimental results allowing for a metastable ion beam fraction estimation and the extrapolation of field stripping of recombined Rydberg states. The identification of several trielectronic recombination (TR) resonances has been made, with those of 0 4 + having a dramatic effect on the low temperature plasma rate coefficient. More details regarding the AUTOSTRUCTURE calculations and experimental results can be found in Fogle et al. (2005).

2. Experiment The Be-like ions C 2 + , N 3 + , and 0 4 + were produced in an electron cyclotron resonance (ECR) ion source. The ions were extracted, transported, and injected into the synchrotron storage ring CRYRING at the Manne Siegbahn Laboratory in Stockholm, Sweden. The ions were accelerated, via an RF drift tube, to full storage energies of several MeV/amu as defined by the magnetic rigidity of 1.44 T m. Final stored ion currents were of the order of 100's of nA. The ions were cooler by the electron cooler coupled to CRYRING by velocity matching the electrons and ions in a coaxial configuration. The electrons are adiabatically expanded from a superconducting magnet region around the cathode to the lower field interaction region resulting in a factor of 25 times expansion - the electron cooler is capable of 100 times expansion but this was limited to 25 times in order to maintain electron densities of approximately 3 x 107 cm - 3 . The final electron beam

276

diameter was 20 mm while the final ion beam diameter was 1 mm. At the velocity matched cooling condition, RR is the dominant recombination process as this is near 0 eV CM energy. To investigate DR (and TR) processes the cathode voltage, and hence electron velocity, is varied in a systematic fashion over selected CM energies. Ions which undergo recombination are separated from the main stored beam by the dipole magnet following the electron cooler and are detected by a unity efficiency ionimplanted surface barrier detector. More details regarding this technique can be found in discussions by DeWitt et al. (1996) and Zong et al. (1997). The error in the determined CM energy is estimated at 10 meV, which is derived primarily from the uncertainties in the cathode voltage measurement and correction of the drag force that the electrons exert on the ions during the energy scanning process. The error in the rate coefficients is estimated at 15% with the primary uncertainty being the estimation of the total electron-ion interaction length, given that the electrons must merge and demerge with the stored beam via toroidial bending sections. The ion beam metastable content, i.e., the ions initially in the 2s2p 3 P state, was determined to be 60%, 40%, and 35%, respectively. This was determined primarily by adjusting the pure ground state AUTOSTRUCTURE results for the resonances leading up to the 2s2p 1Pnl series limit to the experimental results. The metastable fraction for C 2 + was also confirmed by a seperate electron-impact ionization measurement carried out in conjunction with the recombination experiment using the same source and storage parameters (Loch et al. 2005). The error in determining the metastable fraction is estimated at 10%.

3. Results and Discussion The experimental results are show in Fig. 1. These results represent the given metastable fraction as determined by fitting the AUTOSTRUCTURE results for a pure initial ground state ion beam fraction to the 2s2p 1 Pn/ resonances leading up to the series limit. While there are few resonances resulting from the metastable fraction, these must be identified and removed in order to produce a pure ground state plasma rate coefficient. Also because of the metastable content, the apparent rate coefficients for the initial ground state ions are suppressed and must be increased to account for the metastable ion beam fraction stored in the ring. The AUTOSTRUCTURE results, along with level energies reported in the NIST levels database, provided the means to identify most of the resonances and determine if they

277

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Figure 1. Experimental rate coefficients for C 2 + , N 3 + , and 0 4 + . T h e 2s2p 1Pnl and 2s2p 3Pnl final recombined state Rydberg series are show on each plot, for both initial ground and metastable states for the 2s2p 1 P n / series, with the lowest allowable recombined n-state and the n-cutoff indicated on each series. For N 3 + and 0 4 + , the short vertical arrows on the energy axis indicate the position of T R resonances.

were from an initial ground or metastable state. In making the plasma rate coefficients, all metastable portions of the spectra were removed, the series limits were extrapolated using AUTOSTR.UCTURE to n = 1,000, and the low energy RR contribution was subtracted by fitting the experimental RR result with rate coefficients determined from Kramers RR cross sections (1923). The fitting parameters were

