Advances in
ATOMIC, MOLECULAR, AND OPTICAL PHYSICS VOLUME 45
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Advances in
ATOMIC, MOLECULAR, AND OPTICAL PHYSICS VOLUME 45
Editors B B New York University New York, New York H W Max-Planck-Institut für Quantenoptik Garching bei Munchen Germany
Editorial Board P. R. B University of Michigan Ann Arbor, Michigan M. G F.O.M. Instituut voor Atoom-en Molecuulfysica Amsterdam The Netherlands M. I Argonne National Laboratory Argonne, Illinois W. D. P National Institute for Standards and Technology Gaithersburg, Maryland
Founding Editor S D R. B
Supplements 1. Atoms in Intense Laser Fields, Mihai Gavrila, Ed. 2. Cavity Quantum Electrodynamics, Paul R. Berman, Ed. 3. Cross Section Data, Mitio Inokuti, Ed.
ADVANCES IN
ATOMIC, MOLECULAR, AND OPTICAL PHYSICS Edited by
Benjamin Bederson ,
Herbert Walther -- ¨ ,
Volume 45
San Diego San Francisco Boston London Sydney
New York Tokyo
This book is printed on acid-free paper. Copyright 2001 by Academic Press All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. The appearance of code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for chapters are as shown on the title pages; if no fee code appears on the chapter title page, the copy fee is the same for current chapters, 1049-250X/00 $35.00 ACADEMIC PRESS A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.academicpress.com Academic Press Harcourt Place, 32 Jamestown Road, London NW1 7BY, UK International Standard Book Number: 0-12-003845-5 International Standard Serial Number: 1049-250X
Printed in the United States of America 00 01 02 03 MB 9 8 7 6 5 4 3 2 1
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Comparing the Antiproton and Proton, and Opening the Way to Cold Antihydrogen G. Gabrielse I. II. III. IV. V. VI.
World’s Lowest Energy Antiprotons by a Factor of 10 . . . . . Million-Fold Improved Comparison of Antiproton and Proton Opening the Way to Cold Antihydrogen . . . . . . . . . . . . . . . . . Technological Spinoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Medical Imaging with Laser-Polarized Noble Gases Timothy Chupp and Scott Swanson I. II. III. IV. V. VI. VII. VIII.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Polarization Techniques . . . . . . . . . . . Basics of Magnetic Resonance Imaging (MRI) Imaging Polarized Xe and He Gas . . . . . . NMR and MRI of Dissolved Xe . . . . . . . . . Conclusions — Future Possibilities . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Polarization and Coherence Analysis of the Optical Two-Photon Radiation from the Metastable 22S1/2 State of Atomic Hydrogen Alan J. Duncan, Hans Kleinpoppen, and Marlan O. Scully I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. On the the Theory of the Two-Photon Decay of the Metastable State of Atomic Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. The Stirling Two-Photon Apparatus . . . . . . . . . . . . . . . . . . . . . . . . IV. Angular and Polarization Correlation Experiments . . . . . . . . . . . . . V. Coherence and Fourier Spectral Analysis — Experiment and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Time Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Correlation Emission Spectroscopy of Metastable Hydrogen: How Real are Virtual States? . . . . . . . . . . . . . . . . . . . . . . VIII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
100 101 108 111 127 133 133 144
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Contents
IX. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Laser Spectroscopy of Small Molecules W. Demtröder, M. Keil, and H. Wenz I. II. III. IV. V. VI. VII.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High Vibrational Levels in Electronic Ground States . . . . . . . . . . . Laser Spectroscopy of Electronically Excited Molecular States . . . . . Sub-Doppler Spectroscopy of Small Alkali Clusters . . . . . . . . . . . . . Time-Resolved Laser Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Coulomb Explosion Imaging of Molecules Z. Vager I. II. III. IV.
The Principle of Coulomb Explosion Imaging . . . . . . . . . . . Scientific Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of Recent Coulomb Explosion Imaging Studies and Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Contributors Numbers in parentheses indicate pages on which the authors’ contributions begin
T C (41), Departments of Physics and Radiology, University of Michigan, Ann Arbor, Michigan 48109 W. D¨ (149), Fachbereich Physik, Universita¨t Kaiserlautern, D67663 Kaiserlautern, Germany A J. D (99), Unit of Atomic and Molecular Physics, University of Stirling, Stirling FK9 4LA, Scotland G. G (1), Harvard University, Cambridge, Massachusetts 01238 M. K (149), Fachbereich Physik, Universita¨t Kaiserlautern, D-67663 Kaiserlautern, Germany H K (99), Unit of Atomic and Molecular Physics, University of Stirling, Stirling FK9 4LA, Scotland M O. S (99), Department of Physics, Texas A&M University, College Station, Texas 77843; and Max-Planck-Institut fu¨r Quantenoptik, D-85748 Garching, Germany S S (41), Departments of Physics and Radiology, University of Michigan, Ann Arbor, Michigan 48109 Z. V (203), Department of Particle Physics, Weizmann Institute of Science, 76100 Rehovot, Israel H. W (149), Fachbereich Physik, Universita¨t Kaiserlautern, D-67663 Kaislerlautern, Germany
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 45
COMPARING THE ANTIPROTON AND PROTON, AND OPENING THE WAY TO COLD ANTIHYDROGEN G. GABRIELSE Harvard University, Cambridge, Massachusetts 02138 I. World’s Lowest Energy Antiprotons by a Factor of 10 . . . . . . . . . A. First Slowing and Trapping of Antiprotons . . . . . . . . . . . . . . . . B. Capturing and Cooling Antiprotons . . . . . . . . . . . . . . . . . . . . . . C. Vacuum Better than 5 ; 19\ Torr . . . . . . . . . . . . . . . . . . . . . . D. Stacking Antiprotons: Making the Antiproton Decelerator (AD) Possible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Transporting Trapped Antiprotons . . . . . . . . . . . . . . . . . . . . . . . F. Later Duplication of TRAP Techniques by Others . . . . . . . . . . . G. Lower Temperature Antiprotons are Coming . . . . . . . . . . . . . . . II. Million-Fold Improved Comparison of Antiproton and Proton . . . . A. Testing PCT Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Comparing Cyclotron Frequencies . . . . . . . . . . . . . . . . . . . . . . . C. TRAP I: One Hundred Antiprotons Compared to One Hundred Protons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. TRAP II: Alternating One Antiproton and One Proton . . . . . . . E. TRAP III: Simultaneously Trapped Antiproton and H\ Ion . . . III. Opening the Way to Cold Antihydrogen . . . . . . . . . . . . . . . . . . . . . A. Cold Antihydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. 4.2 K Positrons in Extremely Good Vacuum . . . . . . . . . . . . . . . C. Demonstrating the Nested Penning Trap . . . . . . . . . . . . . . . . . . D. Closer to Cold Antihydrogen than Ever Before . . . . . . . . . . . . . . E. Recombination Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Selecting Processes within a Nested Penning Trap . . . . . . . . . 2. Other Formation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . F. Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Technological Spinoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Abstract: Our TRAP collaboration has developed and demonstrated slowing, trapping, and electron-cooling techniques that enable antiproton storage in thermal equilibrium at 4.2 K. This is an average energy that is more than 10 times lower than the energy of any previously available antiprotons. Months-long confinement of a single antiproton, at a background pressure 5 ; 10\ torr, and nondestructive detection of the radio signal from a single trapped antiproton, made it possible to show that the charge-to-mass ratios of the antiproton and proton differ in magnitude by 9 parts in
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Copyright 2001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003845-5/ISSN 1049-250X/01 $35.00
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G. Gabrielse 10. This 90 parts per trillion comparison is nearly a million times more accurate than previous comparisons, and is the most stringent test of PCT invariance with a baryon system by a similar amount. The availability of extremely cold antiprotons makes it possible to pursue the production of antihydrogen that is cold enough to trap for precise laser spectroscopy. The closest approach to cold antihydrogen to date is our simultaneous confinement of 4.2 K antiprotons and positrons. All cold antiproton experiments so far were carried out at the CERN Laboratory with antiprotons coming from its Low Energy Antiproton Ring (LEAR). This unique facility has now closed. Future antihydrogen experiments will be pursued at the new Antiproton Decelerator ring at CERN, which was constructed for this purpose. Using the techniques developed by TRAP, antiprotons will be accumulated within traps rather than in storage rings, thereby reducing the operating expenses to CERN.
I. World’s Lower Energy Antiprotons by a Factor of 1010 Stored antiprotons are now available in thermal equilibrium at 4.2 K. This is an energy that is 10 times lower (Fig. 1) than the lowest energy antiprotons available before our TRAP Collaboration (Table 1) developed and demonstrated new techniques over the last decade. Our extremely cold antiprotons made possible a series of three comparisons of the charge-tomass ratio of the antiproton and proton that improved this comparison by nearly a factor of 10, the most precise test of PCT invariance with baryons by approximately this factor. The extremely cold antiprotons, and a method to accumulate them in a trap, make it possible to pursue the production and study of cold antiprotons at the new Antiproton Decelerator facility at the CERN laboratory. Antiprotons are the antimatter counterparts of protons, the familiar constituents of ordinary matter (along with electrons and neutrons). Antiprotons occur naturally only as the very occasional products of a collision between a high energy cosmic ray and an atom in the atmosphere. Although believed to be stable particles, the naturally occurring antiprotons nonetheless live for only a short time. A single collision between an antiproton and any proton in ordinary matter can annihilate both particles. The antiproton and proton cease to be and a variety of lighter particles (mostly pions) are formed. Antiprotons can thus be stored only in a container that has no walls and essentially no ordinary matter within. Starting in 1955, in the Bevatron storage ring at Berkeley, usable numbers of antiproton have been produced and studied using giant storage rings within which antiprotons travel at speeds close to that of light. Protons of extremely high energy are made to collide with ordinary matter. In a small fraction of these collisions, antiprotons are formed, which can be directed into large circular storage rings. Technological improvements allowed the CERN Laboratory in Geneva to accumulate much larger
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F. 1. Our trapped antiprotons are the lowest energy antiprotons in the world by more than a factory of 10. The vast energy scale for charged particles is represented on a logarithmic ‘‘thermometer.’’
TABLE I TRAP C: CERN PS-196 Harvard University: Prof. G. Gabrielse?, Dr. S. Rolston, Dr. L. Orozco, Dr. W. Jhe, Dr. W. Quint, Dr. T. Roach, K. Helmerson, R. Tjoelker@, X. Fei@, D. Phillips@, A. Khabbaz@, D. Hall@, P. Yesley?, J. Estrada?. University of Bonn: Dr. H. Kalinowsky?, Dr. G. RouleauA, J. Haas@, J. GrobnerB, C. Heimann@. University of Washington: Prof. T. Trainor. Fermilab: Dr. W. Kells. ?Continuing on ATRAP. @Ph.D. earned at TRAP. AContinuing on ATHENA. BDiploma Thesis earned at TRAP.
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numbers of antiprotons that were collided with protons so that the shortlived W and Z particles could be observed and studied. At Fermilab in Illinois, higher energy collisions between antiprotons and protons are being investigated to learn about the top quark. Such high energies and velocities are desirable for experiments in which antiprotons are made to collide with other particles. However, new experiments became possible when the CERN Laboratory began operating the Low Energy Antiproton Ring (LEAR) in 1982. It has a modest circumference of only 79 m (much smaller than the 27 km circumference for the LEP ring at CERN). LEAR slowed and cooled antiprotons to an energy of 6 MeV, a speed that is approximately 0.1 of the speed of light, and sent them to various particle and nuclear physics experiments. The ‘‘Low’’ in Low Energy Antiproton Ring was initially appropriate insofar as at the time these antiprotons were much lower in energy than any other antiprotons available in the world. However, the energy of antiprotons in LEAR was nonetheless much higher than the average energy of particles in the sun. Compared to the much lower energy we needed to do precision mass spectroscopy of antiprotons, and to prepare for antihydrogen that is cold enough to be trapped for high precision laser spectroscopy, the LEAR energy was very high indeed — by at least a factor of 10. The new techniques developed by TRAP, listed in what follows, allow slowing and cooling of antiprotons to energies that are lower by the required factor of 10. The slowed and cooled antiprotons reside within a small volume (less than 1 mm) of an ion trap in a nearly perfect vacuum (better than 5 ; 10\ torr). Their average kinetic energy is so low, 1 MeV, that temperature units are often used. The energy ‘‘thermometer’’ of Fig. 1 contrasts the energy of antiprotons and protons in various giant storage rings at the top with LEAR energies in the middle. Towards the bottom, 10 times lower in energy than is possible in LEAR, is the new low energy frontier at only 4° above absolute zero (4 K). Even lower antiproton temperatures should be possible as illustrated by the 70 mK temperatures we recently realized with trapped electrons in a similar ion trap (Peil and Gabrielse, 1999). 1. Slowing in matter to very low energy. Some of the 6 MeV antiprotons from LEAR slowed below 3 keV while passing through a thin window of matter. The fraction was initially measured during a 24-h beam time allocation in 1986 (Gabrielse et al., 1986, 1989a). 2. Trapping antiprotons. Antiprotons slowed below 3 keV are captured whilew they are within the electrodes of a Penning trap (Brown and Gabrielse, 1986) by the sudden application of a 3-kV trapping potential (Gabrielse et al., 1986). This was first demonstrated in a 24-h beam time allocation in 1986.
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3. Electron cooling of trapped antiprotons. The trapped antiproton, with keV energies, cooled via collisions with simultaneously trapped electrons (Gabielse et al., 1989b). The electrons radiated synchrotron radiation to return to thermal equilibrium with their 4.2 K surroundings. 4. L ong-term storage of 4.2 K antiprotons monitored nondestructively. We held antiprotons for months, monitoring them via the currents induced in surrounding electrodes by their motion, without loss of antiprotons (Gabrielse et al., 1990). 5. A pressure 5;10\ torr. Antiprotons remained trapped for months without any detectable loss, establishing a 3.4 month limit for our antiproton storage time and for antiproton decay into all channels. Calculated cross sections allow us to convert this storage time limit to the pressure limit already mentioned here (Gabrielse et al., 1990). 6. Nondestructive monitoring of one trapped p (or a p and H\ together). Good control and detection sensitivity with one or two trapped particles allowed the comparisons of q/m for the antiproton and proton to be improved by almost a factor of one million (Gabrielse et al., 1990, 1995, 1999b). These techniques were reported in Physical Review L etters and in the Rapid Communications of Physical Review, as indicated. A semipopular account was presented in Scientific American (Gabrielse, 1992). A. F S T A The apparatus used to cool antiprotons to low temperatures and to measure accurately their charge-to-mass ratio falls in the realm of ‘‘table top’’ experiments in that its size would allow it to be mostly located on the top of a table. A big complication is that the table top must be located at a large particle physics facility capable of supplying antiprotons. My trip to Fermilab in 1981 did not succeed in generating much interest in low-energy antiproton experiments. An intense focus on the primary Fermilab mission of studying TeV collisions between protons and antiproton left no room for the low energy experiments envisioned, even though a small operating ring (used for cooling studies) might have been adapted for this purpose. In 1985, Bill Kells of Fermilab came to work with me for one year, bringing the news that the small storage ring was shut down and pieces were being shipped to other laboratories. We thus turned our attention to mounting an experiment in Geneva, since the unique LEAR facility at the CERN laboratory was the only place in the world that could slow antiprotons to the MeV energies that a table top apparatus could accept. Hartmut Kalinowsky of the University of Mainz in Germany joined
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forces with us, as did Tom Trainor of the University of Washington in Seattle. Initially there was some skepticism at CERN about our proposals to slow antiprotons in matter, capture them in an ion trap and cool them within the ion trap via collisions with cold electrons in the same trap. These unproven techniques were very different from the normal high-energy collision experiments done at CERN. Moreover, one of our physics goals was in direct competition with an experiment in which CERN had already invested a great deal. There was also concern because we had no financial support while making our proposal. Funding agencies in the United States, with limited resources in tough economic times, were cautious about a large new program to be carried out at CERN but which did not yet have CERN approval. CERN and the funding agencies were not reassured by the fact that none of us had regular academic positions with tenure. Fortunately, first the Atomic Physics Division of the National Science Foundation, then the Air Force Office of Scientific Research and the National Bureau of Standards (now National Institute of Standards and Technology (NIST)) decided jointly to fund the quest for low-energy antiprotons. Only after the experiments succeeded did we learn that an NSF consensus found the opportunity too good to pass up despite an estimated likelihood of success in trapping cold antiprotons of 20%. Eventually CERN allowed us 24 h access to LEAR antiprotons to demonstrate that it really was possible to slow antiprotons from MeV energies down to 3 keV. Figure 2a shows the gas cells and time-of-flight apparatus, and Fig. 2b shows the number of antiprotons and protons transmitted through the gas cells and degrader as the gas mixture was changed to tune the energy of these particles. When we were able to demonstrate that enough low-energy antiprotons were available for trapping in 1986, we were given a second 24-h access to antiprotons two months later, to demonstrate that we could capture the slowed antiprotons. This demonstration experiment took place before there was time to purchase very much modern equipment. An ancient superconducting magnet was loaned to us by the University of Mainz. An ion trap was constructed in one day from glass-to-metal seals of unknown origin that were found abandoned in glass blower’s drawer. After testing in our own laboratory, we shipped the apparatus by air owing to time pressure and the delicate nature of the helium Dewar we had constructed. After the Dewar arrived broken in Geneva, we learned that our ‘‘air’’ shipment actually traveled across Europe in trucks of unknown suspension quality. It is hard to forget aiming a misbehaving hand torch at ‘‘borrowed’’ hard solder within a Dewar that dangled from a rope slung over a beam in a CERN hallway.
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F. 2. (a) Gas cells and time-of-flight apparatus used to measure the number of antiprotons slowed to keV energies in a degrader. (b) Number of transmitted antiprotons as a function of the gas mixture varied to decrease the energy of the antiprotons incident on the degrader window. (Taken from Gabrielse et al., 1989a.)
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F. 3. (a) Scale outline of the apparatus that first trapped antiprotons. (b) Annihilation signals from the first trapped antiprotons when they were released from the trap after being held for 1000 s. (Taken from Gabrielse et al., 1986.)
The repaired apparatus (Fig. 3a) was ready several days before antiprotons were scheduled to arrive at noon on Friday. Feverish computer programming was continuing (‘‘just one half hour more of Basic’’) to read out information about attempted antiproton captures in real time. Then, late Thursday evening, disaster struck. Routine tests, done dozens of times before, revealed that we could no longer apply high voltages to our trap electrodes without causing an arc inside the part of the Dewar that was cooled to 4 K. It was 12 h before the antiprotons were scheduled to arrive and the apparatus had never been warmed to room temperature and then cooled back to 4 K in less than several days. Half of our team went to bed convinced that we had failed.
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Given CERN’s ambivalence about the feasibility of the proposed experiments, a failure in this test experiment would clearly be a major setback, so a repair had to be attempted. As the cold apparatus was prematurely opened, water condensed on it and streamed out, despite the hot air directed in from three industrial-strength hair dryers. The breakdown point was located and fresh copper cables installed to handle the high voltages. After much mopping of water, drying and cleaning, we reassembled the apparatus during the night and began cooling by 10 a.m., Friday. We informed the LEAR control room that we would indeed be ready for our antiproton test by shortly after noon. Our euphoria was short-lived. Their reply indicated that CERN was not yet ready to deliver antiproton to us. Such particles were indeed available in the large Antiproton Accumulator (AA) storage ring at CERN, but the ‘‘kicker’’ device used to extract antiprotons from this ring had broken. It was most likely that we would leave CERN without receiving antiprotons. I explained the urgency of the situation (how far we had come, the stakes involved etc.), then stumbled off to bed exhausted and discouraged. The test experiment appeared doomed for some time, since LEAR was soon scheduled to be shut down for more than 1 year. Several hours later I was awakened. An accelerator magician at CERN had managed to make a backup ‘‘kicker’’ work. Soon LEAR was ready to try to send us intense pulses of antiprotons (about 10) in short bursts (200 ns). This ‘‘fast extraction’’ mode of operation was new at LEAR. The operators counted ‘‘five, four, three, two, one,’’ in various versions of English, and then pushed a newly installed green button with a loud ‘‘go.’’ After several hours of adjusting the timing electronics, we started to see clear and unmistakable signals that indicated we were able to trap antiprotons in our ion trap at energies 3 keV. The emotional roller coaster that this antiproton test experiment had become ended on a pronounced high. The LEAR operators and physicists from other experiments crowded around during the countdown. Applause broke out any time the histogram (see Fig. 3b) on the computer monitor indicated that antiprotons had been trapped and stored. A few antiprotons were held as long as 20 min, thereby establishing the feasibility of the proposed measurements. B. C C A This success turned CERN ambivalence into CERN enthusiasm. A connection to LEAR was constructed and dedicated to these experiments while LEAR was shut down for 1 year. Our new apparatus, installed in the fall of 1988, included a state-of-the-art superconducting solenoid and a carefully constructed ion trap suited to precise measurement of the antiproton mass.
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F. 4. (a) Outline of trap electrode surfaces and the location of cold trapped particles. (b) Typical potential well on axis.
The electrodes of the particle trap (Fig. 4a) were a stack of gold plated copper rings to which appropriate voltages could be applied. The electrodes resided within a 6-tesla magnetic field directed along the symmetry axis of the cylinders and produced by the superconducting solenoid. Charged particles make circular orbits around the direction of a magnetic field. Antiprotons and electrons in the trap thus orbit in circular trajectories rather than traveling radially outward to hit the trap electrodes. Before antiprotons are allowed into the trap, electrons are loaded into the small region indicated by the representation of the axial potential wells of the trap in Fig. 5. Internally generated electrons sent through the trap strike the flat plate at the left and dislodge adsorbed gas atoms. Other electrons collide with some of these atoms within the small region in such a way as to produce low-energy electrons in this location. Positive tens of volts on the electrodes at this location attract the negative electrons, keeping them from exiting at either end. The electrons in circular orbits about the magnetic field direction rapidly radiate their energy (typically in 0.1 s) and cool to the temperature of the surrounding electrodes near 4 K. The 6-MeV antiprotons in an intense pulse from LEAR crash through the flat plate electrode at the left of the trap, losing energy via collisions within the goldplated aluminum degrader. Approximately one in a few thousand of the antiprotons emerge with an energy (along the axis of the trap) of 3 keV. These can possibly be trapped using the voltages described here. Antiprotons that emerge from the aluminum with higher energy are not turned around by the modest 93 kV being applied to the electrode at the far right, so are annihilated upon hitting this electrode. Others lose too much energy by collisions within the aluminum, slow to a stop within the plate, and eventually annihilate. The flat degrader electode is kept slightly
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F. 5. (a) Cold trapped electrons in a small central trap well await the introduction of a pulse of hot antiprotons into the long ‘‘half well.’’ (b) When the maximum number of antiprotons are in the trap volume a high voltage is applied to complete the well. (c) On a much longer time scale hot antiprotons cool via collisions with cold electrons and eventually join the electrons in the small trap well.
positive while the antiprotons are passing through to keep secondary electrons from leaving the degrader and filling the trap. After the antiprotons enter the trap, but before they return to the entrance plate, this potential is changed to 93 kV to prevent them from striking the plate upon their return. To shut this door before the rapidly moving antiprotons can escape, this potential is changed in 20 ns. Figure 6 shows the relative number of antiprotons trapped as a function of the time that the door is shut and Fig. 7 shows how the number of antiprotons trapped is optimized by tuning the energy of the antiprotons incident on the degrader window (by changing the gas mixture). Captured antiprotons oscillate back and forth along the 12-cm length of the trap, with energies ranging between 0 and 3 keV, passing through the cold, trapped electrons. Just as a heavy bowling ball would eventually be slowed by collisions with light ping-pong balls, the antiprotons cool (in 100 s time we typically reserve for cooling) to thermal equilibrium with
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F. 6. Number of antiprotons trapped as a function of the time at which the trap is closed (below), with the injected antiproton pulse shown (above) on the same time scale.
F. 7. The energy of antiprotons that arrive at our apparatus at 6 MeV is tuned downward (by varying the amount of SF in the beam path) to maximize the number of trapped antiprotons.
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F. 8. Energy spectrum for hot trapped antiprotons. (Taken from Gabrielse et al., 1989b.)
the trapped electrons at 4 K. Cooled antiprotons now reside in the same small region of the trap as do the electrons and their energy is 10 times lower than the energy of the antiprotons that came from LEAR. Figure 8 shows the trapped antiproton energy distribution before electron cooling. The number of annihilations is measured as the potential on one end of the long well is reduced. After electron cooling the greatly narrowed spectra of Fig. 9 are observed. The energy width of these spectra is only an upper limit insofar as the space charge of the low-energy antiprotons allows some of them to escape at a well depth that is higher than their kinetic energy. The cooling process is remarkably efficient in that upwards of 95% of the antiprotons in the long trap are so cooled, as illustrated in Fig. 10. As many p as will fit, limited by space charge to about 0.4 million, end up in the small inner, harmonic well with approximately 10 cooling electrons. We trap up to 0.6 million antiprotons from a single LEAR pulse in inner and outer traps together (Fig. 11), with an efficiency (compared to the number of antiprotons measured to leave LEAR) shown in Fig. 12. To selectively expel the cooling electrons they are heated by driving them at frequencies that correspond to their preferred oscillation frequencies. When the voltages on the neighboring electrodes are lowered for a very short time the hot electrons leak out of the trap. The cold, heavy antiprotons remain and are subsequently cooled using cold resistors connected between various nearby electrodes. Residual antiproton motions induce currents through these resistors. Power dissipated in the resistors is thereby extracted from the antiproton motion, cooling the antiprotons into thermal equilibrium with the resistors, which are near 4 K.
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F. 9. Energy spectra for decreasing numbers of cold antiprotons. (Taken from Gabrielse et al., 1989b.)
F. 10. Fraction of antiprotons cooled into the center harmonic well as a function of cooling time with 4 ; 10 cooling electrons.