278

Figure 2. Temperature dependent plasma rate coefficients for C 2 + , N 3 + , and 0 4 + . The thick solid curve represents the RR and DR data presented in this Progress Report. This is compared to various values from the literature: (thin solid curve) RR + DR total rate coefficients of Nahar & Pradhan (1997) for C 2 + and N 3 + , Nahar (1999) for 0 4 + ; (solid circles) DR data of Badnell (1987, 1988); (triangles) DR data of Nussbaumer & Storey (1983); (dash-dotted curve) DR data of Aldovandi & Pequignot (1973); and (dashed curve) RR rate coefficient of Pequignot et al. (1991). The short dashed curve for 0 4 + indicates the DR rate coefficient with the large T R resonance at 60 meV artificially removed.

latter used to determine the plasma RR rate coefficient up to n = 1,000. The resulting hybrid spectra were then convoluted with Maxwellian distributions representing mean electron temperatures ranging from 10 2 -10 r K.

279 The resulting plasma rate coefficients, for both RR an DR, and shown in Fig. 2 by the thick solid curves, with RR falling off rapidly with increasing temperature and resonant recombination becoming the dominant channel. Several calculated DR and RR rate coefficients prominent from the literature are given for comparison. Notable are the low temperature DR rate coefficients of Nussbaumer & Storey (1983) and the AUTOSTRUCTURE results of Badnell (1987, 1988). These represent the some of the best available low temperature DR rate coefficients. Naturally, the AUTOSTRUCTURE results shown in Fig. 2 are indicative of the calculation used here to extrapolate the experimental n-cutoff and used to fit the 2s2p 1 PnZ series limit for determining the metastable contribution. The main differences are in the low energy resonances which prove difficult to reproduce, even using large intermediate-coupling calculations. This is discussed in more detail by Fogle et al. (2005). The most striking effect of low energy resonances to the plasma rate coefficient can be seen for 0 4 + . There are several TR resonances at low energy with one large TR resonance at 60 meV which results in the low temperature bump in the plasma rate coefficient at around 400 K. To illustrate the effect of this single large TR resonance, it has been artificially removed and the plasma rate coefficient reconstructed as before. The result is the short dashed curve in the 0 4 + plot of Fig. 2. From an astrophysical observation point-of-view, it would be interesting to study the decay of this triply excited state and the associating line emission. The total photon yield will naturally be greater than if it where strictly DR and perhaps this large rate coefficient from a single recombined state can prove to be a valuable diagnostic tool in astrophysical observations and laboratory plasmas. Acknowledgments MF, PG, and RS would like to acknowledge the Swedish Research Council for financial support. We are also grateful for the assistance received from the CRYRING staff at Manne Siegbahn Laboratory. SL and MP would like to acknowledge support by a grant for theoretical research in plasma and fusion science (DE-FG02-96ER54348) and a grant for scientific discovery through advanced computing (DE-FG02-01ER54644) to Auburn University by the U.S. Department of Energy. References 1. S. M. V. Aldrovandi and D. Pequignot, Astron. Astrophys. 25, 137 (1973)

280 2. 3. 4. 5.

N. R. Badnell, J. Phys. B: At. Mol. Opt. Phys. 19, 3827 (1986) N. R. Badnell, J. Phys. B: At. Mol. Opt. Phys. 20, 2081 (1987) N. R. Badnell, J. Phys. B: At. Mol. Opt. Phys. 21, 749 (1988) N. R. Badnell, M. S. Pindzola, L. H. Andersen et al. J. Phys. B: At. Mol. Opt. Phys. 24, 4441 (1991) 6. D. R DeWitt, R. Schuch, H. Gao et al., Phys. Rev. A53, 2327 (1996) 7. P. F. Dittner, S. Datz, H. F. Krause et al., Phys. Rev. A36, 33 (1987) 8. M. Fogle, N. R. Badnell, P. Glans, S. D. Loch, et al., accepted to Astron. Astrophys. (2005) 9. J. B. Kaler, Astrophys. J. 249, 201 (1981) 10. A. F. Kholtygin and T. Feklistova, Baltic Astronomy 1, 514 (1992) 11. H. A. Kramers, Philos. Mag. 46, 836 (1923) 12. C. A. Laughlin, Phys. Lett. 75A, 199 (1980) 13. X.-W. Liu, Rev. Mex. Astro. Astrof. (Serie de Conferencias) 12, 70 (2002) 14. S. D. Loch, M. Witthoeft, M. S. Pindzola. et al., Phys. Rev. A71, 012716 (2005) 15. S. N. Nahar, Astrophys. J. Suppl. Ser. 120, 131 (1999) 16. S. N. Nahar and A. K. Pradhan, Astrophys. J. Suppl. Ser. I l l , 339 (1997) 17. H. Nussbaumer and P. J. Storey, Astron. Astrophys. 126, 75 (1983) 18. D. Pequignot, P. Petitjean, and C. Boisson, Astron. Astrophys. 251, 680 (1991) 19. W. Zong, R. Schuch, E. Lindroth et al, Phys. Rev. A56, 386 (1997)

DISSOCIATION AND EXCITATION OF MOLECULES AND MOLECULAR IONS BY ELECTRON IMPACT

A. E. O R E L AND J. ROYAL* Department of Applied Science University of California, Davis One Shields Ave. Davis, CA 95616, USA E-mail: [email protected]

In the collision of electrons with molecules and molecular ions, excitation and dissociation are dominated by resonant processes, where the electron becomes temporarily trapped, changing the forces felt by the nuclei. We will outline our method for treating these collision processes, where one or more resonant states exist. We separate the problem into two steps. First, the resonance parameters are obtained from accurate electron scattering calculations using the Complex Kohn variational method. Then these parameters are used as input to the dynamics calculations. We will illustrate the method with the study of dissociative attachment in C1CN and BrCN, and dissociative recombination in HeJ.

1. Introduction In general, when an electron collides with a molecule or molecular ion, there is inefficient transfer of energy from the electron into the motion of the nuclei, leading to little vibrational excitation or dissociation. This is due to the large difference in mass between the electron and the nuclei. However, in certain special cases, the electron can temporarily attach to the molecule and change the forces felt between its atoms for a period of time comparable to a vibrational period. This leads to a large coupling between the electron interaction with the target and the nuclear dynamics of the target. The results of such an interaction can be quite dramatic. This can lead to resonant vibrational excitation and dissociative attachment, for neutral targets, or dissociative recombination in the case of ions. •This work is supported by the National Science Foundation, Grant No. PHY-02-44911 and the U.S. DOE Office of Basic Energy Science, Division of Chemical Sciences.

281

282

Therefore we can simplify the calculation by first considering the capture of the electron into a resonant dissociative state, and then describing the dynamics of the molecule moving on the excited state (resonant) potential energy surface. The dynamics must be able to describe autoionization since the molecule can re-emit the electron. If no autoionization occurs, the molecule fragments into products, during which the probability may be distributed into various product states due to non-adiabatic coupling. A brief description of the method of calculation used will be given the next section, followed by two examples: dissociative attachment in C1CN and BrCN and dissociative recombination in HeJ. 2. Method Our studies of this process will follow the comparable treatment of quantum reactive scattering. First we will carry out ab initio electron scattering calculations at fixed internuclear geometries to determine the resonant energy surfaces and the corresponding surface of autoionization widths. In the work described here we have used the Complex Kohn variational method. Only a brief discussion will be presented here, for further details we refer the reader to previous reviews on this subject.1 The Complex Kohn variational method uses a stationary principle for the T-matrix:

TZt = T£& - 2 J *r(H - E)*r0 •

(1)

The trial wave function is the usual coupled channel expression for the scattering system given by * = ^A[$ r (xi..x A r)i ; r(xjv + i)] + ^ d p e M ( x i . . x J V + i ) r n

(2)

where the $ r are N-electron target eigenstates, x$ denote space-spin coordinates, A antisymmetrizes the coordinates of the target and scattered electrons and the 0 M are square-integrable N + 1-electron configuration state functions (CSFs) described further below. The first sum, which we denote as the P-space portion of the wave function, runs over the energetically open target states. We denote the second sum as the correlation portion of the wave function. In the Kohn method, the Fr, which represent the wave functions of the scattered electron, are expanded as a linear combination of symmetry-adapted molecular orbitals (Gaussians) and numerical continuum functions. The N+1-electron CSFs describe short-range correlations and the effects of closed-channels and are critical to striking