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F. 11. Energy spectrum of 0.6 million antiprotons trapped from a single 250-ns pulse of antiprotons from LEAR. Approximately 0.4 million (below) were able to fit in the small central trap well with the electrons that cooled them. An additional 0.2 million were cooled somewhat but remained in the long well (above). (Taken from Gabrielse et al., 1999.)
F. 12. Number of trapped antiprotons versus the number of 6 MeV antiprotons sent down our beamline as measured by the LEAR beam monitor; gives an efficiency of 5 ; 10\.
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When only one antiproton is needed for q/m measurements we slowly reduce the well depth of the small trap to let all but one antiproton escape. We monitor the cyclotron signal (we will discuss this presently). When only a few antiprotons remain we can resolve the signals from each antiproton because of the relativistic shift in their cyclotron frequencies. C. V B 5 ; 19\ It seems that we can store the cold antiprotons indefinitely. In one trial we held approximately 10 antiprotons for about 2 months before deliberately ejecting them (Gabrielse et al., 1990). We actually observed no antiproton loss at all, but imprecision in our knowledge of the number of antiprotons initially loaded into the trap limits the lifetime we can set to p 3.4 months
(1)
Despite the much lower energies (and hence much higher annihilation cross sections), this lifetime limit is longer than directly observed for high-energy antiprotons in storage rings for decays into all channels. Based upon calculated cross sections (Morgan and Hughes, 1970), our containment lifetime limit given here requires a background gas density 100 atoms/cm. For an ideal gas at 4.2 K this corresponds to a pressure 5 ; 10\ torr. The low pressure is attained by cooling the trap and its sealed container to 4.2 K. D. S A: M A D (AD) P We typically captured a pulse of antiprotons from LEAR and let it cool via its interaction with 4.2 K electrons over the following 100 s. For charge-tomass measurements we would then eject all but one antiproton. To facilitate the production and study of cold antihydrogen, however, the largest possible number of cold, trapped antiprotons is desired. To this end we demonstrated that once captured antiprotons had been cooled into an inner potential well it was possible to capture additional pulses of antiprotons from LEAR right over top of the first (Gabrielse et al., 1990). After the capture and cooling process represented in Fig. 5 is completed, one simply repeats it as many times as desired. The number of trapped antiprotons thus increases over what can be captured in a single pulse. The TRAP demonstration of ‘‘antiproton stacking’’ in a trap is the foundation upon which the new antiproton decelerator is based. Antiprotons delivered from LEAR were initially captured in the antiproton
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collector ring (ACOL), accumulated in the antiproton accumulator ring (AA), then slowed and cooled within the low energy antiproton ring (LEAR) and sent to our trap. When we demonstrated that antiprotons could instead be accumulated in a small trap, and much more inexpensively than in the large storage rings, the CERN management decided to shut down two of the three rings to save expenses. (The alternative was to entirely discontinue all low-energy antiproton physics.) The ACOL Ring was substantially modified to make the new antiproton decelerator (AD). The good news is that the experimental efforts to produce and precisely study cold antihydrogen can continue. The bad news is that the new facility brings additional challenges. To obtain the same number of cold, trapped antiprotons that we captured from LEAR in 250 ns will require us to accumulate (i.e., stack) antiprotons from the AD for an hour or more. E. T T A From our initial proposal at CERN, we stressed that our Penning trap was an intrinsically portable device. Trapped antiprotons could certainly be transported within our Penning trap if ever there was a good reason to do so. Although the compelling reason never emerged, we were nonetheless often asked about this possibility. Finally, in 1993 we used the opportunity of the delivery to our Harvard laboratory of a new superconducting solenoid constructed in California to make an experimental demonstration. In a Penning trap apparatus that was essentially identical to our antiproton apparatus, we transported stored electrons from California to Nebraska, then from Nebraska to Cambridge (see Fig. 13) (Tseng and Gabrielse, 1993). (The tale of an avoidable adventure in a Nebraska truck stop will not be retold here.) Electrons were used because they were much more readily available in California and Nebraska, but there is no doubt whatever that antiprotons could just as easily be transported if there had been a good reason. F. L D TRAP T O For many years, the techniques to obtain cold antiprotons, all of which were developed and demonstrated by TRAP, were used exclusively by TRAP. More recently, some of these techniques were duplicated by the PS-200 collaboration, which has since developed into ATHENA. The PS-200 motivation was to measure the gravitational acceleration of antiprotons using a time-of-flight technique. Most of a decade was spent puruing this goal but unfortunately this effort was not successful. As one would expect, the gravitational force of the earth on an antiproton is simply
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F. 13. Trapped electrons were transported from California to Nebraska, and then from Nebraska to Massachusetts. (Taken from Tseng and Gabrielse, 1993.)
too small compared to the electric force from stray charges in the apparatus. The conditional approval of PS-200 offered antiprotons only after the desired gravitational sensitivity in the time-of-flight measurements was demonstrated with negative ions. When the end of the LEAR program was in sight, however, permission was granted to try to duplicate the TRAP techniques for trapping and cooling antiprotons despite the absence of the promised demonstration. The trap used (Holzscheiter et al., 1996) was a larger version of the open endcap cylindrical trap used by TRAP (Gabrielse et al., 1989c). A higher trapping potential was also used. Up to a million antiprotons were trapped at the same time. The vacuum was not so good as that demonstrated by TRAP due to higher trap temperatures and the presence of warm surfaces in the vacuum system, and the antiproton storage time was of the order of 10 s rather than months. Antiprotons were eventually cooled with electrons — but not to 4 K. The only new feature of the PS-200 measurements was the surprising claim that antiprotons stored in poor vacuum annihilate much less rapidly than expected (Holzscheiter et al., 1996). However, very little quantitative study was done and the actual vacuum within the trapping volume was estimated rather than measured. Hopefully, this surprise will eventually be tested under more controlled conditions.
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G. L T A C For some years single component plasmas of elementary particles have been studied at temperatures down to 4 K. We have now managed to cool stored electrons down to 70 mK and below. So far, only one trapped electron (at a time) has been studied in detail at this low temperature, though there is no reason to expect any difficulties with larger numbers. Quantum jumps between Fock states of a 1-electron oscillator reveal the quantum limit of a cyclotron (Peil and Gabrielse, 1999). With a surrounding cavity inhibiting synchrotron radiation 140-fold, the jumps show a 13 s Fock state lifetime, and a cyclotron in thermal equilibrium with 1.6—4.2 K blackbody photons. These disappear by 80 mK, a temperature 50; lower than previously achieved with an isolated elementary particle. The cyclotron stays in its ground state until a resonant photon is injected. A quantum cyclotron offers a new route to measuring the electron magnetic moment and the fine structure constant. Although the demonstration was done with trapped electrons, there is every reason to believe that the same apparatus would also cool antiprotons to the same 70 mK temperature. Our ATRAP collaboration, an expanded version of TRAP formed to study cold antihydrogen, plans to pursue this option.
II. Million-Fold Improved Comparison of Antiproton and Proton Our proposal to improve the comparison of the charge-to-mass ratio of the antiproton and proton to 1 part in 10 was a surprise at CERN. One reason was that the proposed techniques were very unfamiliar at CERN. Another was that CERN had already invested in an experimental program with similar goals (CERN PS-189), employing a large Smith-type mass spectrometer. (Unfortunately, the angular acceptance of the spectrometer was so small that it was never able to make any antiproton measurements.) Over several years we were able to achieve the accuracy we had proposed and even to do an order of magnitude better. Our series of three mass measurements (Gabrielse et al., 1990, 1995, 1999) began as soon as we produced 4.2 K antiprotons and eventually improved the comparison of antiproton and proton by approximately 10. Figure 14 shows how comparison of the antiproton and proton improved in time, starting with the first observation of the antiproton, and concluding with the three measurements by TRAP. A. T PCT I The P in PCT stands for a parity transformation. Suppose we do a certain experiment and measure a certain outcome. As we do the experiment, we
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F. 14. (a) Accuracy in comparisons of p and p. (b) The measured difference between q/m for p and p (TRAP III) is improved more than ten-fold. (Taken from Gabrielse et al., 1999.)
also watch what the experiment and outcome look like in a mirror. We then build apparatus and carry out a second experiment that is identical to the mirror image of the first. If our reality is invariant under parity transformations P then we should obtain the outcome seen in the mirror for the second experiment. Until 1956 it was universally believed that reality was invariant under parity transformations. Then Lee and Yang noted that this basic tenet of physicists’ faith had not been tested for weak interactions — those interactions between particles that are responsible for beta decay of nuclei. Shortly after, Wu and collaborators, and then several other experimental groups in rapid succession, showed in fact that experiments and mirror image experiments produced strikingly different results when weak interactions were involved. The widespread faith that reality was invariant under parity transformations had clearly been misplaced. A new faith, that our reality was invariant under PC transformations, rapidly replaced the discredited notion. The ‘‘C’’ stands for a charge conjugation transformation, which for our purposes is a transformation in which particles are turned into their antiparticles. To test whether reality is invariant under PC transformations, a mirror image experiment is constructed as described here but this time all the particles within it are also changed into antiparticles. It was widely believed that these two different experiments could not be distinguished by their outcomes until Cronin and Fitch surprised everyone by using kaon particles to explicitly demonstrate that our reality is not invariant under PC transformations. The experiment has been repeated by different groups in different locations and related measurements are still being pursued.
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F. 15. Comparison of the accuracy of baryon, lepton and meson PCT tests
Now most physicists believe that reality is instead invariant under PCT transformations, the ‘‘T’’ standing for a time reversal transformation. The PCT invariance seems more well-founded insofar as theorists find it virtually impossible to construct a reasonable theory that violates this invariance. To experimentally test for PCT invariance, one again compares the outcomes of two experiments. This time one makes a movie of the goings on in a mirror image experiment in which the particles are switched to antiparticles. The second experiment is constructed to mimic what one sees in the movie when the movie is run backwards (i.e., when ‘‘time is reversed’’). In practice, the cyclotron oscillation frequencies of a proton and an antiproton oscillating in the same magnetic field would be identically the same if reality is invariant under PCT transformations. The antiprotonproton frequency comparisons discussed in what follows thus test whether reality is PCT invariant and establish that any departures from this
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invariance must be smaller than the experimental error bars. This comparison is by far the most precise test of PCT invariance done with baryons, particles made of three quarks or three antiquarks. The antiproton-toproton charge-to-mass ratio comparison thus joins an experiment with kaons (made of a quark and an antiquark) and a comparison of the magnetic moment of an electron and positron as one of the most precise experimental tests of whether our reality is invariant under PCT transformations. The improved comparison of the antiproton and proton which we discuss next strengthens our belief in PCT invariance. The various tests of PCT made by comparing the measured properties of particles and antiparticles are represented in Fig. 15. The stable particles and antiparticles in these tests come in several varieties that are important to distinguish. The proton (antiproton) is a baryon (antibaryon). The proton (antiproton) is composed of three quarks (antiquarks) bound together. The K mesons, like all meson particles and antiparticles, are instead composed of a quark and an antiquark bound together. The third variety of particle is the lepton; the electron and the positron are one example of lepton particle and antiparticle. Leptons are not made of quarks. In fact, so far as we know, leptons are perfect point particles. No experiment has yet been devised that gives evidence of any internal structure at all. It seems crucial to test PCT invariance in a sensitive way for at least one meson system, one baryon system, and one lepton system. The comparison of q/m for the antiproton and protons, discussed next, is the most sensitive test of PCT invariance with a baryon system by approximately a factor of million. The proposed comparison of the hydrogen and antihydrogen, discussed later, is of great interest in that it promises to give a much more sensitive test of PCT invariance with leptons and baryons. B. C C F The first measurement with extremely cold antiprotons was a greatly improved comparison of the charge-to-mass ratios of the antiproton and the proton. Figure 14 represents previous comparisons (with different techniques) along with the series of three TRAP measurements. The basic ideas for TRAP comparisons are illustrated in Figs. 16 and 17. An antiproton, proton, or H\ ion makes a circular orbit in a plane perpendicular to the magnetic field direction as shown. The orbit angular frequency is simply A related to the charge of the particle q, its mass m, and the strength of the magnetic field B, by q : B A m
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F. 16. (a) For TRAP I and TRAP II, antiprotons and protons are alternated in the trap. (b) For TRAP III, a simultaneously confined antiproton and H\ ion were interchanged between larger and smaller concentric orbits.
In the strong magnetic field we use, antiprotons, protons and H\ ions make approximately 90 million revolutions. We detect the 90-MHz signal (Fig. 19) induced across the RLC circuit attached to the electrodes of the trap (Fig. 19) using a refined version of an FM radio receiver, and measure the oscillation frequency. The points in Fig. 14b indicate the amount that the ratio of measured antiproton and proton cyclotron frequencies differs from 1. If the magnetic field does not change between measurements of for the A antiprotons and protons, the ratio of cyclotron frequencies can be interpreted as a ratio of q/m. In reality, an antiproton confined in a Penning trap follows the slightly more complicated orbits represented in Fig. 18. The small circular oscillation is the cyclotron motion discussed in the preceding except that the oscillation frequency is slightly modified by the trap to . This cyclotron A motion is superimposed on another circular orbit perpendicular to the magnetic field, called magnetron motion, at a much lower frequency . In K addition, the antiproton oscillates up and down along the direction of the
F. 17. The cyclotron motion induces a detectable voltage across an RLC circuit attached to a 4-segment ring. (Taken from Gabrielse et al., 1999.)
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F. 18. Superimposed cyclotron, axial and magnetron orbit of a particle in a perfect Penning trap. (Taken from Brown and Gabrielse 1986.)
magnetic field at the axial frequency . The desired cyclotron frequency X A is deduced from the three measurable frequencies , , and using an A X K invariance theorem which Lowell Brown and I discovered (Brown and Gabrielse, 1982), : ; ; (2) A A X K Much of the experimental effort goes into understanding and/or eliminating any imperfection in our apparatus that could change the measured frequencies even slightly. Nonetheless, each of the three measurable frequencies is slightly shifted from the ideal — by a misaligned magnetic field for example. Fortunately, the invariance theorem holds even when the three measurable frequencies are shifted by this misalignment and the other largest sources of frequency shifts. Depending on the accuracy of the measurements, approximations to this general expression can sometimes be used. It is essential that the magnetic field B not change between the time the proton frequencies are measured and the antiproton frequencies are measured. This is challenging in an accelerator environment in which magnetic fields in the accelerator rings are being changed dramatically as often as every couple of seconds. One important aid for all three of our measurements is a superconducting solenoid that not only makes the strong magnetic field but also senses when this field fluctuates and cancels the fluctuation at the location of our trapped particles. This invention (Gabrielse et al., 1988, 1991) is now patented (Gabrielse and Tan, 1990) because of applications in magnetic resonance imaging and ion cyclotron resonance. It illustrates the interplay between ‘‘pure science’’ and technology. Technology is pushed so hard in the pursuit of fundamental physics goals that practical applications with wider applicability can emerge.
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C. TRAP I: O H A C O H P In our first measurement (Gabrielse et al., 1990), the cyclotron frequency of the center-of-mass of approximately 100 antiprotons was compared to that of protons. This measurement showed that the charge-to-mass ratios of the antiproton and proton are the same to within 4 ; 10\, which is 40 ppb. The self-shielding solenoid kept the magnetic field drift from being a major factor at this accuracy. The improvement over earlier comparisons of antiprotons and protons using exotic atoms was more than a factor of 1000. D. TRAP II: A O A O P The second mass measurement compared a single trapped antiproton to a single trapped proton (Gabrielse et al., 1995). The radio signal of single antiprotons was detected nondestructively (Fig. 19a). Owing to our high resolution, this measurement provided a spectacular illustration of special relativity (Fig. 19b,c) at eV energies insofar as the antiproton’s cyclotron frequency qB : A m
(3)
depends upon the familiar relativistic factor : (1 9 v/c)\ : E/mc.
F. 19. Special relativity shifts the cyclotron frequency of a single trapped p as its cyclotron energy is slowly and exponentially dissipated in the detector. Cyclotron signals for three subsequent times in (a) have frequencies highlighted in the measured frequency versus time points in (b). A fit to the expected exponential has small residuals (c) and gives the cyclotron frequency for the limit of no cyclotron excitation. (Taken from Gabrielse et al., 1995.)
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This second measurement showed that the charge-to-mass ratios of the antiproton and proton differed by less than 1 ; 10\. The 1 ppb uncertainty arose almost entirely because the antiproton and proton have opposite sign of charge, and thus require externally applied trapping potentials of opposite sign. After the cyclotron frequency of one species was measured it would be ejected from the trap, the trapping potential would be reversed, and the second species loaded for measurement. Reversing the applied potential does not completely reverse the potential experienced by a trapped particle (e.g., due to the path effect on the inner surfaces of the trap electrodes). During the measurements of their respective cyclotron frequencies, the antiproton and proton thus reside at slightly different locations, separated by up to 45 m in this case. If the nearly homogeneous magnetic field differs slightly between the broad locations, the measured for the different species A differs even if the charge-to-mass ratios do not.
E. TRAP III: S T A H\ I The third and final measurement utilized a single antiproton and a single H\ ion trapped at the same time (Gabrielse et al., 1999b). Both had the same sign of charge and were confined simultaneously, eliminating the systematic effect that limited the previous measurement. To keep the two from interfering with each other, one particle was always ‘‘parked’’ in a large cyclotron orbit. Measurements were made of the cyclotron frequency of the other particle in a small orbit at the center of the large orbit. The electron-to-proton mass ratio, the hydrogen binding energy, and the H\ electron affinity were well enough known that no additional error was contributed by substituting an H\ ion for a proton. In the initial proposal to CERN I suggested that the most accurate q/m comparisons would come by comparing an antiproton and an H\ ion. During the TRAP I and TRAP II measurements we speculated occasionally about whether H\ ions might be formed during antiproton loading, but never got around to looking until we encountered the unavoidable disruption of an H\ ion loaded with a single antiproton. When we did look we found that we could always load negative ions with antiprotons. By reducing the number of cooling electrons we were able to typically load of order 500 H\ at the same time as antiprotons, presumably as hydrogen atoms liberated from the degrader picked up cooling electrons. The electrons then had to be ejected quickly to avoid collisional stripping of the H\. Loading a single antiproton and H\, and preparing them for measurement, typically required 8 h.
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F. 20. (a) Special relativity shifts the cyclotron frequency of an H\ as our detector slowly removes its energy. (b) Similar signals from a p kept simultaneously in a large orbit by three pulsed excitations. (Taken from Gabrielse et al., 1999.)
This mass measurement established that q q ( p ) ( p) : 90.999 999 999 91 (9) m m
(4)
The accuracy exceeds that of the second TRAP measurement by more than a factor of 10 (Fig. 14b), and improves upon the earlier exotic atom measurements by a factor of 6 ; 10. At a fractional accuracy f : 9 ; 10\ : 90 ppt there is thus no evidence for PCT violation in this baryon
F. 21. Alternating cyclotron decays of p and p (from H\) superimposed upon a slightly drifting magnetic field. (Taken from Gabrielse et al., 1999.)
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system. This is the most precise test of PCT invariance with a baryon system by many orders of magnitude as is illustrated in Fig. 15. The comparison of p and H\ also uniquely establishes the limit r&\4; SA 10\, where r&\ : ( p ) f /(mc) quantifies extensions to the standard SA A model that violate Lorentz invariance, but not PCT (Bluhm et al., 1998). Such violations would make ( p ) and (H\) differ in addition to the A A familiar mass and binding energy corrections, without making q/m different for p and p. Our apparatus was clearly capable of a higher accuracy, perhaps even another factor of 10, but LEAR closed down before these measurements could be pushed to their limit.
III. Opening the Way to Cold Antihydrogen A. C A Antihydrogen is the simplest of antimatter atoms, being formed by a positron in orbit around an antiproton. The pursuit of cold antihydrogen began some time ago, long before a few antihydrogen atoms traveling at nearly the speed of light (Baur et al., 1996) generated great publicity. Unlike the extremely energetic antihydrogen, cold antihydrogen that can be confined in a magnetic trap for highly accurate laser spectroscopy offers the possibility of comparisons of antihydrogen and hydrogen at an important level of accuracy (Fig. 22). Gravitational measurements can also be contemplated (Gabrielse, 1988) because the antimatter atom is electrically neutral
F. 22. Relevant accuracies for the precise 1s—2s spectroscopy of antihydrogen are compared to the most stringent tests of PCT invariance carried out with the three types of particles — mesons, leptons, and baryons.
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and hence not very sensitive to electric and magnetic forces. In my 1986 Erice lecture (Gabrielse, 1987), shortly after we had trapped antiprotons for the first time (Gabrielse et al., 1986), I discussed the possibility of forming cold antihydrogen from cold, trapped antiprotons and positrons. I concluded: For me, the most attractive way . . . would be to capture the antihydrogen in a neutral particle trap. . . . The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time.
I was inspired by the attempts to confine neutrons and the first trapping of atoms (Migdall et al., 1985). During the time that we were developing the techniques to make cold antiprotons and positrons available for the production of cold antihydrogen, the trapping of atoms including hydrogen (Cesar et al., 1996) also was becoming common. The formation of cold antihydrogen requires first that its ingredients, cold antiprotons and cold positrons, be available in the extremely high vacuum that is desirable for accumulating these particles and for storing cold antihydrogen. The first half of this chapter focused upon the techniques required to slow, trap, cool, and accumulate 4.2 K antiprotons. In the following section we summarize the availability of 4.2 K positrons. The next step on the path to cold antihydrogen is to bring the cold ingredients together. The ‘‘nested Penning trap’’ (Section III.C), proposed for this purpose, has since been demonstrated. Section III.D summarizes an experiment in which we stored cold antiproton and positrons for the first time in either a nested trap or at 4.2 K — the closest approach yet to cold antihydrogen. Several different recombination mechanisms (Section III.E) will be investigated whereby cold antiprotons and cold positrons could recombine to form cold antihydrogen. B. 4.2 K P E G V Cold positrons are the other required ingredient for cold antihydrogen. Since only a few cold positrons had ever been confined in the extremely high vacuum that is desirable for cold antihydrogen experiments we set about capturing large numbers of cold positrons in this environment. We first used electronic damping (Haarsma et al., 1995). Then we discovered and developed a new technique in which we produced Rydberg positronium and ionized it within a trap. This approach yielded a vastly improved accumulation rate (Estrada et al., 2000), up to 10 positrons per hour for a 2.5 mCi Na source. Figure 23a shows the simplicity of the apparatus. A thin transmission moderator, a 2-m tungsten crystal W(110), is added to an open access
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F. 23. The electrodes of an open access Penning trap (a) are biased to produce an electric potential (b) and field (c) along the central axis that confines e> (solid curves) or e\ (dashed curves). A 5.3 T magnetic field parallel to this symmetry axis guides fast positrons entering from the left through the thin crystal and towards the thick crystal. (Taken from Estrada et al., 2000.)
Penning trap (Gabrielse et al., 1989c) at one end. A thick reflection moderator, a 2-mm tungsten crystal W(100), is added at the other. Positrons from the radioactive source, traveling along field lines of a strong magnetic field (5.3 T), pass through the transmission moderator to enter the trap from the left. The electric field of the trap ionizes the Rydberg positronium, which then accumulates in the location shown. Figure 24 shows the accumulation of more than a million positrons. We expect soon to increase the accumulation rate dramatically by simply increasing the size of the 2.5 mCi source to 150 mCi. The crucial time period for positron accumulation at the AD is of order of an hour, the amount of time it will take to stack a reasonable number of antiprotons in a trap. C. D N P T The production of cold antihydrogen requires that antiprotons and positrons be allowed to interact. The nested Penning trap (Fig. 25) proposed for this purpose (Gabrielse et al., 1988) was demonstrated experimentally (Hall and Gabrielse, 1996) with protons and electrons. The demonstration shows that a nested Penning trap should allow antiprotons and positrons to interact with a low relative velocity, as illustrated in Fig. 26. Without cooling electrons in the central well, hotter antiprotons retain the higher energy distributions, illustrated on the right-hand side of the figure. With cooling electrons in the well the antiproton energy spectrum cools dramatically as shown on the left-hand side of the figure.
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F. 24. (a) Accumulation of 1.1 million positrons and (b) their electrical signal. (Taken from Estrada et al., 2000.)
D. C C A E B In the last week of LEAR’s operation we got closer to cold antihydrogen than anyone has ever been before (Gabrielse et al., 1999a). Figure 27 shows the first simultaneous confinement of 4 K antiprotons and positrons, and Fig. 28 shows trapped positrons heated by trapped antiprotons.
F. 25. Scale outline of the inner surface of the electrodes (a), and the potential wells (b), for the nested Penning trap. (Taken from Hall and Gabrielse, 1996.)
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F. 26. Energy spectrum of the hot protons (right-hand side) and the cooled protons (left-hand side), obtained by ramping the potential on electrode K downward and counting the protons that spill out to the channel plate. The hot and cooled spectra for 4 initial proton energies are summed. (Taken from Hall and Gabrielse, 1996.)
F. 27. (a) Electrode cross sections and the initial position of the simultaneously trapped p and e>. (b) Trap potential on the symmetry axis. Fits (solid curves) to the electrical signals from simultaneously trapped e> (c) and p (d) establish the number of trapped particles. (Taken from Gabrielse et al., 1999a.)
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F. 28. The signal from cold trapped positrons (below) changes dramatically (above) when heated antiprotons pass through cold positrons in a nested Penning trap, showing the interaction of antiprotons and positrons. (Taken from Gabrielse et al., 1999a.)
E. R M To form antihydrogen, a positron and antiproton must have kinetic energy to approach each other, and this energy must be removed to form an atomic bound state. Energy and momentum cannot be conserved unless a third particle is involved. Different antihydrogen formation processes provide different ways to conserve energy and momentum. Of course, this recombination must occur within the extremely good vacuum demonstrated with antiprotons or else the antihydrogen will not live long enough to be studied to an interesting accuracy. Long ago we compared different mechanisms by which cold antihydrogen might be formed in a Penning trap (Gabrielse et al., 1988), suggesting that a ‘‘nested Penning trap’’ might provide the most useful environment. Three of the antihydrogen formation processes that have been studied (and possibly one hybrid) are attractive candidates. A very nice feature of the nested Penning trap we have demonstrated is that it gives a very easy way to select one process from another, and to rapidly switch between them within the same apparatus. A shallow central trap will select a three-body recombination process. A deep central trap will select radiative recombination, whose rate can be enhanced by switching on an appropriate laser. We will first consider the processes that look most attractive (Section III.E.1), then briefly look at other processes (Section III.E.2). 1. Selecting Processes Within a Nested Penning Trap Within a shallow nested Penning trap, the electric field is very low. Antihydrogen initially formed in a high Rydberg state will be less easily
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ionized when the electric field is low. (The positron plasma will screen the electric field along the axis of the magnetic field, but not in the radial direction.) The dominant process should then be the three-body processes p ; e> ; e> ; H ; e>
(5)
because this promises to have a much higher rate than any other process (Gabrielse et al., 1988). De-excitation to the ground state takes some time (Glinsky and O’Neill, 1991; Fedichev, 1997), but not nearly so long as was originally thought (Menshikov and Fedichev, 1995). In a shallow central well it should be possible to use 10 antiprotons at 4 K, submerged within an extended plasma of 4 K positrons at a density of 10/cm. (This density is lower by 10 than what we have already achieved in a deeper well.) Under these conditions, except with no magnetic field, the calculated recombination rate is an astounding 10/s (Gabrielse et al., 1988). A strong magnetic field (e.g., from the trap containing antiprotons and positrons) would reduce this high rate (Glinsky and O’Neill, 1991) by approximately a factor of 10, and an electric field (also part of the trap) also has some effect (Menshikov and Fedichev, 1995), but the rate is still higher than for any other recombination processes. The related three-body recombination process p ; e> ; e\ ; H ; e\
(6)
has also been mentioned (Gabrielse et al., 1988). Within a deeper nested Penning trap, there will be a much stronger electric field in the central region where antiprotons and positrons interact. The rapid three-body mechanism (Eq. 5) should thus be essentially turned of since antihydrogen initially formed in a high Rydberg state will be ionized before de-excitation occurs. The slower radiative recombination process would then be selected, and it could be enhanced by the illumination of an appropriate laser. Radiative recombination can be thought of as producing an excited hydrogen atom that radiates a photon to conserve energy and momentum, p ; e> ; H ; h
(7)
This process suffers from a lower rate because it takes approximately a nanosecond to radiate a photon, much longer than the duration of the interaction between a p and an e>, even when these particles have an energy low enough to correspond to 4 K. For 10 antiprotons at 4 K within a 4 K positron plasma of density n : 10/cm (a positron density that we have C already realized), the estimated recombination rate (Gabrielse et al., 1988)
COMPARING THE ANTIPROTON AND PROTON
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is 3 ; 10/s. The radiative recombination process has the attractive feature that most of the antihydrogen is formed in the ground state. If we succeed in increasing the positron density to 10/cm, this rate would be 100 times higher. The radiative recombination rate can be increased by stimulating the process with a laser, p ; e> ; h ; H ; 2h
(8)
Laser-stimulated, radiative recombination has been observed in merged beams (Schramm et al., 1991; Yousif et al., 1991) but has yet to be observed in a trap. It has the useful diagnostic feature that the formation rate will increase sharply as the laser is tuned through resonance. For cold positrons and antiprotons, the two transitions that are easily accessible with relatively high power lasers are to n : 3 at 820.6 nm, and to n : 11 at 11,032 nm (Gabrielse et al., 1988). Stimulating to n : 11 has the higher rate, and subsequent radiation will take 99% of the population to the ground state. A N O laser or a CO laser with a modest and manageable power of 10 W/mm will nearly saturate the transition. Nearly 2% of the antiproton should be converted to antihydrogen at this power for a positron density of 10/cm. We use this low positron density because here a hybrid process could be even more attractive. The rate would be much higher if a three-body recombination to approximately 4 kT below the ionization limit was followed by a laserstimulated recombination to n : 11. 2. Other Formation Processes Another antihydrogen formation process has been extensively discussed. The process uses positronium, the bound state of an electron and a positron, with the electron carrying off the excess (Humbertson et al., 1987). p ; e>e\ ; H ; e\
(9)
One advantage is that the antihydrogen is produced preferentially in the lowest states. When antiprotons are not available, the charge-conjugate process can be studied (recombining protons and positronium to form hydrogen and positrons). This was recently observed (Merrison et al., 1997) using a beam of protons. Unfortunately, comparable quantities of antiprotons are very difficult to arrange. It should be possible to increase the recombination rate by initially exciting the positronium atom with a laser
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(Charlton, 1990). Nonetheless, the disadvantage of the recombination using positronium is that the projected rate is still extremely low for both realizable numbers of antiprotons and existing positronium beams. Estimates place the production rate at perhaps 100 atoms per day for continuous production at the AD, or perhaps 2 antihydrogen atoms per pulse of 10 positrons if this could be arranged (Surko et al., 1997). With such a low rate, and an apparatus somewhat different from what is required for the other formation processes, we do not plan to pursue this approach. However, we are intrigued by the possibility that the high Rydberg positronium we have already realized may allow us to resurrect it. Finally, there are more recent suggestion. Charge exchange processes may provide a route to the formation of cold antihydrogen (Hessels et al., 1997). Recombination of electrons and positive ions aided by an electric field, has recently been observed (Wesdorp et al., 2000); this technique may be applicable to antihydrogen formation as well. We are investigating both routes. F. F A substantial Antiproton Decelerator (AD) facility is nearing completion at CERN to carry forward experiments with low energy antiproton. It looks like the AD will be delivering useful numbers of antiprotons in fall 2000, and meeting (or even exceeding) its design specifications in summer of 2001. Two large collaborations have formed to produce and study cold antihydrogen. Our TRAP collaboration expanded to become ATRAP (ATRAP, 2000). Our competition is ATHENA (ATHENA, 2000), which grew out of the attempt mentioned earlier to measure the gravitational acceleration of antiprotons. In July, our ATRAP colloboration announced the first trapping of antiprotons from the AD, the first electron-cooling of these trapped antiprotons, and began stacking antiprotons in a trap. ATHENA apparatus should be ready soon. Experiments to build upon the TRAP foundation have just begun. Despite some claims to the contrary, antihydrogen production is a very difficult undertaking that will take some time. Estimated production rates are dautingly low even though it should be possible to detect single antihydrogen atoms, by detecting the pions from antiproton annihilation and the gammas from positron annihilation. New techniques must be devised to cool antihydrogen to the low energies required for trapping, since current hydrogen cooling techniques involve collisions with cold surfaces that would cause the antihydrogen to be annihilated. It also remains to be demonstrated that useful spectroscopic measurements can be done with only a few antihydrogen atoms in a trap. The cause is worthy but many challenges remain.
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IV. Technological Spinoffs In the pursuit of fundamental measurements it is not uncommon to push technology very hard with the result that unpredicted new techniques and devices emerge. I mention two examples from our antiproton studies: ( The charge-to-mass measurements required a very stable magnetic field, but were performed in an accelerator hall where the cycle of the Proton Synchrotron (PS) caused the magnetic field in our experiment to make a large change every 2.4 s. Our solution was to invent a self-shielding superconducting solenoid (Gabrielse and Tan, 1988). We demonstrated (Gabrielse et al., 1991) that this addition reduced the size of the fluctuations in the magnetic field by a factor of 150 or more. Without this invention the extremely accurate q/m measurements would not have been possible. The same invention makes it possible to do more accurate ion cyclotron resonance (ICR) measurements (to analyze the composition of potential drugs, etc.) and nuclear magnetic resonance. The self-shielding solenoid is now patented (Gabrielse and Tan, 1990) and available commercially. ( The open endcap Penning trap (Gabrielse et al., 1989c) we developed to allow antiprotons to enter our trap will also provide ready access for any other charged particle, laser beams, etc. This design is increasingly being used as the cell design of choice for ICR measurements
V. Acknowledgments It was an honor and pleasure to lead the TRAP collaboration (Table I); a succession of gifted students and postdocs immersed themselves in this work. I am especially grateful to early collaborators, Kells and Trainor, and my long time collaborator, Kalinowsky, for their courage in embarking upon an adventure few thought would succeed or even be supported. Without the unique LEAR facility at the CERN laboratory, the antiproton experiments would not have been possible. We profited from the help and personal encouragement of the LEAR staff, the SPSLC, the research directors and the directors general of CERN. Most of the support for the antiproton experiments came from the NSF and AFOSR of the USA, with an initial contribution from NIST. The German contribution to these experiments came from the BMFT. The positron experiments were supported by the ONR of the USA.
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VI. References ATHENA (2000). httpp://athena.web.cern.ch/athena/. ATRAP (2000). http://hussle.harvard.edu/:atrap. Baur, G. et al. (1996). Production of antihydrogen. Phys. Rev. B 368:251. Bluhm, R., Kostelecky, V. A., and Russell, N. (1998). CPT and Lorentz tests in Penning traps. Phys. Rev. D57, 3932—3943. Brown, L. S. and Gabrielse, G. (1982). Precision spectroscopy of a charged particle in an imperfect Penning trap. Phys. Rev. A 25:2423—2425. Brown, L. S. and Gabrielse, G. (1986). Geonium. Theory: Single Electrons and Ions in a Penning trap. Rev. Mod. Phys. 58:233—311. Cesar, C. L., Fried, D. G., Killian, T. C., Polcyn, A. D., Sandberg, J. C., Yu, I. A., Greytak, T. J., Kleppner, D., and Doyle, J. (1996). Two-photon spectroscopy of trapped atomic hydrogen. Phys. Rev. L ett. 77:255. Charlton, M. (1990). Antihydrogen production in collisions of antiprotons with excited states of positronium. Phys. Rev. A 143:143. Estrada, J., Roach, T., Tan, J. N., Yesley, P., Hall, D. S., and Gabrielse, G. (2000). Field ionization of strongly magnetized Rydberg positronium: A new physical mechanism for positron accumulation. Phys. Rev. L ett. 84:859—862. Fedichev, P. O. (1997). Formation of antihydrogen atoms in an ultra-cold positron-antiproton plasma. Phys. Rev. A 226:289—292. Gabrielse, G. (1987). Penning traps, masses and antiprotons, in Fundamental Symmetries, P. Bloch, P. Paulopoulos, and R. Klapisch, eds., New York: Plenum, p. 59—75. Gabrielse, G. (1988). Trapped antihydrogen for spectroscopy and gravitation studies: Is it possible? Hyper. Int. 44:349—356. Gabrielse, G. (1992). Extremely cold antiprotons. Sci. Amer., December, 78—89. Gabrielse, G., Fei, X., Helmerson, K., Rolston, S. L., Tjoelker, R. L., Trainor, T. A., Kalinowsky, H., Haas, J., and Kells, W. (1986). First capture of antiprotons in a penning trap: A keV source. Phys. Rev. L ett. 57:2504—2507. Gabrielse, G., Fei, X., Orozco, L. A., Rolston, S. L., Tjoelker, R. L., Trainor, T. A., Haas, J., Kalinowsky, H., and Kells, W. (1989a). Barkas effect observed with antiprotons and protons. Phys. Rev. A 40:481—484. Gabrielse, G., Fei, X., Orozco, L. A., Tjoelker, R. L., Haas, J., Kalinowsky H., Trainor, T. A., and Kells, W. (1989b). Cooling and slowing of trapped antiprotons below 100 meV. Phys. Rev. L ett. 63:1360—1363. Gabrielse, G., Fei, X., Orozco, L. A., Tjoelker, R. L., Haas, J., Kalinowsky, H. Trainor, T. A., and Kells, W. (1990). Thousand-fold improvement in the measured antiproton mass. Phys. Rev. L ett. 65:1317—1320. Gabrielse, G., Haarsma, L., and Rolston, S. L. (1989c.). Open-endcap Penning traps for high precision experiments. Intl. J. Mass Spec. and Ion Phys. 88:319—332. Gabrielse, G., Hall, D. S., Roach, T., Yesley, P., Khabbaz, A., Estrada, J., Heimann, C., and Kalinowsky, H. (1999a). The ingredients of cold antihydrogen: Simultaneous confinement of antiprotons and positrons at 4 K. Phys. L ett B 455:311—315. Gabrielse, G., Khabbaz, A., Hall, D. S., Heimann, C., Kalinowsky, H., and Jhe, W. (1999b). Precision mass spectroscopy of the antiproton and proton using simultaneously trapped particles. Phys. Rev. L ett. 82:3198—3201. Gabrielse, G., Tan, J. N., Clateman, P., Orozco, L. A., Rolston, S. L., Tseng, C. H., and Tjoelker, R. L. (1991). A superconducting solenoid system which cancels fluctuations in the ambient magnetic field. J. Mag. Res. 91:564—572.
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Gabrielse, G., Phillips, D., Quint, W., Kalinowsky, H., Rouleau, G., and Jhe, W. (1995). Special relativity and the single antiproton: forty-fold improved comparison of P and P charge-tomass ratios. Phys. Rev. L ett. 74:3544—3547. Gabrielse, G., Rolston, S. L., Haarsma, L., and Kells, W. (1988). Antihydrogen production using trapped plasmas. Phys. L ett. A 129:38—42. Gabrielse, G. and Tan, J. N. (1988). Self-shielding superconducting solenoid systems. J. Appl. Phys. 63:5143—5148. Gabrielse, G. and Tan, J. (1990). US patent 4974113, issued 27 Nov. 1990. Glinsky, M. E. and O’Neil, T. M. (1991). Guiding center atoms: Three-body recombination in a strongly magnetized plasma. Phys. Fluids B 3:1279. Haarsma, L. H., Abdullah, K., and Gabrielse, G. (1995). Extremely cold positrons accumulated electronically in ultrahigh vacuum. Phys. Rev. L ett. 75:806—809. Hall, D. S. and Gabrielse, G. (1996). Electron-cooling of protons in a nested Penning trap. Phys. Rev. L ett. 77:1962—1965. Hessels, E. A., Homan, D. M., and Cavagnero, M. J. (1997). Two-stage rydberg charge exchange: An efficient method for production of antihydrogen. Phys. Rev. A 57:1668. Holzscheiter, M. H., Feng, X., Goldman, T., King, N. S. P., Nieto, M. M., and Smith, G. A. (1996). Are antiprotons forever? Phys. L ett. A 214:279. Men’shikov, L. I. and Fedichev, P. O. (1995). Theory of elementary atomic processes in an ultracold plasma. Zh. Eksp. Teor. Fiz. 108:144. (JETP 81, 78). Merrison, J. P., Bluhme, H., Chevallier, J., Deutch, B. I., Hvelplund, P., Jorgensen, L. V. Knudsen, H., Poulsen, M. R., and Charlton, M. (1997). Hydrogen formation by proton impact on positronium. Phys. Rev. L ett. 78:2728—2731. Migdall, A. L., Prodan, J. V., Phillips, W. D., Bergeman, T. H., and Metcalf, H. J. (1985). First observation of magnetically trapped neutral atoms. Phys. Rev. L ett. 54:2596. Morgan, D. L., Jr. and Hughes, V. W. (1970). Atomic processes involved in matter-antimatter annihilation. Phys. Rev. D 2:1389. Peil, S. and Gabrielse, G. (1999). Observing the quantum limit of an electron cyclotron: QND measurements of quantum jumps between Fock states. Phys. Rev. L ett. 83:1287—1290. Schramm, U., Berger, J., Grieser, M., Habs, D., Jaeschke, E., Kilgus, G., Schwalm, D., Wolf, A., Neumann, R., and Schuch, R. (1991). Observation of laser-induced recombination in merged electron and proton beams. Phys. Rev. L ett. 67:22. Surko, C. M., Greaves, R. G., and Charlton, M. (1997). Stored positrons for antihydrogen production. Hyper. Int. 109:181—188. Tseng, C. and Gabrielse, G. (1993). Portable trap carries particles 5000 kilometers. Hyper. Int. 76:381—386. Wesdorp, C., Robicheaux, F., and Noordam, L. D. (2000). Field-induced electron-ion recombination, a novel route towards neural (anti-) matter. Phys. Rev. L ett. 84:3799—3802. Yousif, F. B., Van der Donk, P., Kucherovsky, Z., Reis, J., Brannen, E., Mitchell, J. B. A., and Morgan, T. J. (1991). Experimental observation of laser-stimulated radiative recombination. Phys. Rev. L ett. 67:26.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 45
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES TIMOTHY CHUPP and SCOTT SWANSON Departments of Physics and Radiology, University of Michigan Ann Arbor, Michigan 48109 I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Historial Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Nuclear Polarization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Optical Pumping and Spin Exchange . . . . . . . . . . . . . . . . . . . . . 1. He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Xe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Lasers for Spin Exchange Pumping . . . . . . . . . . . . . . . . . . . . 4. Optical Pumping with Laser Diode Arrays . . . . . . . . . . . . . . B. Metastability Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Lasers for Metastability Exchange . . . . . . . . . . . . . . . . . . . . . C. Polarization and Delivery Systems . . . . . . . . . . . . . . . . . . . . . . . III. Basics of Magnetic Resonance Imaging (MRI) . . . . . . . . . . . . . . . . A. Nuclear Magnetic Resonance (NMR) . . . . . . . . . . . . . . . . . . . . B. One-Dimensional Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Magnetic Resonance Imaging and k-Space . . . . . . . . . . . . . . . . D. Imaging Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Selective Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Back Projection Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Gradient Echo Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Chemical Shift Imaging (CSI) . . . . . . . . . . . . . . . . . . . . . . . . E. Contrast in Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . F. Low Field Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Imaging Polarized Xe and He Gas . . . . . . . . . . . . . . . . . . . . . . A. Magnetic Resonance Imaging of Polarized Gas: General Concerns 1. Sampling of the Magnetization . . . . . . . . . . . . . . . . . . . . . . . 2. Diffusion and k-Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Airspace Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Injection of He and Xe Carriers . . . . . . . . . . . . . . . . . . . . . . V. NMR and MRI of Dissolved Xe . . . . . . . . . . . . . . . . . . . . . . . . . A. Spectroscopy of Xe in Vivo . . . . . . . . . . . . . . . . . . . . . . . . . . B. Xe Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Lung Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Time Dependence and Magnetic Tracer Techniques . . . . . . . . . 1. Dynamics of Laser-Polarized Xe in Vivo . . . . . . . . . . . . . . VI. Conclusions — Future Possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Copyright 2001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003845-5/ISSN 1049-250X/01 $35.00
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Timothy Chupp and Scott Swanson Abstract: The field of medical imaging with polarized rare gases, just five years old, has brought optical scientists together with medical researchers to perfect techniques and pursue new opportunities for biomedical research. This review, written for the likely reader of these volumes, aims to present the field from several perspectives. The historical perspective shows how applications of nuclear polarization for experiments in nuclear and particle physics led to techniques for production of large quantities of highly polarized He that are increasingly reliable and economical. The atomic/optical physics perspective details the underlying processes of optical pumping, polarization, and relaxation of the rare gases. The biomedical perspective describes work to date and the potential applications of imaging in medicine and research.
I. Introduction Five years ago, a short article was published in the journal Nature showing magnetic resonance images (MRI) of Xe gas that had filled the airways of an excised mouse lung (Albert et al., 1994). The images were acquired at SUNY, Stony Brook, on Long Island, NY. But the gas, prepared by laser optical pumping methods, in Princeton, New Jersey, was transported over 100 km by car in a small glass cell immersed in a cup of liquid nitrogen. (The gas was ‘‘polarized’’ in Princeton to provide 10,000 times greater NMR signal per atom than produced by ‘‘brute force.’’ This compensated for the 10,000 times lower concentration of gas.) Reading the Nature article led many in the field of laser optical pumping to turn their attention to the new possibilities, and many radiologists sought out laser physicists as collaborators to help develop potential biomedical applications. Today, physicists, radiologists, neuroscientists, medical researchers, and clinicians are working together in teams around the world. The promise of entirely new ways to use NMR and MRI information from He and Xe images of gas in the lungs and of xenon dissolved in lung, heart, and brain tissues has attracted the attention of scientists and physicians, as well as the pharmaceutical industry. The promise is that this marriage of laser/optical physics and medical imaging will provide new ways to study and map brain function, measure physiological parameters, and diagnose diseases of the lungs, heart, and brain that depend on the flow of gas and blood through the vital organs. In Figs. 1 and 2 we show magnetic resonance images produced with laser polarized He and Xe. In Fig. 1, a series of consecutive images of a slice through the human lungs shows the flow of gas into the air spaces after a breath is taken and exhaled (Saam et al., 1999). This moving picture of gas flow is called a ventilation image. Ventilation images made with scintigraphy of radioactive gas (usually Xe) are used to assess lung function and find nonfunctioning portions of the lung. Combined with measures of blood flow through the lung, ventilation scans help diagnose a variety of lung diseases, such as pulmonary embolism, with moderate specificity. (The efficacy of a diagnostic technique is characterized by its sensitivity and
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F. 1. A He ventilation image: a series of images taken at 0.8-s intervals after a breath of laser polarized He is inhaled while the human subject is in the MRI scanner. The gas starts in the trachea, then moves out and down to the lower parts of the lung. The last frame shows the beginning of exhalation as the upward motion of the diaphragm expels gas from the lungs. Images courtesy of Brain Saam. Used with permission.
specificity. Sensitivity is essential to discover a malady while specificity is required to determine the exact problem and the course of treatment.) In Fig. 2 (see also Color Plate 1), we show images of Xe gas in the lung and dissolved in tissue and blood of a rat that had been breathing a polarized xenon-oxygen mixture. In contrast to helium, xenon crosses the blood-gas barrier in the lungs, dissolves in blood, and is carried to distal organs where it diffuses into tissue as the blood flows through capillaries from artery to vein. The NMR frequencies of Xe differ by about 200 ppm for gas and dissolved phases, and vary by several ppm among different types of tissue and blood. The development of techniques of laser-enhanced nuclear polarization (or hyperpolarization), has been most strongly motivated by nuclear and particle physics. Targets of polarized He are used in accelerator experiments such as those that probe the elementary particle, short-range structure of the neutron (Chupp et al., 1994a). Polarized He is also used to polarize neutrons for nuclear physics and neutron scattering research (Coulter et al., 1988). These driving motivations and applications along with other historical developments are described in Section I.A. The requirements
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F. 2. Magnetic resonance images of Xe in the lungs and dissolved in the blood and tissue of a rat. The gray-scale images are conventional proton MRI (spin-echo) images that show the animal’s anatomy. The false-color images show the concentration of Xe magnetization for each of three spectral features corresponding to xenon in the gas phase (C and F), dissolved in tissue (B and E) and dissolved in blood (A and D). Panels (A through C) are called axial images across the body, and (D through F) are coronal images through the body. (See also Color Plate 1).
of these experiments have pushed us to understand the physics and technical limitations of optical pumping at high densities. We can now produce liters (at STP) of He, polarized to 50% or more, and similar quantities of Xe. Optical pumping, polarization techniques, lasers, and other technical details are discussed in Section II, and the basics of NMR and MRI are described in Section III. The exciting new possible applications to medical imaging described in Sections IV and V deal with air space imaging and dissolved phase imaging, respectively. We conclude in Section VI by emphasizing some of the potential applications and future promise of this new technique — it gives a wonderful example of transfer of technology motivated by fundamental physics research. A. H P The atomic nucleus of an odd-A or odd-Z isotope in general has nonzero nuclear spin and nonzero magnetic moment. These nuclear spins and
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moments have long been important in the development of nuclear physics through the comparison of experiment with the nuclear shell model theory (see, e.g., Ramsey’s book on nuclear moments, 1953). Nuclear spin has also been an important variable for a range of approaches to studying nuclear interactions. Perhaps the best example is He. The stable A : 3 isotope He has been extremely important in nuclear physics. Calculation of the magnetic moment has clarified the role of meson exchange corrections. Nuclear reactions induced by He and H allow study of isospin symmetry and isospin dependence in a unique way because the A : 1 isodoublet is much more difficult experimentally — accelerated neutron beams are not feasible. Perhaps most important is the fact that the neutron polarization in a polarized He nucleus is 87%. This has allowed important short-range properties of the neutron to be measured including the neutron electric charge distribution — the electric form factor GL — and the neutron deep # inelastic scattering spin structure functions g (x). Therefore, beams and L targets of polarized He have been sought since at least the 1950s. It was the late 1980s before the basic physical processes and technology came together to foresee practical polarized He targets. The He isotope was accidently discovered by Alvarez (1987) at the Berkeley cyclotron in a test run intended to use the cyclotron as a mass spectrometer to detect He produced in nuclear reactions. (It had been assumed, following the suggestion of Bethe, that He was unstable.) After the experiment, the magnet was ramped down with the RF on, revealing an ion with Z/A : 2/3. Once the cyclotron magnet was shimmed properly for this mass, the discovery of He was confirmed. One surprising consequence of that discovery was that He and not H is the stable A : 3 isotope. With two protons and one neutron, the He nucleus must have half-integer spin, and naive consideration of the Pauli principle suggests that the protons’ spins pair in a singlet l : 0 state. In that case the entire angular momentum and magnetic moment of the He nucleus would be due to the neutron. In fact He as well as H are spin 1/2, but the tensor component of the nuclear force and isospin breaking lead to a complicated many-component wave function with l : 0, 1 and 2, and mixed isospin states (Afnan and Birrell, 1977). The total angular momentum of the nucleus has contributions from the D-state and a small proton polarization opposite the He polarization. Even this is not enough to account for the measured magnetic moments: isovector meson exchange currents apparently contribute opposite amounts to the He and H magnetic moments. Therefore the total magnetic moment of He can be written
(He) : PL ; PN ; ( L ; A I ) +#! X X L N , X
(1)
46
Timothy Chupp and Scott Swanson
where PL : 2 sL : 0.87 and PN : 90.027 are, respectively (Friar et al., X 1990), the neutron and proton polarizations, and L : 0.061. The meson X exchange correction is A I : 90.35 for the isospin projection +#! X I : 91/2. The nuclear magneton is : e /2m c. X , N The He isotope is rare, and this is a problem. Primordial abundance of He produced in Big Bang nucleosynthesis is [He]/[He] : 0.00004 (Arnett and Turan, 1985). Additional He has been produced in stellar burning (Trimble, 1982), in the atmosphere due to cosmic ray interactions, and underground due to natural radioactivity. Cosmic ray production of He on the moon, which does not have atmospheric shielding from cosmic rays, has left much greater abundances embedded in lunar rocks (Wittenberg et al., 1986), although mining the moon may remain so expensive as to be impractical. Most of the stored He reserve, 1000 kg, has come from the decay of tritium (H) produced for thermonuclear weapons. Another feature of He has motivated work to develop polarization techniques. It turns out to be a potentially perfect spin filter for polarization of neutrons. The strong neutron absorption reaction n;He ; p ; H is nearly 100% polarization dependent, due to an unbound J : 0 resonance in He. With the neutron and He spins opposite, the absorption cross section is (v) : 5230v /v barns (v : 2200 m/s is the rms velocity of ? thermal neutrons). Other n ; He interactions are negligible. Passing a neutron beam through a filter of polarized He produces a beam polarized parallel to the He, though reduced in flux (Williams, 1980; Coulter et al., 1988; Coulter et al., 1990). The polarization and transmission for a filter with He thickness [He]t and polarization P are given by P : tanh( [He]tP )P : cosh( [He]t)P exp( [He]tP ) L ? R ? ?