283 a proper balance between intra-target electron correlation and correlation between target and scattered electrons. From the results of these scattering calculations, we obtain elastic and inelastic (excitation into excited states) cross sections and eigenphase sums. Near a resonance these quantities show dramatic structure in their energy dependence. The elastic cross sections exhibits peaks whose position is the resonance energy and whose width yields the autoionization width which is inversely proportional to the lifetime. The eigenphase sum shows steps of flat the resonance energy. The steepness of the rise determines the autoionization width. In practice, it is the eigenphase sum (not the elastic cross section) which is fit to a Breit-Wigner form to abstract this information. These resonance positions and widths are then used as input to a dynamics study to determine the cross-section and product distributions for the dissociation or excitation process. The theory has been derived in a number of ways,2,3,4 we will just give a brief summary. We start with the nuclear wave equation at total energy E (E-KR-

Vret)iu = 4>v

(3)

where KB. is the nuclear kinetic energy operator and £„ is the nuclear wave function associated with the electronic resonance state. We then introduce a complex, energy-dependent, nonlocal potential, Vres , defined as open

Vres(R, R') = Eres(R)S{R - R') - iff ^

Uu(kv, R)Uv(ku, R').

(4)

V

Eres is the real part of the potential energy curve of the negative ion from electron-molecule scattering calculations (or bound-state calculations in its bound region), and kv is the momentum of the scattering electron when the molecule is left in the final vibrational state f]„. The sum runs over the energetically open vibrational states of the ion. Following Hazi et al. 4,e we approximate U,/(kl/,R), the matrix element coupling the resonance to the non-resonant background associated with a vibrational level v, as Uv{kv,R)={^\

nv{R)

(5)

The driving term for the nuclear wave equation, or "entry amplitude", „ is defined as UR)=(^j\u{R\

(6)

284

where r)u is the initial vibrational wave function of the neutral target. In general, cross sections computed with the entry amplitude in Eq.(6) will not have the correct energy dependence near threshold and will thus be inaccurate at very low scattering energies. To address this problem, the equations can be modified, introducing an ad hoc function of the momentum of the incident electron ki the "barrier penetration factor". 5 For many applications, the heavy-particle dynamics can be treated within the local complex potential or "boomerang" approach. In this case, one can assume that the sum over vibrational states in Eq. (4) is complete to show that in the high-energy limit, the nonlocal potential in Eq.(4) produces the local width function.

£

re R) Uv{kv, R)Uv{kU) B!) = -£+.

(7)

yielding: Vres (R) = Ere3 (R) - iT(R)/2

(8)

The position and width of the resonance that form the anion potential are Ere3 and T respectively. The solution of Eq. (3) is constructed that is regular at the origin and subject to purely outgoing boundary conditions. The integrated cross section for dissociative electron attachment from vibrational state v is then expressed as OV~BA=9%--

lim \UR)\2

(9)

where g is the ratio of resonance state to initial state statistical weights and K2/2/J, is the asymptotic kinetic energy of the dissociated fragments with reduced mass /i, i.e., K2/2fi = E-Vres(R)\R-.00.

(10)

In an alternative approach, when a time-dependent method is used for the solution of Eq. (3), the cross section is calculated by the projection of the wave packet onto final states for long times when the wave packet has reached the asymptotic region of the potential and the autoionization loss has gone to zero7.

285

3. Dissociative Attachment of C1CN and BrCN These systems have the interesting property that since both fragments have positive electron affinities, two fragmentation channels are open. These are: e" + XCN • e~ + XCN •

X- + CN X + CN~

(11) (12)

where X is either CI or Br. Experiment have been carried out on both systems.8,9 Preliminary work on this system was reported previously.10 The

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first channel, producing Cl~, was believed to proceed through a CICN~ 2 E resonance state, formed by the addition of an electron to a a* antibonding orbital. The second channel, producing CN~, has been explained as a twostep mechanism. The first step is the transition to the 2 II resonance, which is the addition of the electron to a 7r* antibonding orbital. However, the dissociation is not believed to be direct, but occurs after energy transfer from the C — N stretching mode into the dissociative CI — CN mode8. The actual mechanism has been found to be much more complicated. More extensive scattering calculations and structure calculations were carried out on both the C1CN and BrCN systems. The potential curves both for the neutral and the resonances are shown in Figure 1 as a function of the X-CN distance, keeping the C-N distance fixed at the initial equilibrium separation. As can be seen in the figures, the lowest resonance curve correlates asymptotically to the X + CN - channel. The resonance corresponding to the X - + CN channel occurs at much higher energy. In n symmetry, the two resonances have an avoided crossing at large R. The wavefunctions were analyzed to abstract the coupling between the states,