(2)
Polarized neutron beams are widely sought for condensed matter and materials science research (Fitzsimmons and Sass, 1989) and for studies of the nuclear interactions of scattered (Heckel et al., 1982), absorbed (Mitchell et al., 1999), and decaying neutrons (Abele et al., 1997). Scattering of neutrons from materials reveals structure and momentum distributions, and the spin dependence is used to study magnetism, for example of multiple thin layers sought for magnetic recording media (Kubler, 1981). In contrast to synchrotron x-rays, the magnetic interactions of neutrons are comparable in strength to electric interactions; for photons, magnetic interactions are suppressed by 300. The decay of polarized neutrons provides the opportunity to study the weak interactions (Jackson et al., 1957), and weaker interactions (Herczeg, 1998), such as those that emerge from extensions of the Standard Model of elementary particle interactions including SuperSymmetry.
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
47
The first attempts to produce usable polarized He targets were not successful in spite of heroic efforts. Most notable was the effort by Timsit et al. (1971a,b). Employing optical pumping of metastable helium atoms with lamps (described in Section II), they developed a mercury Toeppler pump (later adapted by Becker and co-workers, 1994) and provided an important study of He polarization relaxation in the presence of many materials (Timsit et al., 1971b). One particularly crucial conclusion was the importance of a predominantly glass system. Timsit, Daniels, and their co-workers presented a theory for predicting He polarization relaxation rate dependence on helium permeability and glass iron content that confirmed that one should use alumino-silicate glasses such as Corning 1720 (Fitzsimmons et al., 1969), Schott Supermax (Becker et al., 1994), and Corning 7056 (Smith, 1998). Quartz and fused silica, though relatively porous to helium, can be produced with extremely low iron content, and are useful particularly for neutron spin filters since the B in most glasses strongly absorbs low-energy neutrons. Timsit and Daniel’s efforts fell short of the goals of 0.5 l-atm of He with 25% polarization. A decade later, the availability of lasers led to success with the first He neutron spin filter (Coulter et al., 1990) and the first targets for electron scattering for study of the neutron charge form factor GL by quasielastic scattering of # polarized electrons from the polarized He (Woodward et al., 1990; Thompson et al., 1992; Chupp et al., 1992; Becker et al., 1994). (Quasielastic scattering breaks up the nucleus by momentum transfer to a single nucleon. The spin dependence is generally dominated by the neutron.) The next generation of polarized He targets was used for electron scattering at SLAC in a program that revealed the spin content of the neutron’s quarks in deep inelastic scattering (Anthony et al., 1993; Middleton et al., 1993; Abe et al., 1997). These targets employed spin exchange with laser-polarized Rb vapor, a technique that had been considered less favorable for several reasons including the extremely weak hyperfine spin exchange interaction (Walker and Happer, 1997) and problems of radiation trapping — depolarization by multiple scattering of photons in the dense alkali-metal vapor. However, it had been shown that 60—100 torr of N is sufficient to suppress radiation trapping (Hrycyshyn and Krause, 1970) and that optical pumping with lasers was effective at extremely high optical density with [Rb] 10 cm\ (Chupp and Coulter, 1985). More detailed studies of optical pumping at high alkali-metal density (Chupp et al., 1987; Wagshul and Chupp, 1994) showed that laser intensity was the primary limitation and that He pressures of greater than 10 bar in volumes limited only by laser power to 200 cm became possible with CW standing wave titanium::sapphire lasers (Larson et al., 1991).
48
Timothy Chupp and Scott Swanson
The two methods for polarizing He, discovered in the early 1960s, became competing techniques in the 1980s. Metastability exchange was pursued by Becker et al. (1994) and Bohler et al. (1988). This led to the neutron spin filter program at ILL, Grenoble (Surkau et al., 1997; Heil et al., 1998), and quasielastic scattering measurements at Mainz (Becker et al., 1994, 1998), both using a two-stage, titanium pump compressor to increase the He pressure from 1 torr to 1 bar. The metastability exchange technique has also been used to pump He into a cooled cell in a quasielastic scattering experiment (Woodward et al., 1990) and to fill a ‘‘storage cell’’ that is coaxial with the circulating 30 GeV positron beam in the HERA ring at DESY, Hamburg, Germany (Ackerstaff et al., 1997). Spin exchange has been most successful in producing high-density polarized He that is essential for targets used in extracted beam experiments such as the SLAC End Station A deep inelastic scattering program (Abe et al., 1997; Anthony et al., 1996) and recent efforts at TJNAF in Newport News, Virginia (Gao, 1998). The possibility of nuclear spin gyroscopes also emerged as optical pumping techniques were developed (Colgrove et al., 1963; Grover, 1983). A nuclear spin gyroscope does not require the large quantities of highly polarized He demanded by applications of polarized nuclear targets and polarized neutrons. However, the concept does rely on the longest possible spin-relaxation and spin-coherence times. Long spin-relaxation times are also important for high polarization, and the development of gyroscopes at industry laboratories helped advance the study of surface relaxation mechanisms. While the technical advances in polarized He have been largely motivated by work on polarized targets for nuclear and high energy physics, Xe polarization was advanced in optical pumping studies (Zeng et al., 1985). Early in the 1980s they began extensive investigations of spin exchange between noble gases and optically pumped alkali-metal vapors (Happer et al., 1984). They studied many processes involved in optical pumping of alkali-metal vapors in the presence of buffer gases, providing extensive data on the xenon-Rb system (Zeng et al., 1985). The Xe polarization of nearly 100% in small cm volumes was produced; experiments included studies of I : 3/2 Xe as well as radioactive isotopes (XeK, Xe, and XeK) (Calaprice et al., 1985). The work of Cates and Happer with co-workers (Cates et al., 1990; Gatzke et al., 1993) on polarized frozen Xe as a means for accumulating large quantities of polarized gas may have been the initial inspiration for the development of MRI with laser-polarized xenon. The first experiment at Stony Brook with gas polarized in Princeton relied on freezing the xenon for transport by car. The magnetization lifetime of frozen Xe is generally much longer than in the gas phase (Gatzke et al., 1993).
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
49
Studies of spin exchange between Rb and lighter noble gases Ne (Grover, 1983) and He (Chupp and Coulter, 1985; Chupp et al., 1987) were motivated by nuclear physics applications, in particular the use of symmetry violations such as parity (P) and time reversal (T) to study weak interactions in the presence of the dominant strong and electromagnetic interactions (Chupp et al., 1988). Several experiments used I : 3/2 Ne and He simultaneously to search for quadrupolar interactions such as a possible dependence of nuclear binding energy on orientation with respect to an assumed absolute rest frame of the Universe (Chupp et al., 1989). These pulsed NMR experiments were probably the first applications that specifically used laser-polarized rare gases to enhance rare gas NMR signals by many orders of magnitude. A variety of experimenters have since used laser-polarized He and other noble gases to enhance NMR measurements. The low-temperature work at Ecole Normal Supe´rieur has used NMR to measure polarization and probe such phenomena as spin waves (Tastevin et al., 1985) and the properties of Fermi liquids (Leduc et al., 1987), and He-He mixtures (Himbert et al., 1989; Nacher and Stolz, 1995). Geometric phases have been measured with Xe (Appelt et al., 1995). Measurement of the NMR splittings of Xe and He in the presence of an electric field is used to search for T-violation (Rosenberry, 2000). This experiment used a spin exchange pumped Zeeman maser (Chupp et al., 1994b; Stoner et al., 1996) that exploits cavity-spin coupling and the population inversion pumped into the nuclear spins (Robinson and Myint, 1964; Richards et al., 1988). Conventional NMR research with Xe (i.e., not laser enhanced) has focused on a variety of problems including cross polarization, molecular dynamics, xenon molecules (e.g., XeF ), diffusion in porous media, polymers, and liquid crystals. The Xe isotope has been used to study quadrupolar relaxation on surfaces, in macromolecules, and porous media. Xenon has been extremely important because it is normally gaseous, can be easily frozen or liquified, is relatively soluble, and is characterized by large NMR chemical shifts of up to 500 ppm between the gas and dissolved phases. It was recognized that many of these applications of NMR research could be enhanced with laser polarized Xe (Raftery et al., 1991), and this inspired the original pursuit of MRI with laser-polarized noble gases (Song et al., 1999).
II. Nuclear Polarization Techniques Polarization of He and Xe can be contemplated by brute-force, SternGerlach, or optical-pumping techniques. Brute-force polarization uses high magnetic fields and low temperatures to create an imbalance of nuclear spin
50
Timothy Chupp and Scott Swanson
state populations. At low temperatures He atoms in the liquid phase are indistinguishable, obeying Fermi-Dirac statistics with the consequence that neglible polarization can be achieved at reasonable magnetic fields. (The effective spin temperature does not drop below the Fermi temperature of T : 0.18 K.) For solid He, the lattice positions, not the momentum states, $ distinguish atoms and Boltzmann statistics describe the polarization. The result is that solid He can be polarized, achieving the equilibrium value P tanh(B/kT )
(3)
which at 10 mK and 10 T gives P : 91.5%. Low temperature alone is not sufficient to produce solid He — high pressures are also needed. The Pomeranchuk method involves cooling the liquid in an applied magnetic field under pressure. For T 0.32 K, the liquid’s entropy is less than that of the solid and the sample cools itself in a process similar to cooling by evaportation (Lounasmaa, 1974). Frossati (1998) has proposed producing a thousand liters of highly polarized He per day using this method, followed by rapid warming of the polarized He through the liquid phase. It is not known whether Xe can be polarized in this way, though measured spin diffusion times seem favorable. Stern-Gerlach techniques have been used to produce beams of highly polarized He. However, the tradeoffs of acceptance and polarization have limited fluxes to 10/s with P : 0.9 for a hexapole magnet. This is not sufficient for accumulation of useful quantities, though it is useful for applications where a trace amount of highly polarized He is required (Golub and Lamoreaux, 1994). Optical polarization employing either hyperfine spin exchange with an alkali-metal vapor (Bouchiat et al., 1960) for He and Xe or optical pumping of metastable helium atoms for He (Colgrove et al., 1963) both emerged as promising techniques with the availability of lasers. Both techniques are now used to produce liter quantities (at STP) with polarization P 50% that are used for neutron polarization, polarized targets, and medical imaging. In all cases, relaxation of nuclear spin must be balanced by polarization rates. (Note that nuclear spin relaxation in a biological environment in vivo or in vitro is completely different from relaxation in a carefully prepared polarization system as discussed in Sections IV and V.) Rare gas nuclear spin relaxation occurs by bulk collisions with impurities, dipole-dipole interactions in the bulk, magnetic field gradients, and surface wall interactions. The most important impurity is paramagnetic O . Relaxation rates are proportional to the oxygen impurity level with rate constants k(O -Xe) 0.3 s\/amagat (Jameson et al., 1988) and k(O -He)
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
51
0.45 s\/amagat (Saam et al., 1996) at 14.1 kG and at room temperature with temperature dependence T \. (One amagat is the number density of a gas at STP.) In order to achieve high He polarizations, O impurity levels must be below parts per million. Relaxation due to dipole-dipole interactions have rate constants k(Xe-Xe) : 5 ; 10\ s\/amagat (Hunt and Carr, 1963) and k(He-He) : 4 ; 10\ (Mullin et al., 1990; Newbury et al., 1993). Magnetic field gradient contributions to nuclear spin relaxation arise due to nonadiabatic evolution of the nuclear spin as the atoms move in the gradients between collisions. For the high densities encountered in most applications D
B ; B V W B
(4)
Typically, magnetic field gradients of 0.3—1%/cm are sufficient for He and Xe polarization, respectively. Wall interactions are moderately well understood. For He, the work of Timsit and Daniels already described here shows that paramagnetic impurities and sticking time, dominated by diffusion of helium into the surface, are most important. Coating the surfaces of glass or fused silica with cesium has proved effective for attaining He relaxation times of 2 d or more (Cheron et al., 1995; Surkau et al., 1997). For highly polarizable xenon atoms, the sticking times are much shorter, but relaxation rates can be reduced with silane wall coatings (Zeng et al., 1985; Oteiza, 1992; Sauer et al., 1999). Sauer has shown evidence that Xeproton dipolar interactions dominate relaxation in coated cells. With coatings, relaxation times for Xe of 10 min or more are common at low magnetic fields. At 2T, T 2 h has been observed for Xe, indicating decoupling of the wall relaxation mechanisms. A. O P S E Optical pumping (Kastler, 1950) is the means by which the internal degrees of freedom of a sample of atoms can be manipulated with light, and the angular momentum of the photons can be transferred with high efficiency to the atoms (see Harper, 1972). The most effective way to understand optical pumping and spin exchange is by derivation of rate equations describing these processes. For optical pumping, we begin by considering an atom with J : 1/2, such as an alkali-metal atom with nuclear spin I : 0. The polarization, P, is given by P: 9 \\
and
; :1 \\
(5)
52
Timothy Chupp and Scott Swanson
Both polarization and spin destruction processes must be considered. For polarization, we assume that the atoms are illuminated with right circularly polarized ( ) light, and we define the total for the rate per atom of pumping > out of the m : 91/2 state and into the m : ;1/2 state as (1/2). For H H atoms with resonant frequency (r) : k
d (r, )( 9 )
(6)
The laser intensity per unit frequency is (r, ) : dI(r)/d, which is, in general, position dependent. The cross section for absorption of unpolarized light is (), and k is a constant that accounts for the relative probability that an atom, after absorbing a photon, also absorbs its angular momentum. For alkali-metal atoms in the presence of sufficient buffer gas pressure to collisionally mix and randomize the spin projections in the p states, k : 1. The optical pumping rate equations for the two-state system are d( and depolarized. Each unpolarized photon can multiply scatter and depolarize many atoms and therefore radiation trapping can be thought of as an additional relaxation mechanism that is a function of incident laser power. Radiation trapping would limit the density of the mediating alkali-metal species in spin exchange pumped He targets. However, molecular N (Zeng et al., 1985; Chupp and Coulter, 1985) (for He) have been shown to mitigate radiation trapping effects effectively. At high magnetic field the Zeeman splitting of the S and P states causes the scattered photons to be off resonance and only very weakly absorbed in depolarizing transitions. The presence of N or other molecular species quenches the P states nonradiatively, thereby reducing the branching ratio for radiative decay (i.e., resonant scattering) (Wagshul and Chupp, 1989). Assuming that the complication of radiation trapping has been practically eliminated, the steady-state solution to the rate equations predicts electron spin polarization P : 1
(r ) (r ) ; 1"
(8)
and a time constant ( (r ) ; )\ that is typically milliseconds. 1" For atoms with nuclear spin, including alkali-metal atoms and metastable He atoms, the hyperfine coupling results in total angular momentum F. Laser optical pumping must provide the angular momentum for complete atomic polarization, the time dependence becomes more complicated than the single exponentials that describe the two state system, the transients become longer, and the nuclear spin serves as a reservoir of angular momentum (Bhaskar et al., 1982; Nacher and Leduc, 1985; Wagshul and Chupp, 1994; Appelt et al., 1998). However, the levels rapidly reach a
54
Timothy Chupp and Scott Swanson
spin-temperature equilibrium mediated by electron spin exchange (Anderson and Ramsey, 1961) and it is sufficient to consider only the evolution of electron spin S. For the metastability exchange, the discharge itself also leads to relaxation. The spin exchange rate equations, including relaxation, can be written P : (P 9 P ) 9 P ' 1# 1 ' '
(9)
where P : 2 I (for I : 1/2) is the rare gas nuclear polarization and P : ' X 1 2 S is the alkali-metal electron polarization. The steady-state solution is X 1# P :P ' 1 ; 1#
(10)
The goal is therefore to maximize alkali-metal electron spin polarization and effect long relaxation times so that . 1# For He polarized by spin exchange with Rb, 1/ is typically many 1# hours and relaxation times of days have been achieved, resulting in high polarizations 50%. Relaxation seems to be limited by many factors including wall relaxation, interactions with impurity gases (probably paramagnetic O ), and dipolar relaxation in He-He collisions. For Xe, 1/ is typically several minutes but can be a short as 10 s. 1# Relaxation times in silane-coated cells seem to be 10—30 min at low magnetic fields, and several hours at 2T (Zeng et al., 1985; Oteiza, 1992). Deuterated coatings have been suggested to reduce relaxation at low field (Sauer et al., 1999). Relaxation is often dominated by wall collisions, though impurities and dipolar relaxation are also important. In a collision between an alkali-metal atom with electron spin polarization and a rare gas atom with I : 1/2, the electron spin couples to the nuclear spin and to the rotational angular momentum of the pair (Happer et al., 1984). The dominant contributions to the spin dependent Hamiltonian are H : N · S ; AK · S ; A K · S 1#
(11)
where A is the alkali-metal hyperfine interaction and A is the spin 1# exchange hyperfine interaction, both of which are, in general, position dependent. However, the long-range contributions vanish for spherically symmetric collisions, and only the Fermi-contact term acts, so that 8 A : 2 2 (R) ' 1# 3
(12)
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
55
Where (r 9 R) : (R) is the probability that the alkali-metal valence electron (coordinate r) is at the position of the noble gas nucleus (coordinate R). Herman has shown that (R) is in fact enhanced due to the electron exchange interactions as the electron is attracted by the positive charge of the nucleus (Herman, 1965). An enhancement factor is defined in terms of the free alkali-metal electron wave function ( ) by (R) : (R). The varies from about 10 for Rb-He to 50 for Rb-Xe (Walker, 1989). The hyperfine interaction is, of course, time dependent as an alkalimetal atom and rare gas atom move past each other. For He, the time scale is about 10\ s because the collisions are always binary — in contrast to Xe, which can form a Van der Waals molecule with an alkali-metal atom in a three-body collision (Bouchiat et al., 1972). The lifetime of this molecule can be 10\ s or longer, limited in fact by the break up of the molecule in a collision with another buffer gas molecule. One consequence is that the rate constants for spin exchange are much different for He polarization and Xe polarization: k (Rb-He) : 6—12;10\ cm/s and k (Rb-Xe 1# 1# 4 ; 10\ cm/s, with this lower limit set by binary spin exchange in the absence of three-body formation of Van der Waals molecules (Cates et al., 1992). Spin rotation is a sink of angular momentum resulting from the coupling of the electron spin to the rotation of the alkali-metal-noble-gas pair, and is generally dominated by the heavier partner as discussed by Walker and Happer (1997). If we neglect wall interactions, alkali-alkali collisions, and alkali-N collisions, the alkali-metal electron spin destruction rate reduces to the sum of spin exchange and spin rotation: D k E[I] ; k R[I] 1 1 1
(13)
for a rare gas of number density [I]. As the incident, circularly polarized laser photons must balance this spin destruction rate, it is useful to consider the spin exchange efficiency k E 1
: 1# k E ; k R 1 1
(14)
This quantity in principle sets an upper limit on the ‘‘photon efficiency’’ (defined by Bhaskar et al., 1982), with which optical pumping can balance noble gas relaxation. In general, however, photon efficiency is much lower than because of other alkali-metal spin destruction mechanisms, neces1# sarily inefficient optical transport of laser light into the cell, and the fact that lasers used in practical situations are broadband (as discussed in what
56
Timothy Chupp and Scott Swanson
follows). The magnetic field dependence of spin exchange, spin rotation, and relaxation mechanisms are, of course, important, particularly in magnetic imaging applications at fields of 2T and greater (Happer et al., 1984). 1. He Spin exchange cross sections for Rb-He have been estimated by Walker (1989) and measured by several groups. Measurements of He nuclear spin relaxation rates in the presence of Rb (Bouchiat et al., 1960; Gamblin and Carver, 1965; Coulter et al., 1988; Cummings et al., 1995) show that v : 4—8 ; 10\ cm/s. Measurement of the frequency shifts of He 1# NMR and Rb EPR frequencies are consistent with this range (Baranga et al., 1998). The frequency shift measurements also allowed comparison of the Rb-He and K-He spin exchange interaction, showing that they are within 10% of each other. Since He nuclear spin relaxation times are generally tens of hours, polarization times must be only a few hours. This requires alkali-metal density 10/cm. As cell volumes are 100 cm, or greater, the total number of alkali-metal atoms can be 10, the incident photon flux must balance the loss of angular momentum by the alkali-metal atoms. The dominant processes relevant to Rb-He spin exchange can be summarized by the Rb spin destruction rate (Wagshul and Chupp, 1994; Walker and Happer, 1997; Appelt et al., 1998) SD : kRb-He [He] ; kRb-N [N ] ; kRb-Rb [Rb]
(15)
where the k are rate constants for spin destruction due to collisions with each of the species in the optical pumping cell. For a typical application, 500 Hz and 10 photon/s/cm or 100 mW/cm are necessary. 1" 2. Xe There are crucial distinctions for Xe polarization: The xenon-alkali-metal spin exchange and spin rotation rate constants are many orders of magnitude larger than for helium (Cates et al., 1992), and long-lived Van der Waals molecules, formed in three-body collisions with lifetimes comparable to the hyperfine mixing time, may dominate spin exchange and spinrotation. As a result, polarization rates have characteristic time constants in the range of 10 s to several minutes in practical situations (Zeng et al., 1985). These times are comparable to and shorter than Xe nuclear spin relaxation times in the polarization apparatus so the Xe polarization is generally limited by the Rb or K polarization, not relaxation mechanisms, as in the case of He. The situation can be quite different, however, in
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
57
systems designed to collect xenon gas that has flowed through a polarization chamber, such as that developed by Driehuys et al. (1996). In this case, the Rb density is probably not well controlled, and the xenon atoms may not uniformly sample the Rb polarization in the pumping chamber. This may be the reason that the observed Xe polarization is generally much lower than the Rb polarization (Hasson et al., 1999b). 3. Lasers for Spin Exchange Pumping Lasers have been the essential light source for successfully polarized He and Xe experiments. Originally dye lasers were used, producing up to 1 W near 795 nm with linewidths less than or comparable to the pressurebroadened Rb absorption linewidth (Chupp et al., 1987). (Typical standing wave dye laser linewidths are 30 GHz; the Rb D1 line is broadened by about 18 GHz per amagat of He.) In the late 1980s, high-powered arrays of laser diodes (LDA) became available, and their suitability for spinexchange pumped He polarization was of immediate interest (Wagshul and Chupp, 1989). Simultaneously the titanium::sapphire laser was developed for high-power applications and soon became commercially available. By about 1990, the cost per useful watt of LDA and Ti::sapphire lasers was comparable, but a single Ti::sapphire set up could produce 5 W whereas the most powerful available LDA was 2 W. Further, 795 nm was at the edge of reliable LDA production. Several experiments were undertaken, each using one or more Ti::sapphire lasers. Experiment E142 at SLAC ran with up to five (Middleton et al., 1993). By 1994, bars of LDA had become available with a price per watt of $500 and falling rapidly. This has been the single most important technology advance driving this field. By comparison, a Ti::sapphire laser pumped by a large frame argon ion laser has a price per watt of $15—$20 K. Current LDA prices are $100—$200 per W. The LDA will dominate future experiments and make polarized He and Xe much more widely accessible. 4. Optical Pumping with Laser Diode Arrays Laser diodes are widely recognized as work horses in atomic and optical physics. For example, near-IR lasers used in cooling and trapping of K, Rb and Cs are generally single-mode (linewidths on the order of MHz) and low-powered (50—100 mW with 500-mW amplifiers commonly in use). High-powered LDA are produced for a variety of commercial, industrial, and communications applications (including stripping the paint from battleships). Currently available LDA packages utilized for Rb optical pumping consist of bars of individual LDA. Bars with 20—50 W of nominal output
58
Timothy Chupp and Scott Swanson
F. 3. Profile of intensity vs wavelength for a typical GaAlVAs\V LDA (from Optopower Corp.), indicated by a solid line. The total power output per laser is about 15 W. The dotted and dashed lines show the laser profile 5- and 10-cm into the cell, respectively, for cell parameters of: 10 amagat of He and 0.1 amagat N at 180°C (left); 0.1 amagat of Xe, 0.2 amagat N , and 2.7 amagat He at 110°C (center); and 2.2 amagat of Xe, 0.2 amagat N , and 0.5 amagat He at 110°C (right).