286

and the diabatic curves are plotted in Figure 1. The resonance energy as a function of the C — N bond distance was found to be harmonic, with little change in the autoionization width. When XCN is bent, the symmetry of the molecule changes from C^v to C s . It had been speculated that there would be a strong interaction between the £ states that transform as A' and the component of the II state that also transforms as A'. This was not found to be correct. The resonant curves and couplings were used in

Figure 2. Cross section for dissociative attachment for C1CN in ground vibrational state. Solid line refers to left hand scale. Dashed line refers to right hand scale.

as input to a wave packet calculation to determine the cross section for dissociative attachment for C1CN. The results are shown in Figure 2. 4. Dissociative Recombination of HeJ Resonant dissociative recombination of the HeJ molecular ion is an important process in the ionosphere as well as in laboratory plasmas. Recently, there have been two measurements of rate coefficients for this process using ion storage rings11'12. In order to compare to these experiments, calculations were performed in all symmetries, 1,3 E Uig , 1,3 II U , S and 1,3 A u , g and over a range of energies around each expected resonance. In each case, a cross section and an eigenphase sum was obtained from the scattering calculation, which was then fit to the Breit-Wigner form to obtain the resonance energy and auto ionization width. A total of 30 resonances were obtained in the region between 0 and 10 eV. The resonances in this system are Feshbach resonances corresponding to a Rydberg series converging to excited states of the ion. In the 0 to 10 eV region, the Rydberg series is

287

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Figure 3. Potential Energy Curves for HeJ and resonant He2 states . In each case, the two solid curves represent the ground state, 2 E U , and the first excited state, 2 E 9 , respectively. The dotted curves represent the various neutral resonance states included in the calculation. Note that only the triplet states are shown in each of the symmetries.

converging to the first excited state of the ion, 2 S 9 . The resonances in this region have the following configurations (laglaD^nA^

(13)

where A can be a, •n or S. Figure 3 shows the resonance potential energy curves for the various symmetries resulting from the complex Kohn and quantum chemistry calculations. Only the triplet states are shown in the figures because the singlet states lie very similar in energy and shape to the triplet states. Using the calculated potential energy curves and couplings,

2

4 6 8 10 Incident Energy (eV)

Figure 4. Total cross section for He J . Solid line: Calculation. Closed circles: TSR experiment 12 . Open Circles: ASTRID experiment 11 .

288 the dynamics are determined and a cross section is obtained. Figure 4 shows the resulting total dissociative recombination cross section for the energy region 0 to 10 eV, obtained by summing over each of the partial cross sections. There exist two experimental measurements of the cross section. These are also shown in Figure 4. The calculation agrees well with the results of the Astrid ion storage ring 11 and is lower by roughly a constant factor of 2.6 from the experiments reported from the TSR 1 2 . 5. Conclusions We have discussed our progress towards an understanding of excitation and dissociation processes which occur in the collision of electrons with molecules and molecular ions. We have shown how modern ab initio techniques, both for the electron scattering and the subsequent nuclear dynamics studies, can be used to accurately treat these problems. Current calculations have only begun to address these problems and much work remains for the future. References 1. T. N. Rescigno, B. H. Lengsfield and C. W. McCurdy, Modern Electronic Structure Theory vol 1 ed D. R. Yarkony, (Singapore: World Scientific) 501 (1995). 2. T. F.O'Malley, Phys. Rev. 150 14 (1966). 3. L. Dube and A. Herzenberg, Phys. Rev.A 20 194 (1979). 4. A. U.Hazi, T. N.Rescigno, and M. Kurilla, Phys. Rev.A 23 1089 (1981). 5. J. N. Bardsley, in Electron-Molecule and Photon-Molecule Collisions, edited by T. N. Rescigno, B. V. McKoy, and B. I. Schneider, Plenum, New York, p. 267 (1979). 6. A. U. Hazi, A. E. Orel, and T. N.Rescigno, Phys. Rev. Lett 46 918 (1981). 7. A. Larson and A. E. Orel, Phys. Rev. A 59 3601 (1999). 8. F. Briining, I. Hahndorf, A. Stamatovic, and E. Illenberger, J. Phys. Chem., 100, 19740 (1996). 9. R. Parthasarathy, L. Suess, S. B. Hill and F. B. Dunning, J. Chem. Phys., 114, 7962 (2001). 10. A. E. Orel, The Physics of Electronic and Atomic Gollsions, ed Y. Itikawa, K. Okuno, H. Tanaka, A. Yagishita and M. Matsuzawa, (American Institute of Physicis Conference Proceedings 500, Melville, New York) 339 (2000). 11. X. Urbain, N. Djuric, C. P. Safvan, J. J. Jensen, H. G. Pederson, L. Vejby Sogaard and L. H. Anderson, J. Phys. B, 38, 43 (2005). 12. H. B. Pederson, H. Buhr, S. Altevogt, V. Andrianarijaona, H. Kreckel, L. Lammich, N. De Ruette, E. M. Staicu-Casagrande, D. Schwalm, D. Strasser, X. Urbain, D. Zajfman and A. Wolf, J. Phys: Conf. Ser. 4 168 (2005).