consisting of about 20 1—3 W elements with GaAlAs and InGaAsP can be purchased for a few thousand dollars each. The injection current and temperature of the device are used to tune the arrays to 794.7 nm, the Rb DI wavelength, and typical bandwidth is 2—4 nm. Recently, 20-W bars at 770 nm with K D1 wavelength have become commercially available. Though the broadband light from the LDA is spread over 1—2 nm, much greater than the 0.1—0.2 nm typical homogeneously broadened absorption linewidth of Rb, the convolution of the light intensity and the absorption cross section provides a sufficiently high photon absorption rate that light 1 nm or more off resonance can effectively polarize Rb. The photon absorption rate of laser light by Rb atoms is defined in Eq. 6. In the case of LDA, () is spread over 2 nm or more, as shown in Fig. 3. The total power output per laser is about 15 W. As the light propagates through the cell (along z), it is absorbed by the Rb at a rate d () : 9()[S] (z)(1 9 P (z)) 1 dz
where
(z) P : (16) 1 (z) ; 1"
Computer modeling based on numerical integration of these equations is generally reported by several authors to predict results for He and Xe polarization that are within 10% of that measured (Wagshul and Chupp, 1994; Walker and Happer, 1997; Smith, 1998; Appelt et al., 1998). The requirement for significant Rb polarization is . For He, a 1" large portion of the initial laser spectral profile is useful. In Fig. 3, we show
MEDICAL IMAGING WITH LASER-POLARIZED NOBLE GASES
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the spectral profile at three positions along the axis of the cell for He density of 10 amagat with 0.1 amagat N . As light burns its way into the cell, the central portion of the spectral profile is absorbed more strongly than the wings. Therefore, the front of the cell is essentially polarized by the near-resonance light. The more off-resonance light polarizes a greater portion of the cell’s length and is more important in the back of the cell. The large optical thickness of Rb typically used for He polarization ([Rb] : 10\/cm) is the main reason polarization with LDA can be so effective. The pressure broadening of the Rb absorption line is of secondary importance in most cases; in fact, the gains due to pressure broadening tend to saturate above 4—5 amagat of He. The situation is quite different for Xe. The spin destruction rate of Rb due to Xe is so much greater than that due to He that much greater laser intensity or spectral density (or both) is required to satisfy . 1" Consequently, only a much narrower part of the LDA spectrum is useful for Xe, even at very low xenon concentration, as illustrated in Fig. 3. Broadening the absorption line with a buffer gas such as helium, which does not appreciably increase , is helpful, but it is only practical to increase 1" the absorption line to approximately 0.5 nm with 10 amagat of buffer gas (Driehuys et al., 1996). The problem of balancing trade offs of noble gas polarization, production rates, volumes, and/or magnetization involves exploring a large parameter space. For example, increasing the total density of gas produces pressure broadening of the Rb absorption line, increasing the integral , but also increasing . Greater Rb density increases but also increases and 1" 1# 1" the absorption of the light as it propagates through the pumping cell, reducing further into the cell. For example, one can produce 60% Xe polarization in 7.5 torr-liters per hour per watt of standard LDA laser power. The actual photon efficiency is less than 0.5%, compared to the 4% efficiency for Rb-Xe prediction (Walker and Happer, 1997). A standard liter would require about 100 W. For He, over 50% polarization of more than 1 l with 30 W of laser power has been achieved. Significant improvement of Xe polarization is possible if the LDA light is spectrally narrowed. In Fig. 4 we show a calculation of the expected Rb and Xe polarizations for different combinations of xenon density, temperature, that is, Rb density, etc. for 15 W of laser power. The total pressure is held constant at 2000 torr; for example, with 500-torr xenon, we use 100-torr N , and 1400-torr helium. We show results for two cases: low xenon density, that is, 100-torr xenon and high helium buffer gas density as suggested by Dreihys et al. (1996); and high xenon density 1500-torr xenon used by Rosen et al. (1999). Narrowing LDA spectra provide significant gains in either case. The width parameter for the LDA is essentially a
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Timothy Chupp and Scott Swanson
F. 4. Calculated Xe polarization as a function of the LDA linewidth (FWHM). For each temperature, curves for 0.13 amagat, 0.65 amagat, 1.3 amagat, and 2 amagat of Xe are shown from top to bottom, respectively. A constant total density of 2.8 amagat is maintained by loading with helium buffer gas. The solid dot on the 110° shows the measured Xe polarization reported by Rosen et al., 1999.
measure of full width half maximum (FWHM) of the spectrum. We emphasize that narrowing in this case does NOT mean that the lasers need to be single mode as in the case of cooling/trapping/BEC. Recent progress on narrowing off the shelf LDA in external cavities (MacAdam et al., 1992) has been reported (Nelson et al., 1999; Zerger et al., 1999). For example, the Littman Metcalf configuration has been used with 2-W off-the-shelf LDA. The spectral profiles for 1.0—1.5 W output have FWHM 20—30 GHz, and the central frequency could be tuned over several nm. Simulations of the expected performance show that a single 15-W LDA could be replaced by a 3-W external-cavity LDA. With the recent commercial availability of 4-W broad area LDA, 3 W may be possible with a single device. The 2-W LDA is similar to a single facet of a typical multiarray bar. For most commercially available CW bars, the filling factor is only 30%, and efficient optical feedback from the grating would be difficult. However, bars that are intended for pulsed use are available with filling factors of up to 90%. Thermal management problems limit the duty factor of these in normal operation, but reliable operation might be feasible for 10 W or more. B. M E In the metastability exchange scheme, a sample of He atoms is excited by a weak electric discharge so that a fraction of the atoms (:10\) is in the metastable 2S state. This long-lived state can be optically pumped to the 2P and 2P states by 1.083 m circularly polarized light. For example, the 2S state is split into hyperfine levels with F : 1/2 and 3/2. Pumping
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into the F : 3/2, m : ;3/2 state (the C9 line) produces high atomic and $ nuclear polarization of the metastable fraction. Resonant exchange of the excitation energy in metastability exchange collisions does not affect the nuclear spin, because the collision duration is short compared to the hyperfine mixing time. Thus, the ground state population attains high nuclear polarization (Colgrove et al., 1963). In general, the same principles of optical pumping apply to metastability exchange and spin exchange. There are, however, some crucial distinctions. One distinction is the ratio of widths of the atomic absorption line and the Doppler profile. For spin exchange, the high density of He or Xe and N lead to homogeneous collisional broadening of the Rb absorption line of 18 GHz/amagat for He and 14 GHz/amagat for N (Che’en and Takeo, 1957). This greatly exceeds the natural (5.7 MHz) and Doppler widths. Under these conditions, broadband laser light, from standing wave lasers or laser diode arrays, is effective for optical pumping (Wagshul and Chupp, 1989; Cummings et al., 1995). For metastability exchange polarization of He, the densities are hundreds of times less and Doppler broadening is dominant. Effective optical absorption by all of the atoms requires careful matching of the laser frequency distribution to the Doppler distribution. Another distinction between spin exchange pumping and metastable pumping is optical thickness. We can define an absorption length for polarized resonant photons with m : ;1 J : 2([m] (91/2))\
(17)
where [m] is the number density of metastable atoms or the alkali-metal vapor, and is the resonant absorption cross section for unpolarized light. For spin exchange pumping the absorption length is less than the dimension of the optical pumping vessel, which leads to the radiation trapping problems discussed earlier. The quantity is generally more than 1 m for metastability pumping, and radiation trapping does not present any limitations. Under optimum conditions, samples of He gas at a density 1.5 ; 10/cm can be pumped to an equilibrium polarization of over 80% with polarization rates of 10 atoms/s. The dependence of the equilibrium polarization and polarization rate on gas pressure, discharge level, and frequency has been studied in detail by Lorenzon et al. (1993). Metastability exchange polarization of Xe in a discharge has been studied by a few groups with little success (Schaerer, 1969; Lefevre-Seguin and Leduc, 1977). Although electron polarization in the metastable states indicates effective optical pumping, the discharge may induce excessive nuclear spin relaxation. As an alternative, the metastable 5p6s J : 2 state may be populated by two-photon laser excitation with ( : 317 nm), or a
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Timothy Chupp and Scott Swanson
metastable atomic beam used to separate the discharge from the optical pumping region. These methods will probably not become practical for producing large quantities of polarized Xe, but may be useful for studying the physical processes at work. 1. Lasers for Metastability Exchange The success of metastability exchange-based He applications has also been strongly supported by laser developments. The first lasers for 1083 nm were color center F> ; NaF. Two Nd-based laser materials, Nd:Yap (Schearer and Leduc, 1986; Bohler et al., 1988) and Nd:LNA (Hamel et al., 1987) are now available. Five W of laser power at the helium transition is routinely obtained by pumping a crystal of Nd:LNA with a cw, krypton arc-lamp in a commercial Nd:YAG cavity. The laser can be tuned to the different pumping lines by use of a solid uncoated etalon in the cavity (Aminoff et al., 1989). The LDA-pumped LNA lasers have also been used (Hamel et al., 1987). The most recent laser development for metastability pumping of He is the diode-pumped fiber laser and fiber laser amplifier (Goldberg et al., 1998; Lee et al., 1999). C. P D S Several devices combine optical pumping and polarization with delivery of the polarized gas to a subject or a storage container. For He, the basic designs used for polarized targets are applied for both metastability exchange and spin-exchange pumped systems. The metastability exchange systems have a valved port that connects to a transport container. Gentile and co-workers presented in 1999 a relatively compact and inexpensive compressor that may see wide use. For spin exchange systems an additional valve of the appropriate material is straightforward. With He polarization relaxation times of several days typical in glass containers, transport almost anywhere can be contemplated. For Xe, the high rate of Rb electron spin depolarization in spinrotation collisions limits the rate of Xe production, and a method of accumulation is essential. Cates, Happer, and co-workers have shown that frozen and liquid xenon provide very long nuclear spin relaxation times for Xe (Cates et al., 1990; Sauer et al., 1999), and that freezing is an ideal accumulation method (Driehuys et al., 1996). Relaxation times are on the order of an hour at liquid N temperatures and days at liquid He temperatures (Gatzke et al., 1993). For human studies, it is sufficient to collect the polarized gas in a plastic bag, where it is held for several minutes before inhalation and breath-hold.
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For animal studies, voluntary breathing is not possible, and delivery to the animal requires a polarized gas ventilator. There are many technical difficulties, and very few such ventilators have been constructed (Hedlund et al., 1999; Rosen et al., 1999). Delivery of polarized gas by shipping from a geographically centralized production facility is one possible operating procedure for future medical imaging. In the case of He, relaxation times of several days are routine in clean, uncoated, glass containers (Middleton et al., 1993; Chupp et al., 1996), and all that is needed is a portable holding field magnet. Magnetic fields of 10—20 gauss are sufficient to dominate the magnetic field gradients expected in normal commercial shipping. Both battery-operated, wire-wound coils (Hasson et al., 1999a) and permanent magnet systems (Surkau et al., 1999) have been developed. If liquid He transport of polarized Xe becomes practical, its shipment would also be feasible.
III. Basics of Magnetic Resonance Imaging (MRI) Conventional magnetic resonance imaging (MRI) creates a map of the distribution of water protons in the body and has become one of the most versatile and powerful imaging methods in clinical medicine (Wehrli, 1995). The MRI system uses static, RF, and gradient magnetic fields to create images. A large, static magnetic field B , generally between 0.5—1.5 tesla, creates an axis of quantization, energy level separation, and energy level population difference for the spin states. A radio frequency field, B (t), oscillating at the proton larmor frequency causes transitions between the spin states and converts longitudinal magnetization into detectable transverse magnetization. Finally, pulsed magnetic field gradients, B /x(t), X B /y(t), or B /z(t), are used to both localize and spatially encode the X X nuclear spin magnetization in order to create an image. Here we present a synopsis of conventional MRI. A complete treatment can be found elsewhere (Callaghan, 1991). In addition, we review specific aspects of MRI related to imaging laser-polarized noble gases. A. N M R (NMR) MRI is an application of NMR (Abragam, 1961) with the fundamental relationship given by the larmor equation : B
(18)
The precessing spins are detected by tipping the magnetization by an angle
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with a radio frequency pulse B (t) applied orthogonal to the B field. The signal recorded as a function of time in a pick-up coil is s(t) . M sin e\GSR
(19)
where M is the total magnetization of the system and is the ‘‘tip angle’’ of the magnetization relative to the axis defined by B . B. O-D I Lauterbur (1973) realized that a map of the spatial distribution of the magnetization could be obtained by acquiring the NMR signal in the presence of a magnetic field gradient. The frequency of the nuclear spin is then proportional to the position of the spin and given by (x) : (B ; xG ) V
(20)
where x is the position of the spin and G is the gradient of B along the x V axis, B G : X V x
(21)
The time evolution of the transverse magnetization is given by s(t) : M(x)e\GA >V%VR : M(x)e\GA Re\GAV%VR
(22) (23)
Where is a calibration constant that depends on , , and electronic and geometric factors. The only interesting component of s(t), from an imaging point of view, is the additional frequency due to the magnetic field gradient. Moving into a reference frame rotating at , the time evolution of the magnetization is given by s (t) : M(x)e\GAV%VR M
(24)
The signal s (t) is detected by mixing signals from an oscillator at M (64 MHz for protons at 1.5 T) with s(t). One practical consequence of detection in the rotating frame is that the signals can be sampled at audio frequencies rather than RF frequencies. Again, see Callaghan (1991) for a complete description.
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We now consider a one-dimensional (1D) distribution of spins along the x-axis. The time evolution of the magnetization is given by
s (t) : M
V
:
M(x)e\GAV% VR dx
(25)
M()e\GSVR dx
(26)
V
This is the Fourier transform of M(x). Mansfield and Grannell (1973) showed that a 1D image could therefore be created by taking the Fourier transform of the NMR signal in the presence of a magnetic field gradient. 1 M() : F(s (t)) M
(27)
C. M R I k-S For imaging, the goal is to create a plot of the intensity of magnetization as a function of a spatial coordinate. A more appropriate representation for MRI is a coordinate system with spatial dimensions x and inverse spatial dimensions k where V 2 k : G t V V
(28)
Equation (26) can then be rewritten s(k ) : V
V
M(x)e\GLI VV dx
(29)
In this formulation, k and x are the conjugate Fourier variables. The V Fourier transform with respect to k provides a 1D map of the magnetizV ation. The applied gradient, and hence k , may be time dependent, V 2 k (t) : V s(k ) : V
V
R O
G () d V
M(x)e\GLI VRV dx
(30) (31)
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Generalizing to two dimensions, we then have s(k , k ) : V W
V W
M(x, y)e\GLI VRV>IWRW dx dy
(32)
Much of the progress in MRI over the last decade has been made by controlling the amplitudes and durations of gradients to appropriately sample k-space. These advances have been made possible by improvements in the hardware that produce the magnetic field gradients. It is important to realize that each point acquired in k-space is spread throughout real space. The point at k : 0 represents the dc component of V the magnetization and is proportional to the magnitude. As k increases, V we measure the Fourier coefficients of higher frequency terms. By summing together all of the Fourier components in real space, one obtains an image of the magnetization. Artifacts in MRI arise because some of the terms in k-space are not sampled correctly or are lost. For example, a beating heart introduces time dependence not due to G (t). The artifact does not appear V at one location in real space, rather it is spread according to the sampling error in k-space. A solution to such an artifact is cardiac gating of the signal, triggered by heart monitors. Another important concept in k-space is prephasing and rephasing of transverse magnetization. Applying a gradient adds a phase to the spins that depends on their position in the sample. (x) :
xG (t) dt V
(33)
If the direction of the gradient is reversed, the spins at each position acquire an opposite phase. When the G (t) dt of the two gradients is of equal V magnitude, all transverse magnetization is in phase and a gradient echo occurs. In the language of k-space, we first move to a point where k is V negative. Changing the sign of the gradient changes the direction we move in k-space. The gradient echo occurs when we traverse the point where k : 0. Most pulse sequences are designed to symmetrically sample k-space V in order to maximize signal-to-noise. D. I S In most cases an MRI tomograph is a two-dimensional (2D) image of a slice of the body. The slice is isolated by selective excitation of spins along the third dimension. The spatial information is encoded by either frequency
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dispersion or phase dispersion, as discussed in the sections that follow. 1. Selective Excitation Slice selection is typically accomplished by simultaneous application of a magnetic field gradient and a shaped RF pulse with relatively long duration (1—10 ms) and correspondingly narrow bandwidth. This gradient creates a frequency ramp along its direction and the shaped RF pulse excites spins only within a relatively narrow slice. The sinc pulse, sin(t)/t, is the most common because its Fourier transform is a rectangle. In practice, the sinc shape does provide a reasonable approximation of a rectangular pulse in space coordinates. The combination of a gradient and a frequency selective pulse only excites spins within a region defined by z
2 G V
(34)
where G is the strength of the magnetic field gradient and is the duration V between the first zero crossings of the sinc pulse. 2. Back Projection Imaging Back projection imaging in MRI detects the NMR signal in the presence of a magnetic field gradient, applied immediately after the slice selective RF pulse. This was the first type of imaging to be performed (Lauterbur, 1973) and is most directly related to other imaging methods such as computed tomography (CT) or positron emission tomography (PET). For the most part, back projection imaging has been replaced by Fourier imaging. However, it still maintains a niche in studies of tissues with a short transverse relaxation time T . In laser-polarized noble gas imaging, back projection imaging is useful because all views acquired contain the dc component of k-space, which is proportional to the total intensity of the image. Therefore, if image intensity changes from pulse to pulse due to a different amount of gas magnetization, it is possible to normalize the acquired signals for proper reconstruction. This is not possible in Fourier imaging sequences such as gradient echo imaging. The pulse sequence needed for 2D back projection imaging is shown in Fig. 5. The frequency selective RF excitation pulse only excites spins in a slice of magnetization along the z-axis in the magnet. Signal acquisition commences immediately after the RF pulse is applied, and the NMR signal is recorded in a constant magnetic field gradient. The direction of the
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F. 5. Pulse sequence for back projection imaging in two dimensions. The slice-selective gradient and the frequency-selective RF pulse only excite spins in a slice or slab along the z-axis. The half sinc slice-selective pulse does not require that the transverse magnetization be refocused. The two projection gradients are varied in a sinusoidal pattern.
applied gradient is varied by changing the magnitude of both the x and the y gradients according to G : G cos( ) V G G : G sin( ) W G
(35) (36)
The different amplitudes in the x-projection- and y-projection-gradients are represented in Fig. 5 by the lines of different heights. Each radial step in k-space corresponds to a different value of . For each step, a slice selective G pulse is followed by application of the gradients during which the MRI signal is acquired. Typically is varied from 0 to 2 in 128 steps. The G sampling of k-space is shown in Fig. 6. Sampling of k-space is radial. Back projection images are reconstructed with a specialized algorithm and not by a 2D Fourier transform. 3. Gradient Echo Imaging All the elements of 2D Fourier MRI are contained in the gradient echo imaging sequence shown in Fig. 7. Slice selection and read-out gradients are applied as in back projection. The main difference is phase-encoding, first proposed by Kumar et al. (1975) and later modified by Edelstein et al. (1980). Phase encoding now forms the basis of many MRI pulse sequences. In phase encoding, phase dispersion occurs during an interval t before the signal is acquired during the interval t . The duration of t or the phase encode gradient can be varied to step through k -space, with t fixed. W
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F. 6. Sampling of k-space by back projection imaging. In this example, we illustrate just the first few sampled rays obtained by adjusting the gradients according to Eq. (35—36).
Discrete samples are acquired during the interval t to form a 2D dataset. The 2D Fourier transformation yields a correlation spectrum in f — f space or real space. The slice selective pulse in the back-projection imaging sequence of Fig. 5 is a self-refocusing pulse, allowing the magnetization to be sampled immediately following the RF pulse (Green and Freeman, 1991). In general one needs to apply a slice refocusing gradient of opposite magnitude after the RF pulse so that the spins are in phase at the beginning of acquisition. This is shown in Fig. 7. The area of the negative gradient must be one-half the area of the slice selection gradient pulse. At the same time, the read-out dimension is prephased and the phase encoding gradient is applied. Prephasing in the read-out dimension k is done to allow symmetric V sampling of k-space by first moving in the negative k direction before the V read-out gradient moves in the positive k direction. Phase encoding V gradients are applied along the y-dimension. Part of the trajectory through k-space during the gradient-echo sequence is shown in Fig. 8. Starting in the middle of k-space particular values of k and k are determined by the W V phase-encode and read-out prephase gradients. The amplitude of the phaseencode gradient is changed for the next step to move to a different point in k . By continuing to raster across k for the different values of k , a complete W V W and even sampling of k-space is achieved. In typical imaging sequences, k V is acquired with 256 datapoints and k with either 128 or 256 datapoints. W
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F. 7. Gradient echo imaging (GRAS or FLASH). Magnetization is sampled in k and k V W as shown in Fig. 8. A 2D Fourier transform of uniformly sampled k-space creates the image.
Each value of k requires repeating the sequence. This is not true for k , W V which is called the free dimension in MRI. The number of k points is V typically determined by the desired resolution and the transverse relaxation time T . 4. Chemical Shift Imaging (CSI) Chemical shift imaging (CSI), a hybrid application of imaging and spectroscopy, is used to obtain spatially resolved spectral information or images of specific spectral components. Since gradients, which would disperse frequency across spatial dimensions, cannot be applied during acquisition, phase encode gradients are applied along either one, two, or three dimen-
F. 8. Sampling of k-space by the gradient echo pulse sequence. The phase-encode gradient varies from scan to scan and allows complete sampling of k . The readout gradient is prephased W to 9k and runs to ;k . The resolution of the image is determined by the value of k V V V and the field-of-view of the image is determined by the step size in k-space.
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F. 9. Two-dimensional chemical shift imaging (CSI) sequence. After slice selection, phase encode gradients are simultaneously applied along k and k . After the gradients are applied, V W the magnetization precesses freely in the B field so that a frequency spectrum can be measured.
sions. A 2D chemical shift imaging pulse sequence is shown in Fig. 9. After the gradients are applied, the magnetization freely precesses in the B field so that a frequency spectrum can be measured. This pulse sequence has been used to separate the different components of xenon magnetization in both the rat brain and body (Swanson et al., 1997; Swanson et al., 1999b) and it will be described in Section V. The CSI sequence requires discrete steps through each dimension of k-space, and is much slower than back projection and gradient echo sequences, which step through only one dimension in k-space. To collect a 16 ; 16 image, 256 different acquisitions are required. E. C M R I Proton density varies only slightly in tissue, and MRI contrast therefore depends on changes in the magnetization characterized by relaxation times. The longitudinal or spin-lattice relaxation time T determines the time required for the spin polarization to return to equilibrium following excitation by a radio-frequency (RF) pulse. If the spin magnetization is flipped by /2, the longitudinal magnetization recovers according to M (t) : M(1 9 e\R2) X X
(37)
The transverse or spin-spin relaxation time T is the time constant for decay of magnetization in the transverse plane M (t) : M (e\R2 ) VW VW
(38)
Both T and T weightings require the spin-echo sequence. The spin-echo sequence is similar to the gradient echo sequence, but a pulse refocuses spins that dephase in the intrinsic magnetic field inhomogeneities of the sample. The pulse is typically applied 10 and 50 ms after the initial
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Timothy Chupp and Scott Swanson TABLE I T R T P B T †
Gray matter White matter †
T
T
1000 ms 650 ms
110 ms 70 ms
Bottomley et al., 1984.
RF pulse for T and T weighting, respectively. In brain imaging, for example, proton concentrations in white matter and gray matter are nearly equal, in contrast to the relaxation times given in Table I. For cerebral spinal fluid (CFS), motion effectively increases T . The relaxation time differences are exploited to produce images such as those shown in Fig. 10. F. L F I Nuclear magnetic resonance with nuclei polarized by laser optical pumping is less dependent on large magnetic fields than is conventional NMR, and the potential of low-field imaging has emerged. The signal to noise ratio
F. 10. Conventional proton MRI tomographic images of the human brain. The images were acquired using spin-echo sequences. The detected magnetization depends on T or T , depending on the echo time. This provides the contrast. Both white and gray matter in each lobe of the cerebrum are distinguished in the T weighted image on the left. Cerebral spinal fluid and tissue are distinguished in the T weighted image on the right.
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(SNR) is the important parameter, and we therefore consider both signal and noise. For conventional NMR, the signal S due to a nuclear spin I : /2 (for H, H, and Xe) with concentration [I] is proportional to the product of precession frequency () and magnetization: S . [I]P ' '
(39)
where I : B and the brute-force polarization is P B/kT. Thus ' ' ' S
. B[I] '
(40)
In contrast, for NMR with laser-polarized nuclei, P is independent of field, ' and S . B[I] '
(41)
The most important MRI noise sources are Johnson noise due to the pick-up coil resistance, R , amplifier noise, and dissipation in the sample due A to loading characterized by R . Skin depth effects generally increase the coil Q resistance so that R . (B. The SNR for brute force and laser polarization A for fixed bandwidth are B SNR . (1 ; B\
1 SNR . (1 ; B\
(42)
where (0.2 T)\ (Edelstein et al., 1986). This shows that above 0.2 T, the SNR for laser-polarized NMR and MRI increases very little, that is, it is approximately independent of B. There are many advantages that may be gained from NMR and MRI at lower fields. The cost of magnets is less, open geometry permanent and conventional magnets may provide friendlier NMR scanners (important for pediatrics), and high-field effects such as susceptibility dependence may be less. Low-field work has been most effectively pursued by Darrasse et al. (1998). They have shown that the combination of 0.1 T magnet and a low-polarization metastability pumped He polarizer can produce lung images with resolution comparable to standard Xe nuclear medicine techniques such as shown in Fig. 11. One-dimensional images of polarized He have been used to study diffusion effects (Saam et al., 1996). Very low-field imaging at 0.003 T has been demonstrated by Tseng et al. (1998).