STATE-SELECTIVE X-RAY STUDY OF THE RADIATIVE RECOMBINATION OF U 9 2 + IONS WITH COOLING ELECTRONS

M. P A J E K 1 , TH. S T O H L K E R 2 ' 3 , D. BANAS 1 , H. F . B E Y E R 2 , S. B O H M 4 , F. BOSCH 2 , C. BRANDAU 2 ' 4 , M. CZARNOTA 1 , S. C H A T T E R J E E 2 , J.-CL. DOUSSE 5 , A. G U M B E R I D Z E 2 ' 6 , S. HAGMANN 2 , C. KOZHUHAROV 2 , D. LIESEN 2 , A. MULLER 4 , R. REUSCHL 2 - 3 , E. W. S C H M I D T 4 , D. S I E R P O W S K I 7 , U. SPILLMANN 2 ' 3 , J. S Z L A C H E T K O 1 ' 5 , S. TASHENOV 1 ' 2 , S. T R O T S E N K O 2 , P. V E R M A 2 , M. WALEK 1 , A. WARCZAK 7 AND A. W I L K 7 Institute of Physics, Swietokrzyska Academy, Kielce,Poland Gesellschaft fur Schwerionenforschung, Darmstadt, Germany Institut fur Kernphysik, Universitdt Frankfurt,Germany Institut fur Kernphysik, Justus-Liebig Universitdt, Giessen, Germany Department of Physics, University of Fribourg, Switzerland Tbilisi State University, Georgia Institute of Physics, Jagiellonian University, Cracow, Poland We report on a state-selective x-ray experiment on recombination of bare U 9 2 + ions with low-energy electrons which was performed, for the first time at non-zero relative electron energies (0-1000 meV), by observing the x-ray photons emitted directly from radiative recombination (RR) and subsequent deexcitation cascades (DC). The results are discussed in terms of the nonrelativistic dipole approximation (NDA). The recombination enhancement effect is observed for K-RR photons at zero relative energy, while for higher energies the discrepancies between data and NDA calculations indicate the importance of the relativistic effects.

1. Introduction The availability of cooler storage rings has opened up the experimental possibilities to study the processes of recombination of ions with free electrons. Consequently, in the recombination experiments performed at existing heavy ion cooler/storage ring facilities (TSR, CRYRING, ESR) the radiative recombination (RR) and the dielectronic recombination (DR) processes have been studied in last decade quite systematically for a number of ions, including bare uranium (U 92+ ) ion beam 1,2,3 ' 4 available at the ESR ring at GSI. The bare ions can recombine with electrons only via the ra-

289

290 diative recombination or the three-body recombination (TBR) processes, while for few-electron ions the dielectronic recombination is possible, which can play important role at very low5,6 electron energies. The x-ray recombination experiments performed up to now in the electron cooler of the ESR storage ring with Au 79+ and U 92+ ions were focused on the spectroscopy of K-RR and Lyman a x-ray lines to extract precisely the Lamb shift in high-Z ions1'3'4-7.

4000 3500 3000

Lyman

U92++e^U91++fe 9 =0.5"

1

L

y„

2500 2000 1500

Balmer

1000 500 0

ULu. 20

40

60

80

100

120

140

160

180

Energy (keV)

Figure 1. The x-ray spectrum measured with Ge(i) at 6 = 0.5° showing both the RR and Lyman and Balmer series x-ray lines from recombination of U 9 2 + ions with electrons.

The effect of recombination "enhancement" observed in several experiments2,5'6'8 on the recombination of high-Z bare ions with cooling electrons in ion storage rings attracted a wide interest during the last years. Up to now, this effect was studied by observing recombined ions separated in a dipole magnet of the storage ring. Consequently, the measured recombination rates included a wide range of n-states, up to very high Rydberg states limited only by the field ionization effect. 2. Experiment The experiment was performed at the SIS-ESR heavy ion facility at the GSI, Darmstadt, using a beam of bare U 92+ ions decelerated to an energy of 23 MeV/amu and cooled in the electron cooler to a transverse temperature of about kTj. =120 meV and much smaller longitudinal temperature (kT|| <
H e + ( l s ) + e e j .

(2) 2

Notice that for both these the overall ionization process is ns —> ns + eej; only this type will be considered here. 'Supported by the US National Science Foundation under grant PHY-9987861.

297

298

Typical experiments for both these reactions measure angular distributions. For reaction (1) the angular distribution of (slow) electrons ejected in a direction kej is measured in coincidence with fast incident electrons scattered through a chosen angle 6SC. An important quantity for this type of reaction is K = ko — k, the momentum transferred in the collision; here feo(fc) is the incident (scattered) electron momentum. In the limiting case that the plane wave Born approximation (PWBA) is valid, the ejected electron angular distribution is rotationally symmetric about K, but is asymmetric with respect to reflection in a plane whose vector direction is K: the binary peak around K is usually more intense than the recoil peak around —K. As explained below, this is due to interference effects between the dominant dipole term and weaker opposite parity multipoles. For reaction (2) the angular distribution of photoelectrons is almost, but not quite, rotationally symmetric about the polarization direction (electric unit vector) E. As is the case in high incident energy (e, 2e) reactions, this asymmetry is due to interference between the dominant dipole, and the weak quadrupole, terms. This interference results in an angular distribution that favors the forward, photon, direction k over the backward direction — k. For both reactions this asymmetry may be quantified in terms of the angular behaviour of complex interference cross terms in a partial wave expansion of the ejected electron wavefunction. For the s-shell ionization considered here, there is a direct correspondence between this expansion and a multipole expansion {I = 0,1,2, • • •; m = £, £ — 1, • • • , -£) of the scattering amplitude. The ejected electron angular distributions may then be written 2

Iej{kej)

= 2^lmatmyim(kej)

i

(3)

where Yim is a spherical harmonic, and the complex coefficients a(m = \aem\eiS«»

(4)

contain the dynamics of the ionization process. This is a coherent summation which contains cross terms of the form hml'm'

= |a*m||a*'m'| COs(<Sfm - 5t,m,)YtmYi,m,,

(5)

involving magnitudes \atm\ and phases 5em. The spherical harmonics gives the cross terms a parity property Iemt'm'{-kej)

= (-1)

+

Ilmt'm'ikej).

(6)

For the experiments considered here, the dipole (£ = 1) amplitude dominates and other multipoles are an order of magnitude weaker. The

299 asymmetric angular distributions are then due to interference cross terms between the dipole and even parity multipoles: because of (6) the interference changes sign for ±kej. Note that there are no cross terms I ± H! in the angle integrated electron scattering or photoabsorption cross sections because of the orthogonality of the spherical harmonics. Thus if the dipole magnitude is |aio| = 1 and the quadrupole magnitude is |a2o| = 0.1, then the dipole cross section is proportional to |oio| 2 = 1, but the quadrupole cross section goes as |a2o|2 = 0.01, which is small and may be neglected in comparison to the dipole cross section. On the other hand the angular distribution contains a cross term of magnitude |aio||o2o| = 0.1, which is sufficiently large to affect the angular distribution. Thus the cross terms in the angular distributions enhance weak processes which cannot be seen in total cross sections. The cross terms also contain information about relative phases; this is not present in total cross sections.