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Timothy Chupp and Scott Swanson
F. 11. Lung images of a healthy volunteer produced with laser-polarized He at 0.1 T using a multispin-echo sequence. The slice thickness is 5 cm. Less than 30 cm of He with initial polarization 15% was mixed with a buffer gas just prior to inhalation. Image courtesy of Laboratoire Kastler-Brossel of ENS, Paris. Used with permission.
IV. Imaging Polarized
129
Xe and 3He Gas
Although either He or Xe may be used for gas imaging, the majority of lung ventilation imaging studies have used He. Helium has a number of advantages over xenon for creation of high-resolution gas images: The magnetic moment of He is nearly three times larger than that of xenon, and it has generally been easier to create high magnetization with He. The He polarizations are generally of 20—50% whereas typical Xe polarizations used for imaging are currently at 5%. A recent study imaging both gases concluded that in general helium is approximately 10 times more sensitive than xenon for MRI studies (Moller et al., 1999a). Helium also has fewer biological effects than xenon. Helium is biologically inert and the only consequence of helium inhalation (apart from the well-known change in voice pitch) is the risk of lowering the blood oxygen content due to oxygen being removed from the inhaled gas. Xenon on the other hand is anesthetic at concentrations of 35%. These effects are well known and have been addressed in CT studies where xenon is used to measure regional cerebral blood flow (rCBF) by monitoring the spatial and temporal attenuation of x-rays. Although helium provides greater signal strength and fewer medical complications, a major concern for widespread clinical studies with helium
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F. 12. Three lung images. Left: A Xe nuclear medicine scan of a patient with chronic obstructive pulmonary disease (COPD). Center: A laser-polarized He MRI of the same patient. Right: Laser-polarized He MRI of a healthy volunteer. Image courtesy of the University of Virginia. Used with permission.
will be the limited supply of He discussed earlier. Most studies are performed with He gas with an isotopic concentration of approximately 99% at a cost of approximately 100—150 USD/liter. Xenon is present in the air at a concentration of approximately 0.04%. The abundance of the spin 1/2 isotope, Xe, is 26.44%. Naturally abundant xenon can be purchased for approximately 10 USD/liter. The Xe enriched to approximately 75% can be purchased for about 300 USD/liter. This price is determined primarily by demand and could drop dramatically if specific clinical uses are identified. A. M R I P G: G C 1. Sampling of the Magnetization In conventional MRI, longitudinal magnetization is sampled by an RF pulse and then replenished by relaxation to thermal equilibrium with time constant T . For laser-polarized gases, the longitudinal magnetization in the body must be replenished by a fresh supply of polarized gas. With each sampling of the magnetization, the RF pulse destroys a portion of the longitudinal magnetization. The nonequilibrium polarization created by optical pumping would be entirely lost if sampled by a /2 RF pulse. Since MRI requires many excitations in order to appropriately sample k-space, /2 pulses cannot be used. The gradient echo sequence shown in Fig. 7 with a small tip angle is the most widely used approach. As the gas is sampled,
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Timothy Chupp and Scott Swanson
the longitudinal magnetization decays, with magnetization after n pulses given by M (n, ) : M cosL() X X
(43)
where is the tip angle. Thus the sampled magnetization in the initial pulses is larger than that in the later pulses if the tip angle is constant. For instance, if the tip angle is 10°, the value of the magnetization at the end will be only 20% of the initial value for the 128 pulses typically used to collect an image. This will cause different Fourier components of k-space to have intensities modified by an exponential decay. This leads to blurring of the real space image as each pixel is the convolution of the true magnetization with a Lorentzian (the Fourier transform of the exponential loss of magnetization to pulsing). Variable tip angle series have been applied to economically use laser-pumped magnetization in two-species experiments that probe fundamental principles (Chupp et al., 1989; Oteiza, 1992). An MRI sequence with variable pulse angle that produces the proper intensity of the Fourier coefficients in k-space has been proposed (Zhao et al., 1996). In principle, the variable flip angle sequence has better SNR because all of the magnetization is sampled. In practice, it is difficult to program this sequence on clinical MRI systems and most studies use a constant flip angle. 2. Diffusion and k-Space The basic description of MRI in Section III neglected effects due to the diffusion of spins during acquisition. For gas imaging, these effects are large and present many problems, as well as a few opportunities. The main problem stems from the fact the positions and therefore the frequencies of the spins change due to diffusion as k-space is sampled during the read-out gradient. As k-space is sampled along one dimension, the mean path length for 1D self-diffusion is d : (2Dt where D is the diffusion constant and t is the time. At 1 atm xenon has a self-diffusion constant of approximately 0.06 cm/s and helium approximately 2.0 cm/s. Therefore, during a typical MRI experiment with a sampling time of about 6 ms, the resolution for He is limited to about 1.5 mm. This assumes that the spins are free to diffuse. In lung alveoli and other porous media free diffusion is restricted. This allows measurement of pore size, which has recently been applied to lung imaging. A full treatment of diffusion and restricted diffusion can be found in Callaghan (1991). A number of studies have investigated this phenomenon. Edge enhancement of the signal intensity near the walls of rectangular glass cells in 1D
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images of polarized He has been observed (Saam et al., 1996). These studies were extended to demonstrate image distortion by molecular diffusion during the read-out gradient (Song et al., 1998). In this study, the investigators varied the strength of the gradient to follow the images from the strong diffusion regime to the weak diffusion regime. In another study using thermally polarized xenon, gas diffusion was used to measure both tortuosity and surface-to-volume ratio in a system of glass beads (Maier et al., 1999). Work from the same group also showed that the gas diffusion constant can be measured in a single experiment (Peled et al., 1999). B. A I Lung ventilation imaging is currently based on nuclear medicine scintigraphy of either Xe or aerosol sprays with Tc. Laser-polarized noble-gas imaging research with animals and human subjects has already shown that tomographic (slice-selected) high resolution images can be produced. A comparison of Xe scintigraphy and laser-polarized He images shown in Fig. 12. The first human ventilation studies with He were performed in Mainz (Ebert et al., 1996) and at Duke. The group at Mainz has continued with more clinical studies of volunteers with diagnosed lung diseases (Bachert et al., 1996; Ebert et al., 1996; Kauczor et al., 1997) (see Fig. 13). Other studies have looked at helium images of the lungs of smokers (de Lange et al., 1999) and ventilation defects have been found in a few cases.
F. 13. Laser polarized He lung image. The patient is suffering from pulmonary artery obstruction. The image shows a large ventilation defect that surprisingly corresponds to an obstruction of the pulmonary arterial branch. Image courtesy of Radiologie Klinik at Mainz University. Used with permission.
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In fact even apparently healthy, active, volunteers have ventilation defects that are revealed in high-resolution laser-polarized He MRI (Mugler et al., 1997). A study of subjects with chronic asthma suggests that ventilation defects may allow a measure of the progression and treatment of the disease (Altes et al., 1999). Although it will be some time before the utility of high-resolution lung images is clarified, it is clear that they provide new information and raise new questions: for example, what are the mechanisms of signal destruction in diseased lungs (Kauczor et al., 1998). The lungs are not the only organ amenable to gas imaging. The sinus cavities (Rizi et al., 1998) and bowel (Hagspiel et al. 1999) can also be imaged with laserpolarized He or Xe. Animal studies provide, appropriate disease models for eventual clinical studies. An advantage of using a small animal model is that the amount of polarized gas needed to create an image is significantly reduced compared to an equivalent human study. Impressive results using specialized small pick-up coils to attain high resolution images of He in animal models have been obtained by the group at Duke University. They showed the first in vivo images of helium in the lungs using 2D and 3D gradient echo imaging (Middleton et al., 1995). They also have demonstrated that the back projection imaging sequence can be used to reduce problems associated with changes in signal amplitude as k-space is sampled. Figure 14 shows images from a guinea pig model. These studies also show that one can vary the tip angle to capture either the early or later phases of inhalation. More recent work has concentrated on the magnetic behavior of both He and Xe gas in the lungs. One study finds that the effective transverse relaxation time (T *) for He is approximately 14 ms in the trachea but 8 ms in the intrapulmonary airspaces. For Xe, T * is 40 ms in the trachea and 18 ms in the intrapulmonary airspaces. This indicates that Xe interacts more strongly with the tissue of the infra pulmonary airspaces as it crosses the blood gas barrier. The regional variation of the diffusion constant was measured in vivo in guinea pigs (Chen et al., 1998). A study from a group in Lyon examined combining an MRI of He gas with proton-based methods to measure lung perfusion (Cremillieux et al., 1999). The goal is to provide a regional assessment of lung function. Methods in nuclear medicine typically provide only low-resolution images that are projections through the entire lungs and are not tomographic. A combination of conventional and laser-polarized gas MRI has the potential to provide very high resolution images for diagnosis of certain lung diseases, such as pulmonary emboli. A collaboration between the Duke and Lyon groups has presented images of guinea pig lungs with 2D resolution of 100 (Viallon et al., 1999).
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F. 14. Ventilation images of a guinea pig lung showing the exceptional spatial resolution possible with polarized He and the specialized techniques of in vivo microscopy. Image courtesy of the Center for in vivo Microscopy at Duke University. Used with permission.
C. I He Xe C Laser-polarized gas dissolved or encapsulated in injectable carriers is also under study (Goodson, 1999). Since xenon is highly soluble in nonpolar liquids, it is possible that images of xenon can be obtained in vivo by injection of xenon dissolved in an appropriate carrier. Work at Pines’s laboratory at the University of California, Berkeley, has shown that xenon dissolved in different carriers may have a significantly greater SNR than can be created by inhalation of xenon gas (Goodson et al., 1997). At Duke, laser-polarized He was trapped in microbubbles and introduced into the tail vein and arterial blood of a rat (Chawla et al., 1998). This new form of angiography provided high-resolution images. Also at Duke, laser-polarized Xe was dissolved in biologically compatible lipid emulsions (Intralipid 30% (Moller et al., 1999b). Measured relaxation times were T : 25.3 <
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2.1 s, and T * : 37 < 5 ms. Analysis of magnetization inflow was used to deduce the mean blood flow velocity in several organs. Several other potential carriers have been investigated including perfluorooctyl bromide (PFOB), which is a blood substitute (Wolber et al., 1998).
V. NMR and MRI of Dissolved
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Xe
In contrast to He, which is most useful for imaging air spaces such as the lungs and colon, Xe is soluble in blood with 17% solubility and tissue with varying solubility (Chen et al., 1980). Many of the biological properties of xenon have been established through research with radioactive isotopes, particularly Xe. Xenon freely diffuses across biological membranes including the blood gas barrier in the lungs and capillary walls between blood and tissue. Xenon is metabolically inert, and is carried to distant organs where it accumulates in tissue. The size of the Xe magnetization signal in a specific region of interest can be a measure of the rate of blood flow or perfusion through the tissue. Studies using radioactive Xe have shown that xenon can be used in diagnosis and research to measure kidney perfusion (Cosgrove and Mowat, 1974), and cardiac perfusion (Marcus et al., 1987). Most exciting may be the study of regional brain activation. A variety of techniques has enormously enriched our understanding of the functional organization of the nervous system. The methods of Kety and Schmidt (1945) for measuring total blood flow following administration of a metabolically inert gas have been combined with radiotracer imaging techniques to measure changes in regional cerebral blood flow (rCBF) correlated with sensory stimulation, motor activity and inferred information processing in the brain. Early experiments used inhaled or injected gamma-emitting gases such as Xe (Lassen, 1980) or Kr (Lassen and Ingvar, 1961) to measure altered blood flow in the cerebral cortices. More recently, PET methods, most notably those employing O-H O, have been used to measure rCBF (Phelps, 1991). However PET techniques have intrinsic resolution limited to 2—4 mm due to the range of positrons in tissue and often require a complementary imaging technique such as MRI or CT for accurate anatomical mapping of the PET functional information. The MRI methods are not subject to these intrinsic limitations and can provide functional information and anatomical registration with a single modality and apparatus. Several methods for measuring brain function with MRI have been explored (Shulman et al., 1993), and techniques based on blood oxygen level dependence of proton NMR have demonstrated high spatial resolution (Ogawa et al., 1990), although the physiological basis for the detected changes in signal is not well understood (Shulman et al., 1993).
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F. 15. Spectra from the body and head of a rat breathing a Xe-O mixture. Left: the body spectrum showing signals from gas in the lungs (at 0 ppm), and dissolved in the blood (210 ppm) and tissue (192 ppm and 199 ppm). Right: the spectrum from the head showing several tissue peaks and possibly the blood peak near 210 ppm.
A. S Xe in Vivo Figure 15 shows an NMR spectrum of Xe from the body and head of a rat that had been breathing a mixture of Xe and oxygen gas (Swanson et al., 1999b). Similar spectra have been observed in humans after a single breath-hold of laser polarized Xe (Brookeman, 1998). The peaks in the rat body-spectrum (Fig. 15a) as well as the time dependence of the peaks have been identified on the basis of work by several authors (Wagshul et al., 1996; Sakai et al., 1996; Swanson et al., 1999b), the location of each resonance determined by imaging (see Fig. 2), and the chemical shifts revealed in in vitro experiments (Wolber et al., 1999a). The chemical shift may also depend on the oxygenation level of the blood (Wolber et al., 1999b) and varies with tissue type. The spectrum from the head (Fig. 15b) reveals at least four peaks in addition to the apparent blood peak at 210 ppm. Although there is not yet a definitive identification of the separate tissue types, this does show that several kinds of brain tissue are highly perfused and/or have large partition coefficients for dissolved xenon. An exciting direction for future research is the identification of each chemical shift component and functional study of the differences. It may become possible to identify the kinds of brain tissue involved in specific neurological functions. B. Xe I As Xe is carried throughout the body by the flow of blood, it is deposited in tissue with time dependent concentration that depends on several factors including the rate of blood flow, that is, perfusion. Perfusion measurement
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F. 16. Illustration of the data provided by the CSI imaging sequence. For each pixel, a frequency spectrum is produced. Spectra for four pixels are shown. The background gray-scale image is a proton MRI acquired with the spin-echo sequence. The oval surrounds the heart region. (See also Color Plate 2).
has many applications, ranging from rCBF measurement and research in cognitive neuroscience to assessment of pulmonary, renal, and cardiac health. One key goal of laser polarized Xe MRI is the development of perfusion measurement techniques (i.e., Xe as a magnetic tracer that uses chemical shifts to isolate each tissue type). The development of such techniques is discussed in Section V.D. Images of each chemical shift component of Xe can be created using the CSI sequence (described in Section III.D.4) and possibly frequency selective excitation. The CSI sequence produces frequency spectra for each pixel as illustrated in Fig. 16 (see also Color Plate 2), where we show spectra acquired for each of four adjacent pixels. The pixel map is superimposed on proton images acquired with the spin-echo sequence described in Section III.5. In Fig. 2, actual images of Xe in gas, blood, and tissue are shown. These images are magnetization maps of the signal in each of the peaks
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F. 17. A CSI image of Xe dissolved in tissue of the rat brain. On the left is the gray-scale Xe image and on the right is that image false-colored and superimposed on a proton spin-echo image.
indicated in Fig. 15a. An image of Xe dissolved in tissue in the rat head (Swanson et al., 1997) is shown in Fig. 17. The images of Xe in dissolved phases shown in Fig. 2 demonstrate some potential medical applications that may emerge in the coming years. Images of the lungs in the gas phase (Fig. 2A,D) show the region of ventilation. In a healthy lung, xenon crosses the blood-gas barrier, appearing also in tissue (Fig. 2B,E) and blood phase images (Fig. 2C,F). We discuss further analysis of lung function in the next section. The blood carries the Xe magnetization from the lungs to the left side of the heart. In the heart, the blood phase signal is dominated by pooled blood in the left heart chambers. Perfusion in the healthy heart is indicated by the appearance of Xe magnetization in the dissolved tissue and fat phases in the heart are also shown in Fig. 2B,E. Restricted blood flow (ischemia) and unperfused regions (infarction) would be revealed by the absence of the dissolved tissue phase in that region. C. L F The main functions of the lung are ventilation and perfusion. Many problems in the lungs result when there is a ventilation-perfusion mismatch. For example, regions of the lung that are ventilated but not perfused characterize about 70% of pulmonary embolism cases. Tomographic measurement of ventilation and perfusion, combining gas phase imaging in the lungs and Xe-dissolved phase imaging of the blood and tissue provide a
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F. 18. Images of ratios of Xe resonances. Left: gas, tissue; middle: gas, blood; right: blood, tissue.
new way to study lung function and may assist in appropriate treatment of lung disease. The data of Fig. 2 can be analyzed to extract ratios of blood and gas Xe concentrations. The image in Fig. 18a shows that the gas tissue ratio is relatively uniform except near the trachea and in the peripheral regions of the lung. The gas blood ratio image (Fig. 18b) shows a similar mismatch in the trachea but also more variation throughout the lungs. Some of this variation may be normal. Other possible pulmonary MRI methods using polarized Xe are venous injection of dissolved gas (see Section IV), followed by simultaneous imaging of the blood and gas components and study of the spatial variation in the frequency of the blood resonance, likely related to the oxygen content of the blood. The rich information content of Xe spectra and images provides interesting opportunities for pulmonary applications. D. T D M T T The time dependence of the different chemical shift components of Xe is important in several applications. As we show here, a laser polarized Xe magnetic tracer can measure blood flow and the dynamics of exchange across blood gas and blood tissue barriers. In general, the time dependence of a chemical shift magnetization component depends on the rate of delivery to the tissue in the region of interest (perfusion) and on the local magnetization relaxation time T . This relaxation time is also, in general, time dependent as oxygen concentration changes. Several authors have developed multicompartment models of Xe magnetization time dependence (Peled et al., 1996; Martin et al., 1997; Welsh et al., 1998). The goal is to measure the time dependence and use the model to extract quantities of interest, in particular T and blood flow independently. Although nuclear medicine methods based on PET are highly developed, MRI-based methods of tissue perfusion measurement may have advantages:
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F. 19. Schematic of the magnetic tracer technique described in the text.
(1) chemical shift information allows blood and various tissue types to be isolated; (2) with an entirely MRI-based technique, the perfusion map can be anatomically registered with conventional proton images; (3) the resolution is not inherently limited, in the way PET is limited to several millimeters by the range of high energy positrons in tissue; and (4) radioactive dose restrictions that limit repeated PET studies do not have an impact on MRI techniques. In Fig. 19 we schematically illustrate how MRI of laser-polarized Xe can be used as a magnetic tracer to measure perfusion. Once inhaled, Xe is carried from the lungs to the heart, brain, and other distal organs. The signal produced at the frequency of the tissue resonance in a given organ (or pixel in an organ) is a measure of the total Xe magnetic moment in the measured volume of tissue. Tissue magnetization M calibrated in units of 2 the arterial magnetization M depends on blood flow F and the local magnetization relaxation rate 1/T in different ways. If M is uncalibrated, 2 data can be used to determine relative blood flow. As the blood carries Xe with magnetization M into tissue, the NMR signal size of the tissue resonance in each volume element of the tomographic image changes with time. The differential equation describing the tissue magnetization (M ) in a voxel is 2 F 1 dM 2 : FM 9 ; M 2 T dt 2
(44)
where F is the rate of blood flow in units of ml /minute/ml , and 2 2 is the blood-tissue partition coefficient — the ratio of concentrations of xenon in blood to that in tissue. The time constant for relaxation of Xe
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magnetization to thermal equilibrium is T . This differential equation is quite similar to that for the standard nuclear medicine formulation describing wash-in of a radioactive tracer (e.g., O-H O for PET or Xe for SPECT). However, there is an extremely important difference — the relaxation time constant T is not uniform, rather it is generally different in different tissues and blood, and it depends on the blood’s oxygenation level (Wilson et al., 1999; Wolber et al., 1999a). Measurement of dynamics of Xe tissue resonance in the rat brain is consistent with T 30 s (Welsh et al., 1998). Techniques have been proposed for separating F and T (Swanson et al., 1999a). Absolute measurement of F in units of ml/min/ml requires calibration of M in units of M . This requires measuring the magnetization signal from 2 known volumes of tissue and blood, respectively. For a quantitative measure of rCBF, it may be possible to image the blood in the carotid artery. For cardiac perfusion, imaging of the pulmonary veins and left heart chambers is possible (see Fig. 16). One important caveat follows from the small separation of the blood and tissue peaks, 150 Hz at 1.5 T. With the observed T * varying from 2 ms in blood to 20 ms in brain tissue, any NMR pulse that tips the magnetization of Xe in tissue will perturb the blood magnetization. Thus M will come to an equilibrium value that is, in general, less than the unperturbed M . However, the perturbation can be relatively small with proper design of the pulse shape and phasing and because the rate of blood flow to the region of interest is high compared to the pulse rate 1/ (Geen and Freeman, 1991). Another possible complication is that the blood and tissue concentrations may not equilibrate rapidly on the time scale of the imaging experiments (about 1 s), resulting in an apparent variation of . 2 1. Dynamics of Laser-Polarized Xe in Vivo Features of the dynamics of laser-polarized Xe in the lungs, body and brain of rats in vivo are shown in Fig. 20 (Swanson et al., 1999b). Frequency spectra collected as a function of time were used to study the dynamics of laser-polarized Xe. Qualitative interpretation suggests that the blood component builds up more quickly and saturates with respect to the lung input function, whereas the tissue component builds up more slowly due to greater tissue capacity for xenon, and falls off more slowly due to the longer intrinsic T in tissue and the relatively slow wash out of xenon. The amplitude of the blood resonance closely follows the amplitude of the scaled gas resonance. The blood resonance plateaus after about 13 s of xenon delivery, but the tissue peak and the fat peak continue to grow and do not level off, even when xenon delivery is stopped at about 25 s.
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F. 20. Dynamics of Xe gas, blood, and tissue resonances.
VI. Conclusions — Future Possibilities The future is exceptionally bright for research in biomedicine, neuroscience, and materials science using laser-polarized rare gas imaging. The scientific problems relating to polarization techniques and the delivery of polarized gas with devices and in solutions are challenging, but progress continues. Ventilation images of animals and humans in the United States and Europe provide unprecedented resolution and are likely to provide new information, as is often the case when we can look at something with greater sensitivity, precision, and resolution. Figure 21 provides a stunning example. The new techniques possible with Xe provide resolution in chemical shift frequency and time that promise to develop into methods to measure perfusion of specific tissues as well as organs, thereby serving to complement PET. The potential for a complexity quantitative measure of perfusion promises broad application. All of these possibilities have been discussed in this chapter. However, research with a new imaging modality does not ensure its application as a medical diagnostic procedure. Among the potential applications of high-resolution lung ventilation imaging, colonscopy, lung function assessment, and perfusion measurement, MRI with laser-polarized gases must pass the tests of: 1. sensitivity to disease or injury; 2. specificity for a unique diagnosis; and 3. effectiveness based on cost and risk. For example, high-resolution lung imaging with He has been shown to be clearly sensitive to small ventilation defects — regions of the lung that do not effectively fill with gas in a normal breath. However the question of which specific malady this indicates is currently open. On the other hand,
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F. 21. A surface rendering of the human lung constructed with laser-polarized He MRI. Image courtesy of the University of Virginia. Used with permission.
lower resolution He or Xe lung images, produced with less gas and lower polarization (see Fig. 13) provide the same ventilation information as a Xe nuclear medicine scintigraphy, but without the radiation dose of nearly 1 rad from a single study. Such lower resolution scans would therefore provide the demonstrated sensitivity and specificity of the widely used nuclear medicine techniques. However, the cost of an MRI is currently many times greater than a Xe nuclear medicine study, and the additional cost of laser-polarized gas would significantly increase the cost of an MRI. Low-magnetic-field imaging systems may bring the cost down. Early diagnosis procedures and repeated studies that would be limited by radiation dose may be developed by physicians with these new tools. Pediatric pulmonary medicine may be an important application of the combination of diagnosis without radiation dose and low-field, open-geometry magnets. With the promise of these and a host of other potential applications, clinical efforts are underway in the United States and Europe. In the United States efforts are organized by commercial interests, which would produce the polarized gas in regional centers and ship it, overnight, to medical facilities. In Europe, a collaboration of industry, academic, and
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hospital-based researchers is developing the clinical program. The goals of both these groups include regulatory approval for administration of polarized gas as a contrast agent and its use for medical diagnosis. Interestingly, the final step in regulatory approval, following demonstration of safety and other issues, is a demonstration of efficacy — the sensitivity and specificity for diagnosis of specific maladies that would prove useful to clinicians/ physicians.
VII. Acknowledgments The authors are grateful to several colleagues for discussions and advice regarding this chapter and for scientific inspiration and guidance. They are Bernie Agranoff, Jim Brookeman, Gordon Cates, Kevin Coulter, Tom Chenevert, Will Happer, Bob Koeppe, Pierre-Jean Nacher, Eduardo Oteiza, Matt Rosen, Brian Saam, Ron Walsworth, Robert Welsh, and Jon Zerger. Images were provided by Brian Saam, Jim Brookeman, Tom Chenevert, Hans-Ulrich Kauczor, Pierre-Jean Nacher, and Al Johnson.