2. T h e o r y The reason that (e, 2e) and photoelectron angular distributions have different asymmetries can be seen from a detailed comparison of the ionization process for each. This is done in figure 1 for the limiting conditions applicable to the experiments described below. The left hand column applies to the (e, 2e) case with high electron beam energy and small momentum transfer; the right hand column corresponds to photoionization with non-relativistic photoelectron energies and low photon energies where the semiclassical treatment of radiation is valid. The (e, 2e) analysis may be approximated as a multipole expansion of the PWBA transition operator e (in terms of spherical Bessel functions jt and Legendre polynomials Pt) where only m = 0 terms are present if the momentum transfer direction K is chosen as the quantization axis. For photoionization using linearly polarized light with the electric vector along z (the quantization axis) and a photon momentum fe in the +x direction, the transition operator in the "length form", kzelkx, is usually expanded as a power series in k.4 For very small K and k, both expansions may be terminated at the first term, in which case the spherical Bessel function is also expanded as a power series in K terminated at the lowest order term. The operators in both the (e, 2e) and photoelectron cases are then proportional to r cos 9; in other words an (e, 2e) experiment simulates the pure dipole transition

300

IONIZATION (s-shell) (e,2e)

Photoelectron

High incident Energies (PWBA; z = K):

Low photon energies (Lin.Pol.i; x = k): kzelkx — kzTiv=Q -^{ikx)

T,f=Q(2e+l)je(Kr)Pe(cos9) K -> 0 limit: Kr cos 6 "poor man's synchrotron"

dipole

Low K limit: Kr cos 8 K2r2

dipole monopole quadrupole (dips- mon.quad)

KV(3cos20-l)

Ang.amp. dipole (p) monopole (s) quadrupole (d)

Yifl Yo,o ^2,0

k -> 0 limit: kz = krcos 8

Low k limit: kr cos 8 k2r2coa8sm8cos

Yija ^2,-1 ~ ^2,1

Ang.Distr. Dipole cross section +p x s,p x d interference

Dipole cross section +p x d interference

K

K=i

E-Z*r

Recoil

Backward

Figure 1. A comparison of (e, 2e) and photoelectron angular distributions. See text for explanation.

associated with low energy photoionization. Before the advent of readily accessible synchrotron radiation (e, 2e) experiments were used to simulate synchrotron experiments. When the dipole term dominates but the next most important terms

301 are significant the expansions are taken to terms quadratic in r. For (e, 2e) this gives rise to the monopole and quadrupole transitions which are of approximately the same importance; the photoelectron case includes only the quadrupole transition. For s-shell ionization the angular distributions are then determined by the spherical harmonics associated with each multipole. Whereas for (e, 2e) only m = 0 terms are present for both dipole and quadrupole, for photoionization the quadrupole process has m ^ 0 only; this is the reason for the different shape of the angular distributions shown at the bottom of the figure. On the left, the (e, 2e) binary-recoil differences are due to monopole-dipole and dipole-quadrupole cross terms with £ + £' odd in Eq. (6). On the right, in the photoelectron angular distribution the dashed line is for pure dipole and the solid line includes dipole-quadrupole interference (with £ + £' odd) which causes the forward - backward asymmetry. It then follows that in both the (e, 2e) and photoelectron cases the sum + ( J + 1 ~ ) and difference ( J + - I~) of the intensities I+ and I~, indicated by the antiparallel arrows in Fig. 1, yield the dipole term and interference cross terms, respectively. In particular the difference/sum ratio, for measurements made for ejected electron (photoelectron) directions the "magic angle" (54.7°) away from the quantization axis, yield the relative dipolemonopole amplitude for the (e, 2e) case:

and yield the non-dipole parameter 7 for the photoelectron case:4 3 V 3 ^ ~ ^_ = 7 = 3 c ^ | cos(a2 -

ft).

(8)

where T>(Q) is the dipole (quadrupole) magnitude. These expressions strip off the large dipole cross section to isolate the non-dipole effects, but do not separately determine the relative magnitudes and phases. In fact it is possible to obtain this information in certain cases, as we shall now show. Consider the following thought experiment. If a process is given by the coherent summation of two complex amplitudes ai = |ai|el<Sl and 02 = |o2|et,S2 then the observed intensity is / = |oi +a2\2 = |ai| 2 + |a 2 | 2 + 2 | a i | | a 2 | cos(