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Viallon, M., Cofer, G. P., Suddarth, S. A., Moller, H. E., Chen, X. J., Chawla, M. S., Hedlund, L. W., Cremillieux, Y., and Johnson, G. A. (1999). Functional MR microscopy of the lung using hyperpolarized He. Magn. Reson. Med. 41(4):787—792. Wagshul, M. and Chupp, T. E. (1989). Optical-pumping of high-density Rb with a broad-band dye-laser and GaAlAs diode-laser arrays: Application to He polarization. Phys. Rev. A 24:827. Wagshul, M. E. and Chupp, T. E. (1994). Laser optical-pumping of high-density Rb in polarized He targets. Phys. Rev. A 49:3854—3869. Wagshul, M. E., Button, T. M., Li, H. F. F., Liang, Z. R., Springer, C. S., Zhong, K., and Wishnia, A. (1996). In vivo MR imaging and spectroscopy using hyperpolarized Xe. Magn. Reson. Med. 36:183—191. Walker, T. G. (1989). Estimates of spin-exchange parameters for alkali-metal noble-gas pairs. Phys. Rev. A 40(9):4959—4963. Walker, T. G. and Happer, W. (1997). Spin-exchange optical pumping of noble-gas nuclei. Rev. Mod. Phys. 69(2):629—642. Wehrli, F. W. (1995). From NMR diffraction and zeugmatography to modern imaging and beyond. Prog. Nucl. Magn. Reson. Spectrosc. 28:87—135. Welsh, R. C., Chupp, T. E., Coulter, K. P., Rosen, M. S., and Swanson, S. D. (1998). Magnetic resonance imaging with laser-polarized Xe. Nucl. Instrum. Methods Phys. Res. Sect. A-Accel. Spectrom. Dect. Assoc. Equip. 402(2—3):461—463. Williams, W. G. (1980). Neutron polarizers. Nukleonika 25:769—786. Wilson, G. J., Santyr, G. E., Anderson, M. E., and DeLuca, P. M. (1999). Longitudinal relaxation times of Xe in rat tissue homogenates at 9.4 T. Magn. Reson. Med. 41(5):933—938. Wittenberg, L. J., Santarius, J. F., and Kulcinski, G. L. (1986). Lunar source of He for commercial fusion power. Fusion Technol. 10(2):167—178. Wolber, J., Cherubini, A., Dzik-Jurasz, A., Leach, M., and Bifone, A. (1999a). Spin-lattice relaxation of laser-polarized xenon in human blood. Proc. Natl. Acad. Sci. USA. 96(7):3664—3669. Wolber, J., Cherubini, A., Leach, M., and Bifone, A. (1999b). Hyperpolarized Xe as a sensitive NMR probe for blood oxygenation. European Radiology 9:B42. Wolber, J., Rowland, I. J., Leach, M. O., and Bifone, A. (1998). Intravascular delivery of hyperpolarized Xe for in vivo MRI. Appl. Magn. Reson. 15(3—4):343—352. Woodward, C. E., Beise, E. J., Belz, J. E., Carr, R. W., Filippone, B. W., Lorenzon, W. B., McKeown, R. D., Mueller, B., Oneill, T. G., Dodson, G. et al. (1990). Measurement of inclusive quasi-elastic scattering of polarized electrons from polarized He. Phys. Rev. L ett. 65(6):698—700. Zeng, X., Wu, Z., Call, T., Miron, E., Schreiber, D., and Happer, W. (1985). Experimentaldetermination of the rate constants for spin exchange between optically pumped K, Rb, and Cs atoms and Xe nuclei in alkali-metal noble-gas Van der Waals molecules. Phys. Rev. A 31(1):260—278. Zerger, J., Lim, M., Coulter, K., and Chupp, T. E. (2000). Polarization of Xe with high power external-cavity laser diode arrays. Appl. Phys. L ett. 76(14):1798 —1800. Zhao, L., Mulkern, R., Tseng, C., Williamson, D., Patz, S., Kraft, R., Walsworth, R., Jolez, F., and Albert, M. (1996). Pulse sequence considerations for biomedical imaging with hyperpolarized noble gas MRI. J. Mag. Res. 113:179.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 45
POLARIZATION AND COHERENCE ANALYSIS OF THE OPTICAL TWOPHOTON RADIATION FROM THE METASTABLE 2S STATE OF ATOMIC HYDROGEN ALAN J. DUNCAN and HANS KLEINPOPPEN Unit of Atomic and Molecular Physics, University of Stirling, Stirling FK9 4LA, Scotland
MARLAN O. SCULLY Department of Physics, Texas A&M University, College Station, Texas 77843; and Max-Planck-Institut fu¨ r Quantenoptik, D-85748 Garching, Germany I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. On the the Theory of the Two-Photon Decay of the Metastable State of Atomic Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. The Stirling Two-Photon Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . IV. Angular and Polarization Correlation Experiments . . . . . . . . . . . . . . A. Two-Polarizer Experiments: Polarization Correlation and Einstein-Podolsky-Rosen Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Tests of Garuccio-Selleri Enhancement Effects . . . . . . . . . . . . . . . C. Three-Polarizer Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Breit-Teller Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Coherence and Fourier Spectral Analysis — Experiment and Theory . VI. Time Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Correlation Emission Spectroscopy of Metastable Hydrogen: How Real are Virtual States? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Abstract: This chapter first summarizes fundamental aspects and results of the quantum electrodynamical theory of the two-photon radiation from the decay of the metastable 2S atomic hydrogen state. After a brief description of the second improved Stirling two-photon coincidence experiment polarization correlations of the two-photon decay are described in which both two or three linear polarizers are applied in order to test predictions of such correlations based upon quantum mechanics and local realistic theories (i.e., Einstein-Podolsky-Rosen type experiments). It is particularly noticeable that the three-polarizer coincidence measurement provided the largest difference (about
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Copyright 2001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003845-5/ISSN 1049-250X/01 $35.00
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Alan J. Duncan et al. 40%) between the Bell limits of local realistic theories and quantum mechanics so far. Apart from confirming in addition the correlations of right-right and left-left circularly polarized two-photon correlations a new type of coherence analysis of the two-photon radiation has been carried out experimentally and theoretically. A result of it is the measured coherence time of : 1.2 · 10\ s and coherence length of l : c : 350 nm of the two-photon emission. By applying a theoretical model of the two-photon radiation linked to cascade transitions the coherence length can be estimated to l 100 nm in agreement by order of magnitude with the experimental data.
I. Introduction It is generally recognized that the spectroscopy of atomic hydrogen has provided crucial tests of the foundation of basic quantum physics, quantum electrodynamics, and even areas of elementary particle physics (Series, 1988; Selleri, 1988; Greenberger and Zeilinger, 1995; and Scully and Zubairy, 1997). As early as 1887 American physicists Michelson and Morley observed that the first spectral line H of the Balmer series of atomic hydrogen was ? split into two components, which Sommerfeld subsequently interpreted as a relativistic effect, afterwards called spin-orbit coupling and described by introducing a further quantum number referred to as electron spin. The experimental detection of the fine structure of the hydrogen Balmer line was the beginning of the precision spectroscopy of atoms. The 2S and 2P states were predicted by Dirac’s quantum mechanics to be degenerate but this was proved incorrect by the sensational detection of an energy difference between these states by Lamb and Retherford (1947) (Lamb shift
E(P 9 S ) 5 1050 MHz). The question as to whether the 2S -state of atomic hydrogen would be metastable in practice was a source of controversy during the first part of this century as discussed in detail by Novick (1969). However, the successful radio-frequency experiment of Lamb and Retherford (1947), which detected transition between the 2S and 2P states, depended on the metastability of the 2S state. The first experiments for the direct detection of two-photon radiation from metastable states was reported for the decay of He>(2S ) by Lipeles et al. (1965) and of H(2S ) by O’Connell et al. (1975) and also by Kru¨ger and Oed (1975). The possibility of a spontaneous two-photon transition in general had been predicted by Go¨ppert-Mayer (1931) based upon her pioneering theory of multiphoton processes of atomic systems. Following this theory, Breit and Teller (1940) estimated that the dominant decay mode of the atomic hydrogen 2S state should be the two-photon emission and much subsequent theoretical work has been carried out on the subject (Series, 1988; Drake, 1988, in the work edited by Series, 1988). In this chapter the data from the Stirling two-photon experiment is summarized and evaluated. This summary will include reports of measure-
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ments of the geometric angular correlations of the two photons and their polarization correlation observed in coincidence (including confirmation of the Breit-Teller hypothesis). As will be discussed, the two-photon metastable atomic hydrogen source also provides a means of carrying out fundamental experiments of the Einstein-Podolsky-Rosen (EPR) type (Einstein et al., 1935). In addition to experiments involving two linear polarizers, following proposals by Garuccio and Selleri (1989), experiments with three linear polarizers are described that provide particularly sensitive tests to distinguish between the predictions of quantum mechanics and local realism. A Stokes parameter analysis of the coincident two photons, which proves the coherent nature of the two-photon transition of metastable hydrogen, is also discussed. An experiment based on a delay of one of the orthogonal polarization components of one photon of the two-photon pair by a multiwave plate leads to the measurement of the coherence length of a single photon of the two-photon pair, which is shown to be extremely short. A novel Fourier-transform spectroscopic method using a Stokes parameter analysis of the two-photon polarization to determine the spectral distribution of the two photons emitted in the spontaneous decay of metastable atomic hydrogen is described. The theoretical analysis (Biermann et al., 1997) of the two-photon correlation spectroscopy of metastable atomic hydrogen in comparison to two-photon cascade emission from a three-level atom will be discussed. Attention is also drawn to more general summaries on the physics of atomic hydrogen (including collision processes) by Series (1988), Basassani et al. (1988) Friedrich (1998) and McCarthy and Weigold (1995).
II. On the Theory of the Two-Photon Decay of the Metastable State of Atomic Hydrogen As already mentioned here, the theory of the two-photon emission of the metastable 2S state of atomic hydrogen was initiated by a paper from Breit and Teller (1940), which was based upon Maria Goeppert’s (1929) and Goeppert-Mayer’s (1931) quantum theory of multiple-photon processes in atomic spectroscopy. Since then substantial progress has been made both theoretically and experimentally with regard to the physics of the two-photon emission of metastable atomic hydrogen. The exact quantum mechanical description of the two-photon process is based upon the four-component Dirac equation. (see, e.g., Drake, 1988). This theoretical approach is well discussed in terms of the matrix formalism of quantum electrodynamics (Akhiezer and Berestetskii, 1965).
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Before we describe some results of the theoretical formalism for the two-photon decay of the metastable 2S state the competing electromag netic transitions in the absence of any perturbation such as an electric field or atomic collisions will be considered. Due to the Lamb shift the 2P state is the only one of the n : 2 states lower than the 2S state. However, as the energy difference is so small the possible spontaneous electric dipole transition from the 2S to the 2P state has a negligibly small transition probability (corresponding lifetime of about 20 yr). Magnetic dipole and electric quadrupole transitions of the 2S state are forbidden in the Pauli approximation but magnetic dipole M transitions are allowed if exact Dirac theory with Dirac wave functions are allowed with a decay rate of 2.496 ; 10\s\, corresponding to a medium lifetime of about 2 days. The two-photon transition probability is much greater and has been estimated to be about 14 s\ for the two-photon transition of metastable atomic hydrogen (corresponding to a mean lifetime of 1/7 s). Figure 1 illustrates spontaneous and field-induced radiative transition modes of the metastable state of atomic hydrogen. While interest here is exclusively related to the two-photon decay, the study of field-induced quenching radiation reveals measurable interference effects and quantum beat phenomena applied in atomic spectroscopy (Andra¨, 1974 and 1979; van Wijngaarden et al., 1974; Drake et al. 1979). The quantum electrodynamical theory of the simultaneous emission of the two photons with vector potentials A (x) and A (x) can be illustrated by the second-order Feynman diagrams shown in Fig. 2. The relevant second-order S-matrix element for these transitions is S : (e/ ) GD
; (e/ )
(x )A *(x )SC (x , x )A (x ) (x )dx dx D D A
(x )A *(x )SC (x , x )A *(x ) (x )dx dx D A
where SC is the electron propagator in the external field of the nucleus. With A substitutions of (r ) (r ) 1 dweGUR\R L L SC(x , x ) : A (1 9 i ) ; 2 i \ L L
one obtains S : (92 i/ )U ( ; 9 ; ) GD GD G D
(1)
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F. 1. Spontaneous and field-induced radiative transitions of the metastable 2S state of atomic hydrogen. The 2E1 denotes the two-photon decay mode, M1 and M2 the magnetic dipole, magnetic quadrupole and E1 the electric dipole decay modes. The states between the metastable and the ground state represent ‘‘virtual’’ states (dotted lines) associated with the emission of the two photons of energies h and h . Single photon decay modes may lead to cross terms to produce quantum beats and interference effects and also contributions to the two-photon decay rates (Drake, 1988). The dashed-dotted lines indicate the mixing of the metastable state with the 2P and 2P states by an external perturbation such as electric fields or atomic collisions. Note that the energy differences are not scaled.
where and are the angular frequencies of the two emitted photons; the positive frequency for the electron and 9 the negative frequency D G for the positron follow from the solutions of the Dirac equation. The preceding equation includes the second-order interaction energy expressed by the formula: f · A*( )n n · A*( )i
e U : 9 GD ; 9
L L G f · A*( )n n · A*( )i
(2) ; ; 9 L G
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F. 2. Feynman diagrams for the two-photon decay of metastable atomic hydrogen: (a) (x ) and (x ) are the wave functions of the final ground state and the metastable state; A (x ) and A (x ) are the vector potentials of the two photons, and SC is the electron A propagator in the external field of the nucleus (Eq. 1); x are the relativistic four-component coordinates (after Akheizer and Berestetskii, 1965). (b) In nonrelativistic electric dipole approximation the energies of the ground, final, intermediate P state and metastable (initial) states, W , W , and W , are connected by the products p A and p A of the canonical momenta D N G p and p and the vector potential A and A to result in the photon energies h and h . It demonstrates that the emission of the two photons can be considered in either order as shown in the Feynman diagram (2b).
The summation in this relativistic expression is taken over both positive and negative frequency states i , f and n denote the initial (2S ), the final (1S ) and the intermediate state for the two-photon emission. The symbol is the usual Dirac matrix. The spectral distribution of the two-photon radiation only requires ; : 9 which means that only one of G D the two-photon frequencies is independent. The so-called triply differential emission rate in the energy interval dE between the two energy states E Q and E is given by Q 2 w( , )d d dE : U ( ) ( )dE GD D D
:
a Q( , )d d dE (2 )
(3)
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where Q( , ) : 9 L
f a · e e\GI Pn na · e e\GI Pi
; 9 L G f a · e e\GI Pn na · e eGI Pi
; ; 9 L G
(4)
where e and e are unit vectors in the polarization directions of the two photons and an average will be taken over the directions of emission and polarization. The interference of the two terms in Eq. (4) results from the fact that complementary pairs of photons of energies hv and hv (or hv , hv ) are indistinguishable. It should be emphasized that the picture of simultaneous emission of the two photons assumed here has some limitations as it follows from the analysis of coherence effects as measured and reported in the chapter by Z. Vager (see p. 203, this volume). In the nonrelativistic electric dipole approximation the following expression is replaced by · e e\GIP ; p · e /mc and the sum in Eq. (4) is restricted to positive frequency intermediate states. The central problem is to evaluate numerically the expressions of Eq. (3). The summation is to be taken over all intermediate states n and their related energy states E : . There are L L several important consequences of the results of the theory: 1. Based upon the preceding replacement of the Dirac matrix , the Feynman diagram of Fig. 2a can be drawn as shown in Fig. 2b with the energies of the states involved. 2. The energies of a complementary pair of two photons add up to the energy difference between the 2S and 1S states. Figure 3 shows shapes of such energy distributions for Z : 1 and Z : 92. 3. According to Breit and Teller (1940), the electric dipole operators in the interaction Hamiltonian are diagonal in nuclear and electron spins. As a result the presence of hyperfine and fine structure effects can be neglected in the two-photon emission process (see Section V). 4. If e and e are the unit vectors of the linear polarizations for the two photons with energies hv and hv the transition probability has a cosine square dependence I(v ) . e · e : cos where is the angle between e and e (Fig. 4). 5. Averaging over these polarizations results in an angular correlation for the coincident detection of the two photons: I(v ) . e 9 e . (1 ; cos) ?T
(5)
where is the angle between the directions of coincident detection of the
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F. 3. Energy distribution of the 2S ; IS two-photon continuum radiation of hydrogen-like atomic systems with nuclear charges Z : 1 and Z : 92 (uranium). Here (y, z) is the spectral distribution function and y is the fraction of the total transition energy transported by one of the two photons; correspondingly 1 9 y is the fraction of the energy of the other photon. The areas under the curves are normalized to unity (from Goldman and Drake, 1981).
two photons. In the chapter by Demtro¨der, Keil, and Wenz such polarization and angular correlations have been confirmed experimentally. In most of the experiments, however, the two photons are normally observed in diametrically opposite directions, that is, with : . A relevant and interesting form to describe the polarization for two photons can be based upon the formulation of a two-photon state vector for : . Conservation of angular momentum and parity implies the following arguments. In the transition H(2S) ; H(1S) no orbital angular momentum change occurs. Therefore the two photons with energies hv and hv must have
F. 4. Diagram illustrating the angular correlation and the correlation angle between the polarization unit vectors e and e involved in the detection of two-photon emission.
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equal helicities and the photon pairs are either right-right R R or left-left L L handed circularly polarised or in a superposition of both kinds, that is, 1 R R < L L : ! (2 The parity operator P transforms the handedness of right- and left-circularly polarized light and the propagation of the two photons in opposite directions: PR : L and PL : R . The two states of 2S and 1S have definite even parity (l : 0) so the two photons should also have even parity (otherwise the resulting parity could be a superposition of even and odd parity), that is, the plus signs should be valid in the preceding equation, viz, 1 R R ; L L : > (2
(6)
Because of the usual relations between circular and linear optical polarizations R : 2\(x ; iy ), L : 2\(x 9 iy ),
R : 2\(x 9 iy ) L : 2\(x ; iy )
(7)
the two-photon state vector can be written alternatively as : 2\(x x ; y y ).
(8)
The following implications of these state vectors should be noted. a. They are invariant with respect to rotation about the detection z-axis (see Fig. 5). b. The state vector represents a pure quantum mechanical state, not a mixture of the R R and L L states (or alternatively not a mixture of the x x and y y states). c. Consider a typical ideal coincidence experiment for measuring linear or circular polarization correlations in the opposite directions of z and 9z (Fig. 5). With such measurements, the state vector * ‘‘collapses’’ into R R or L L or alternatively into x x or y y , each possibility occuring with a probability of one-half. This collapse of the state vector implies that detection of a photon, say in the
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F. 5. Coordinate system with reference to the emission and polarization correlations of the two-photon emission (h and h ) of metastable atomic hydrogen H(2S) detected in the z and 9z directions by the two detectors and D and D . The transmission axes of the two polarizers are at angles and with respect to the directions (after Perrie et al., 1985).
z-direction, with special choices for linear or circular polarizers determines the result of the measurement of the polarization in the other detector, say in the 9z direction, irrespective of the distance between them. The result obtained on one side of the source depends on the choice made for the setting of the polarizer on the other side of the source. This situation clearly violates the ‘‘principle of locality’’ in classical and relativistic physics, according to which the value obtained for a physical quantity at point A cannot be dependent on the choice of measurement made at point B as long as the physical quantities at point A are not correlated with the ones at point B. This discussion already in essence leads to the Bohm-Aharonov (1957) version of the Einstein-Podolsky-Rosen-Paradox concerning the incompleteness of quantum mechanics (see Section IV).
III. Stirling Two-Photon Apparatus Figure 6 illustrates schematically the second improved two-photon apparatus built at Stirling University (Perrie, 1985). Metastable D (2S) atoms were produced as a result of the capture reaction d ; Cs ; D(2S) ; Cs*, which is favored by a high resonance cross section (10\ cm). The deuterium ions (d) were extracted from a radio frequency ion source and passed through a cesium vapor cell constructed after a design by Bacal et al. (1974) and Bacal and Reichelt (1974). Deuterium was used rather than hydrogen since the radiation noise generated by interaction of the deuterium beam with the background gas was less than with hydrogen. Best statistical data of the two-photon coincidences could be achieved at an energy of 1 keV for deuterium. The D(2S) beam leaving the charge exchange cell passed
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F. 6. Schematic diagram of the second Stirling two-photon apparatus.
through a set of electric field prequench plates, allowing the metastables of the beam to be switched on and off by the effect of Stark mixing of the 2S and 2P states. At the end of the beam apparatus the metastables were completely quenched by the electric field of another set of quench plates; the resulting Lyman9(L ) radiation was used to normalize the two-photon coincidence ? signal from the metastables. The L —signal was registered by a solar blind ? UV photomultiplier together with an oxygen filter cell with LiF windows through which dry oxygen flowed continuously. Tests were made regularly to confirm that the two-photon coincidence signal was proportional to the L —signal, which depends linearly on the density of the metastables. ?
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The two-photon radiation was collimated and detected at right angles to the D(2S)-beam. Two lenses of 50-mm diameter were used, each with a focal length of 43 mm at a wavelength of 243 nm. For the linear polarization correlation measurements two high-transmission UV polarizers were used, each consisting of 12 amorphous silicon plates polished flat to at 2 at 243 nm and set nearly at Brewster’s angle as shown in Fig. 6. Additional optical elements such as quarter-wave, half-wave and multiwave plates could be inserted as required for other polarization correlation measurements. The material of the various lenses and plates was high-quality fused amorphous silica with a short-wavelength cut-off at 160 nm. This in turn corresponds to a complementary long wavelength cut-off at 355 nm. Accordingly, all photons in the wavelength range from 185 to 355 nm can contribute to possible two-photon coincidence signals. The quantum efficiency of the photomultipliers was about 20% over this range. The transmission efficiencies and and of the polarizers, for light polarized + K parallel and perpendicular, respectively, to the transmission axes of the polarizer, were measured by making use of the 253.7-nm optical line from a mercury lamp. Two of the polarizers used had transmission efficiencies of
: 0.908 < 0.013 and : 0.0299 < 0.0020; a third polarizer with plates + K from a different manufacturer had values of : 0.938 < 0.010 and +
: 0.040 < 0.002. The pulses detected by fast-rise-time photomultipliers K were fed into a coincidence circuit described by O’Connell et al. (1975). It consisted of the common combination of constant-fraction discriminators, a time-to-amplitude converter, and a multichannel analyzer operating in the pulse-height analysis mode. A typical run for acquiring coincidence signals lasted at least 20 h. Spurious coincidence signals due to cosmic rays and residual radioactivity in the apparatus occurred at a rate of one every 100 s, and decreased as the distance between the photomultipliers increased. The density of the metastable atomic deuterium D(2S) for realistic coincidence measurements was about 10 cm\ (equivalent to a partial gas pressure of about 0.3 · 10\ torr). A typical coincidence signal of the two-photon radiation is shown in Fig. 7. As can be seen, the shape of the coincidence peak is symmetrical, which is expected for the effectively simultaneous emission process of the two photons from the decay of the metastables. The background signal results mainly from the single count rates of the order of 10s\, which were due mainly to radiation produced by the metastable atomic beam interacting with the background gas of the vacuum system at a pressure of 2 ; 10\ torr; uncorrelated photons from the two-photon decay contribute only about 0. 01% to the background coincidence signal.
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F. 7. Typical coincidence spectrum for the two-photon emission from metastable atomic deuterium. The time-correlation spectrum is that which was obtained after subtraction of the spectrum produced when the metastable component of the atomic beam was quenched. Polarizers were removed for this example. Time delay differences between relative channel numbers are 0.8 ns, total collection time 21.5 h. Singles count rate with metastables present (quenched) is about 1.15 · 10 s\ (0.85 · 10 s\). The true two-photon coincidence rate from the decay of the metstable is 490 h\ for this example.
IV. Angular and Polarization Correlation Experiments A. T-P E: P C E-P-R T The first coincidence measurement of the two-photon decay of atomic hydrogen was made by O’Connell et al. (1975) for three different angles between directions of the detected photons (Fig. 8). While the accuracy of these early experiments was limited, the data approached the shape of the theoretical prediction given in Eq. (5) and clearly demonstrated a disagreement with a circularly symmetric angular correlation in the detection plane defined by the directions of the two coincident photons given by the equation proportional to (1 ; cos), which is expected by the theoretical prediction.
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F. 8. Angular correlation data for two-photon coincidences from H(2S) with detectors D and D at the three correlation angles equals 90°, 135°, and 180°. The circle represents a symmetrical angular correlation with the other curve representing the theoretical prediction, which has the form (1 ; cos).
In a subsequent improved experiment involving two linear polarizers (Fig. 5) for the detection of photons in diametrically opposite directions ( : ), the coincidence rate ratio R()/R was measured as a function of M the angle between the transmission axes of the polarizers; R() is the coincidence count rate with the two polarizers inserted while R is the M coincidence count rate with the two polarizers removed. For this case quantum mechanics predicts (Clauser et al., 1969) in the ideal case, a (1 ; cos) dependence of the coincidence signal. In practice, quantum mechanics predicts 1 R() 1 : ( ; ) ; ( 9 )F( ) cos K K 4 + 4 + R M
(9)
where in the current case the transmission efficiency : 0.908 < 0.013, +
: 0.0299 < 0.0020, the half-angle subtended by the lenses near the source K of the two-photon radiation is : 23° and F( ) : 0.996. As can be seen in
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F. 9. Linear polarization correlation of the two photons emitted in decay of metastable D(2S) as measured and compared to Q.M. (quantum mechanics) and two local realistic models (I) and (II). The theoretical curves take account of the finite transmission efficiencies and the angles of acceptances of the lenses. The transmission axes of the polarizers are rotated by the angles and with : 9 .
Fig. 9 the quantum mechanical curve fits the data of our coincidence measurements of the two-photon radiation very well while the predictions of the two local realistic theories discussed in what follows fail to do so. The horizontal straight line (curve I) for R()/R in Fig. 9 is based upon the M following local realistic model. In this model it is assumed that the source emits R pairs of photons per second in the ;z and 9z directions with the M photons emitted on either side independently of each other possessing an isotropic distribution of polarization vector directions. Because, in the ideal case each polarizer transmits only one-half of the photons, the coincidence rate R() observed is reduced to R /4 independently of angle and hence M
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F. 10. Coincidence signal R() divided by the coincidence signal R with the plates of M both linear polarizers removed for the circular polarization experiment as a function of the angle made by the fast axis of the quarter-wave plate in one detection arm of the two-photon coincidence apparatus with respect to the fast axis of the quarter-wave plate in the other detection arm. The solid line represents the theoretical quantum mechanical curve for comparison.
with corrections for the transmission efficiencies and of the polarizers, + K R( )/R : 0.22 (see Fig. 10). Another specific example of a local realistic M model (curve II in Fig. 9) originally due to Holt (1973) can be described as follows. As in the preceding, we assume an isotropic source emitting pairs of photons in the ;z and 9z directions but, in this case, each with the same polarization vector at an angle to the x-axis. These angles have values from 0 to with equal probabilities. Taking R decays per second and M detectors D and D with 100% efficiency the coincidence signal would be dS : R cos( 9 ) cos( 9 )d/ M for photons with polarization angles of between and ; d. Integrating
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over all angles from 0° to gives R() 1 1 : 1 ; cos 2 R 4 2 M
with : 9
This result compares to the quantum mechanical prediction of R() 1 : [1 ; cos 2] 4 R M in the ideal case, which does not have the factor in front of the cosine term found in the local realistic model of Holt (1973). This discussion leads to the Einstein-Podolsky-Rosen (EPR) debate about the completeness of quantum mechanics. The literature on this topic has increased dramatically over the past 15 years so that we refer only to some relevant reviews (Selleri, 1988; Duncan and Kleinpoppen, 1988; Greenberger and Zeilinger, 1995). The controversy between local realistic theories and quantum mechanics may be characterized as follows. Bell (1964) and later Clauser, Horne, Shimony, and Holt (1969) showed that quantum mechanics predicts strong correlations in ideal two-photon experiments of which local realistic theories are incapable. In local theory a measurement of a physical quantity at some point A in a space-time representation is not influenced by a measurement made at another point B spatially separated from A in a relativistic sense. A realistic theory assumes that the world is made up of objects with physical properties, which exist independently of any observation made on them. Contrary to both local and realistic theory quantum mechanics is neither local nor realistic. Bell (1964) showed in the form of his famous inequality that all local deterministic hidden variable theories (which are a subclass of local realistic theories) predict a weaker correlation between photons than that given by quantum mechanics. Freedman’s (1972) form of Bell’s inequality showed that, for local realistic theories, the quantity must satisfy the following inequality: :
R(22.5°) 9 R(67.5°) 0.250 R M
where R(22.5°) is the coincidence rate for 9 : 22.5°, R(67.5°) the coincidence rate for 9 : 67.5°, and R the coincidence rate with the M two polarizers removed. Contrary to these limits quantum mechanics predicts, in the ideal case, a variation as cos( 9 ), which results in the value : 0.354. Taking account of the solid angle of detection, the
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transmission efficiencies of the polarizers and applying Eq. (9), quantum mechanically : 0.273 < 0.011 for this experiment. Experimentally the two-photon data from the results in Fig. 9 provide a value of : 0.275 < 0.016(1) in agreement with quantum mechanics and beyond the limits of Bell’s inequality. A large number of experiments using two-photon radiation from atomic cascades (e.g., Fry and Thomson, 1976; Aspect et al., 1982), from positronium annihilation (Paramanande and Butt, 1987), as well as from interference experiments (Brendel et al., 1992) with laser photon pairs have also clearly confirmed the agreement with quantum mechanics. Positronium annihilation experiments can be criticized on the grounds that quantum mechanics itself must be assumed in order to analyze the experimental data. Doubts about atomic cascade experiments have been expressed (Garuccio and Selleri, 1984; Kleinpoppen et al., 1997), concerning the correctness of the results where rescattering effects may not be completely negligible. The metastable D(2S) experiment is free of these objections but the low efficiency of the photon detectors here and in cascade experiments leaves the possibility that the results could be interpreted in terms of local realistic theories if the assumptions of Clauser et al. (1969) are questioned. In a further experiment the circular polarization correlation of the two photons from D(2S) was measured by inserting a quarter-wave plate between the collimating lens and the linear polarizer in each detection arm of the apparatus. These quarter-wave plates were achromatic with a retardation that varied by only about and \) polarization components as illustrated in Fig. 11 for a normal transition from a n P state to a n S state. Analogous to this picture, the M two-photon transitions can be associated with two linearly polarized and correlated -transitions or or two right-right > >
and left-left \ \ circularly polarized components. In comparing these
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one- and two-photon dipole transitions one has, however, to keep in mind that the two emitted photons are detected in coincidence. B. T G-S E E While the preceding linear and circular polarization experiments of the two-photon radiation appear to agree well with the predictions of quantum mechanics, further critical considerations and suggestions have been made for testing all possible assumptions with regard to quantum mechanics versus local realistic theories. Important proposals were made by Garuccio and Selleri (1984) involving single-photon physics and two-polarizer type experiments to be interpreted in local realistic terms. They assumed that in addition to a polarization vector l, a photon possessed a detection vector and, on this basis, were able to explain experimental results in local realistic terms. However, Haji-Hassan et al. (1987) tested this concept in an extension of the previously described linear polarization correlation experiment. They inserted a half-wave plate in one detection arm between the linear polarizer P and the photomultiplier D . By adding this half-wave plate to the system the plane of polarization of the photons incident on photomultiplier D could be varied independently of the polarization axis of P . At first the transmission axes of the polarizers P and P in both arms of the apparatus and the fast axis of the half-wave plate were set parallel to each other. When polarizer P was rotated by an angle , the fast axis of the half-wave plate was rotated by an angle : /2. With this procedure it was arranged that the orientation of the plane of polarization of the photon incident on the photomultiplier D did not change as the rotation of the polarizer and half-wave plate took place. As the relative angle between the planes of polarization of the photons impinging on the detectors did not change significantly the results could not be distorted by enhancement effects due to the detection vector . Within the limits of experimental error the results were once again in agreement with quantum mechanics as shown in Fig. 12. In a second experiment with the half-wave plate the polarization axes of the two linear polarizers were fixed parallel to each other and the fast axis of the half-wave plate was rotated by an angle relative to the axes of the polarizers. In this way the relative angle between the planes of polarization of the photons impinging on the photomultipliers could be varied continuously. It was also verified that the singles count rates did not vary as the half-wave plate was rotated. The two-photon coincidence measurements with the half-wave plate clearly establish the assumption that the relative angle between the planes of linear polarization of the two photons prior to detection plays no role in establishing experimental observation of polarization correlations. This
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F. 12. Ratios R()/R as a function of the orientation angle of the fast axis of the M half-wave plate inserted between the linear polarizer P and the photomultiplier D . The coincidence signal R() results from the observations with the transmission axes of the two linear polarizers parallel to each other ( : 0°) and the coincidence signal R is obtained with M the linear polarizers removed.
statement confirms the assumption of Clauser et al. (1969) that the probability of the joint detection of a pair of photons that emerge from two polarizers is independent of the relative angle between the polarization planes of the two photons just prior to their detection at the photomultipliers. There is no experimental evidence to support the fore mentioned idea of Garuccio and Selleri (1984) of introducing a detection vector and considering an enhanced or modified photon detection depending on the combined action of the detection vector and polarization vector l. C. T-P E The further proposal by Garuccio and Selleri (1984) to introduce a second linear polarizer in one of the detection arms of the two-photon coincidence apparatus provided an opportunity to test quantum mechanics versus local realistic theories in a hitherto unexplored and novel procedure. The experiment and the relevant geometries for the polarization directions of the three polarizers (Haji-Hassan et al., 1987) are shown in Figs. 13 and 14. The orientation of the polarization plane of polarizer a was held fixed while that for polarizer b was rotated through an angle in a clockwise sense and polarizer a through an angle in an anticlockwise sense. The
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F. 13. Schematic arrangement of the three-polarizer experiment (Haji-Hassan et al., 1987). The orientation of polarizer a is fixed with its polarizer transmission axis parallel to the x axis. The transmission axes of polarizers b and a are rotated, respectively, through angles and relative to the x-axis.
ratio R(, )/R(, -) was measured where R(, ) is the coincidence rate with all three polarizers in place and R(, -) the rate with polarizer a removed. Results of these ratios are shown in Figs. 15 and 16 along with quantum mechanical predictions and the limits of the Garuccio-Selleri local realistic model (1975). The quantum mechanical prediction for : 0 is close to the form cos ; sin with , the transmission efficiencies of + K + K polarizer a. These data confirm the validity of Malus’ cosine-squared law for the transmission of polarized light from a very weak source through polarizer a.
F. 14. Geometry and angles of the transmission axes of the three polarizers used in the Stirling three-polarizer experiment.
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F. 15. Ratios R(, )/R(, -) as a function of and in the experiment by Haji-Hassan et al. (1987). The solid lines represent quantum mechanical predictions for : 0°, 33°, and 6.75°.
On the other hand the model of Garuccio and Selleri (1984) showed that, for any angle 90° (note that is not the angle between the polarizers in this case), arranging the angles of the transmission axes of the three polarizers to satisfy the relations : 3 and ; : the ratio of the quantum mechanical prediction to that of their local realistic model must always be greater than some minimum value as shown in Fig. 17. The * range 58° 80° where 1 can be used in particular as a test between * quantum mechanics and the local realistic theories of Garuccio and Selleri. For the maximum of : 1.447, : 71° and the corresponding value for * is 33° and for is 38°. For these values the approach of Garuccio and Selleri sets an upper limit on the predictions of the local realistic theories of 0.413 for the ratio R(, )/R(, -) while the experimental value according to
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F. 16. Variation of the ratio R(, )/R(, -) as a function of the angle in the experiment of Haji-Hassan et al. (1987) for : 0°, 15°, 30°, 45°, and 60°. The points marked (*) correspond to the results for : 0°, the point marked (●) to : 33°. The solid curve represents the quantum mechanical prediction for : 0°, while the broken curve shows the upper limit for the ratio set by the local realistic model of Garuccio and Selleri (1984) for various angles .
Fig. 17 is 0.585 < 0.029, thereby violating the Garuccio-Selleri model by about six standard deviations or a difference of more than 40%. Even with some modification of the maximum value of to 0.162 suggested by Selleri * (1985), the preceding ratio will be only 0.514, which is still violated by the experimental data by almost three standard deviations or about 15%. Accordingly the three-polarizer experiment appears to rule out the class of local realistic theories of Garuccio and Selleri in a more convincing way than do the currently published two-polarizer coincidence experiments. The quantum-mechanical prediction for : 0° is close to the form cos + ; sin with , the transmission efficiencies of polarizer a. These K + K results thus confirm the validity of Malus’ cosine-squared law for the transmission of polarized photons from a very weak light source passing through polarizer a.
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F. 17. Lower limit of the ratio of the quantum mechanical prediction to that of local * realistic theories with enhancement of the type proposed by Garuccio and Selleri (1984).
As can be seen in Fig. 16 for : 33° and 5 40° there is a relative difference of more than about 40% between the prediction of quantum mechanics and the local realistic theory of Garrucio and Selleri, which is so much larger than from experiments with photons from cascades (see Fry and Thomson, 1976; Aspect et al., 1982), positronium annihilation (Paramannada and Butt, 1987), and in interference experiments with laser photon pairs (Brendel et al. 1992; Tittel et al., 1998; Weihs et al., 1998). We note that the three-polarizer method, which gives a much more sensitive test result as a large difference of at least 40% between quantum mechanics and Bell’s limit for local realistic theories (Fig. 16), is not simply based on a kind of gray filtering effect by the additional polarizer, but is based on an interference effect of the observed polarization correlation. This can be seen as follows (see Fig. 16). With directions of polarization of polarizer a parallel to the x-direction, that of polarizer b at angle and of polarizer a at angle , the polarization correlation of the coincident two-photon radiation becomes P(, ) 5 cos cos
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with : ; and : 9 P(, ) : cos( 9 ) cos : [cos ; sin( 9 ) sin ] : cos ; sin( 9 ) sin ; 2 cos sin( 9 ) sin
(10)
The last part of this equation represents kinds of interference terms. Accordingly, this type of the three-polarizer system for the detection of the two-photon radiation in opposite directions leads to a different polarization correlation and, in a way, a surprisingly larger difference between quantum mechanical and local realistic predictions for certain combinations of the directions of polarization of the polarizer as demonstrated in Fig. 16. D. B-T E It follows from considerations of parity and angular momentum conservation (Section II) that the two-photon state vector can be written as described by Eqs. (6) and (8) for circularly or linearly polarized components. In a coincidence experiment the ‘‘collapsed’’ components of the state vector are the right-right-hand R R or left-left-hand L L circularly polarized components or, alternatively, the linearly polarized components x x
and y y , respectively. These collapsed components of the state vector are compatible with the hypothesis of Breit and Teller (1940) that the fine and hyperfine interaction due to electron and nuclear spin should not affect the two-photon polarization correlation since the Hamiltonian describing the two-photon emission has no off-diagonal components for fine and hyperfine interactions in second order. Figure 18a—c demonstrates the various cases of the polarized components of the collapsed state vectors: with electron and nuclear spin neglected (Fig. 18a); including the electron spin (Fig. 18b); and including both nuclear and electron spin (Fig. 18c). For the case of zero nuclear and electron spin (I : 0, S : 0), only the collapsed state vectors R R , L L , x x and y y are compatible with the two-photon transitions through the intermediate virtual P states (Fig. 18a). For the case S : 1/2, I : 0 (Fig. 18b), possible ‘‘collapsed’’ state vectors would be R x , R x , L x or L x with m : .
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F. 12. The measured x : cos histogram for ND> (independent of X ) and comparison ," to theory.
Before analyzing the differences between experiment and theory, similarity should be emphasized. Although these species have been spectroscopically measured and structural information had been retrieved from parameterized calculations, in the case of quasilinear molecules, it is especially difficult to extract the molecular structure from such measurements. A quotation from Okumura et al. (1992) concerning the structure of NH > is clear on this point:
F. 13. The relative difference of the measured histogram (P ) and the theory (P ) for " 2 ND>.
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F. 14. The measured x : cos histogram for CH> (independent of X ) and comparison !& to theory.
Although the spectrum can be fit to either a linear or an asymmetric rotor Hamiltonian, the large amplitude of the bending vibration prevents us from determining the molecular structure from the observed constants.
For the case of CH >, Ro¨sslein et al. (1992) can be quoted: The spectrum could be fitted equally well to the linear molecule (or a bent one).
F. 15. The relative difference of the measured histogram (P ) and the theory (P ) for " 2 CH>.
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It is evident that in both cases spectroscopy could not determine the structure of these quasilinear molecules and therefore the findings of CEI and their similarity to theoretical predictions should be taken as some confirmation of the theoretical concepts for such close-to-linear structures. 8. Systematics of the Differences between the Data and the Theory The comparison between the best fitted density functions and the theoretical predictions at both 300 and 0 °K are plotted in R-space and shown in Figs. 16, 17, and 18. The statistical error at large bending angles, where the probability approaches zero, is quite large (see Figs. 11, 13, and 15). Therefore, more attention is given to the region near the linear conformation. For all of the studied molecules, the predictions at linearity are significantly lower than experimentally found. For the two nitrogen isotopomers, the predictions at 0 °K have more linear probability, overshooting the trend of the data. On the other hand, for CH > the probability prediction at 0 °K is strictly zero and thus opposite of the nitrogen isotopomers’ theoretical trend. The experimental probability distributions also have trends that can be seen in the cooling plots, the b part of Figs. 5, 6, and 7. The trends here are exactly the same: When the excitations are 300 °K (shorter storage times), the nitrogen isotopomer linear conformations are less populated while for
F. 16. Theoretical and experimental (marked ‘‘Best R’’) probability distributions in R-space for NH>.
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F. 17. Theoretical and experimental (marked ‘‘Best R’’) probability distribution in Rspace for ND>.
F. 18. Theoretical and experimental (marked ‘‘Best R’’) probability distributions in R-space for CH>.
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the CH> species at higher excitations the linear conformation is more populated. If theoretical predictions are taken seriously and used roughly to estimate the measured ensemble temperatures, one obtains for the nitrogen isotopomers ensembles a significantly lower temperature than 300 °K; for the CH> ensemble a significantly higher temperature than 300 °K is ob tained. This absurd situation is a manifestation of the incompatibility of theory with CEI data. For all cases, the experimental linear conformation is more probable than expected with a much larger deviation for CH> species. Thus, the spectroscopically geared latest theoretical predictions for quasilinear molecules are at odds with the CEI results. In the following, a theoretical rationalization of this situation is proposed.
B. A A W L M Traditionally, the theory for linear molecules is only slightly different than the adiabatic theory for nonlinear species. In the first step, potential energy surfaces (PES) are calculated for different fixed point positions of the molecular nuclei. If the ground state electronic eigenenergy near the minimum ‘‘equilibrium’’ conformation is too close to the next electronic eigenstate, then in the next ‘‘dynamic’’ step the two low lying states and the coupling through the nuclear motion have to be taken into account for calculations of full molecular wavefunctions of low lying states. In particular, the electronic projection of the angular momentum at linear conformations takes the values , , . . . . Therefore, except for the case, at linearity at least two degenerate states with a different sign of the electronic angular momentum projection are taken into account. For the species here, the NH> and ND> have the electronic ground state at linearity while for CH > the lowest electronic states are of the nature. If the theory of the lowest states of these species deals only with the foregoing states, such as in Osmann et al. (1999) then the treatment is defined as an adiabatic approximation. Nonadiabatic contributions are then calculations that take into account higher excited states. For CH> this is justified in Osmann et al. (1999) because other electronic states at ‘‘equilibrium’’ have energies in excess of 6 eV. In the following it is argued that the usual adiabatic separation of electrons and nuclei in molecular treatment fails to predict the correct wavefunctions near linear conformations. For the sake of simplicity, spins are ignored and the isolated molecular Hamiltonian is employed. In the isolated molecule approximation, the total angular momentum and its projection along one axis are exactly conserved for stationary states. It will be shown that the last exact requirement, chosen along an inertial
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axis, is inconsistent with the existence of a small parameter for the traditional adiabatic expansion near linear conformations. The center of mass translational motion is irrelevant and so the effective number of particles is reduced by one. For instance, Jacobi coordinates are chosen in the order of decreasing masses of the participating particles. Discarding the kinetic energy of the center of mass operator, the remaining Hamiltonian deals with 3(N 9 1) nuclear coordinates and 3N electronic L C coordinates with their appropriate reduced masses. For example, in an atom, only electronic coordinates are relevant and their reduced masses are approximately equal to their free mass. For diatomic molecules there is only one effective nuclear vector, the vector difference between the two nuclei, with its usual reduced mass (and so on for larger molecules). All of the effective particles are well defined in a Cartesian inertial frame and electrons and nuclei are still easily distinguished by the very different sizes of their reduced masses. Choose arbitrarily an inertial frame z axis, which passes through the center of mass and cylindrical coordinates z , , . For each I I I effective particle (nuclei separately from electrons) the z component of the angular momentum operator is j : 9i (/ ). Notice that these operators I I and their partial or total sum are independent of the masses of the particles, thus, angular momentum conservation rules are independent of the ratio of the electron mass to the nuclear masses. The sum of such operators for N C electrons is defined as J and similarly J for N 9 1 nuclear coordinates. C L L The conjugate coordinates to J and J are defined as and . C L C L It can be shown that the kinetic energy operator includes the following term: T:9 where the dynamic variables
9 2I 2I L L C C
(6)
I and I are C
L
, I : C CG CG
(7)
C
G ,L\ I : LH LH L H
(8)
For stationary states, the angular momentum along the (inertial frame) z axis M is conserved exactly. It is the eigenvalue of the operator J : 9i
; X C L
(9)
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The conserved quantity M is the sum of electronic and nuclear contributions. A few simple remarks are needed. All expectation values of the moments of inertia (or their inverse) are positive. For states of small molecules, the expectation of /2I is of the order of a few eV. C It is possible to transform to new coordinates where the conserved quantity belongs to only one coordinate, conjugate to J (with equivalent X mathematics to the transformation of the two body system into the center of mass coordinate, which is conjugate to the center of mass momentum, and the relative coordinate):
I ;I L L
: C C
: 9 C L
I
(10)
then T :9
9 2J 2I
(11)
where
J\ : I \ ; I \ C L I:I ;I
(12)
(13) C L are the z axis reduced moment of inertia and the z axis total moment of inertia dynamic variables. The angular momentum operator is transformed into: J : 9i
X
(14)
In general, the collective coordinate (Eq. (10)), which carries the angular momentum along the z axis, depends on nuclear and electronic coordinates. For stationary states, the total angular momentum J and its projection M are good quantum numbers. Consider a multiplet of degenerate states, J " 0, with M : 9J, . . . , J. The last term in Eq. (11) can be written as
M/2I and could be included in the potential energy. The corresponding eigenstates have a multiplying factor of the form eG+. For a given J, the M states are degenerate and the M-dependent expectation value of the last term of Eq. (11)
M
I 1 2
(15)
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must be compensated by the expectation value of the rest of the Hamiltonian, which is independent of M. This ought to be expressed in the state itself by more than a phase factor. As for the first term in Eq. (11), the Fourier components of : 9 A L are not restricted by angular momentum conservation rules. Thus far, no approximations were assumed and there is no constraint requiring that the amplitude of any state should vanish when the nuclei are situated on the z axis. The first step in the adiabatic approximation is to find the electronic eigenenergies for different conformations — except that here the exact quantum number M is already set as a demand. Start with linear conformations where the nuclei are fixed along the z axis. The last term of Eq. (11) forces the electronic state of this conformation to be of , , , . . . nature, depending only on the value of M : 0, 1, 2. . . . . The corresponding electronic eigenvalues increase rapidly with M in the scale of electronic energies. The argument can be extended to slightly bent conformations as long as the now constant /I is larger than a few eV. It is very clear now L that the adiabatic approximation where highly excited electronic states are ignored is erroneous because it should take the entire series of electronic excited states to obtain exactly degenerate eigenstates for all of these M states. That alone already makes the adiabatic approximation inconsistent with linear structures when angular momentum is considered properly, as should be the case for gas phase molecules. It might be argued that the choice of M classically corresponds to a choice of orientation; therefore, fixing the nuclei on the z axis is incompatible with that choice. Indeed, the problem lies in treating a linear conformation as a classical entity and trying to fix it later by projections on quantum mechanically allowed states. However, in most of the phase space, I I . Therefore, the coordinate L C
is of almost a pure nuclear nature and the moments of inertia J and I are of almost pure electronic and nuclear natures, respectively. Thus, energy matrix elements can be well approximated by disregarding the remaining small phase space where the adiabaticity fails. The consequence is that for spectroscopy a model that result in reasonably accurate eigenenergies is sufficient and it does not matter whether the model wavefunctions are inaccurate. The expectation value of the last term in Eq. (11) is given by
M
1 2( I ; I ) C L
: M
1 2I · (1 ; I /I ) C L C
As long as I is very small the expectation value is of the electronic energies scale. L
(16)
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A question may be asked: What makes this formulation better than the traditional adiabatic formulation? The answer is that here an exact conservation law was taken into account explicitly and it prevents the wrong assumption to be made regarding the existence of a small parameter (for certain conformations) that can be used for perturbative expansion. C. C C E I E If the consequence of not knowing the behavior of the wavefunction near linearity is accepted, it is still possible to attempt to guess its trend by ignoring the last term in Eq. (11), and to disregard its important influence on the form of the states (as already discussed). Assume that an adiabatic procedure is reapplied and the wavefunction is expanded in Fourier terms A of the now electronic variable . Each A is a function of the K K conformations of the nuclei. At linearity only A differs from zero. The other components may build up for bent conformations starting at a rate slower than I . Even this is essentially different from the traditional adiabatic state L behavior, such as the Renner-Teller treatment where terms such as A are discarded for linear conformations (as in the CH> species) due to energy considerations. Ignoring the last term in Eq. (11) as rotational and then applying the adiabatic approximation on the rest of the Hamiltonian requires dealing with linear conformations with a pure A electronic state and developing a solution for the bent region where traditional solutions normally apply. This has not yet been done by quantum chemistry. As a simple example, consider the CH> species at a very low temperature. In the regular Renner-Teller treatment, the electronic wavefunctions are of a nature near linearity. The state at that conformation is at least 6 eV higher. This means that for fixed nuclei along the z axis the only nonzero Fourier components of are with Fourier indices m : and ND> species at 300 °K. Moreover, it is predicted that the discrepancy between the traditional theory and experiment will vanish at low temperatures for these species and will be enhanced for the CH> species. Without ignoring the last term in Eq. (11), however, it is clear that the adiabatic wavefunction predictions are invalid for linear conformations and, therefore, the CEI results for that region may differ from the traditional theoretical scenario.
V. Conclusions It was shown that for three triatomic species the probability for finding linear conformations is significantly larger than was theoretically expected. It is suspected that the strict singularity of the nuclear centrifugal barrier in the theoretically used PES is the source of the problem. Theoretical arguments to support this are conveyed. As concerns the chemical reactivity of such species, it is not overly difficult to imagine a chemical reaction wherein the reaction rate depends exponentially on amplitude at linearity. For species such as CH>, large discrepancies are expected in reaction rate estimates due to he difference between the results of CEI and the traditional adiabatic approximation. The unique advantages of direct observation on molecular structures that is permitted by the CEI method is clarified by new developments in the
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experimental technique. It is foreseen that, in the near future, new concepts will greatly simplify and add reliability to such experiments. Such results are of importance in understanding better the structure-reactivity relation of molecules and radicals.
VI. References Algranati, M., Feldman, H., Kella, D., Malkin, E., Miklazky, E., Naaman, R., Vager, Z., and Zajfman, J. (1989). J. Chem. Phys. 90:4617. Baer, A. (2000). PhD thesis, Weizmann Institute. Baer, A. et al. (1999). Phys. Rev. A 59:1865. Belkacem, A., Faibis, A., Kanter, E. P., Koenig, W., Mitchell, R. E., Vager, Z., and Zabransky, B. J. (1990). Rev. Sci. Instrum. 61:945. Ben-Hamu, D., Baer, A., Feldman, H., Levin, J., Heber, O., Amitay, Z., Vager, Z., and Zajfman, D. (1997). Phys. Rev. A 56:4786. Bohr, N. (1948). K. Dan V idensk. Selsk. Math.-Fys. Medd. 18:8. Both, G., Kanter, E. P., Vager, Z., Zabransky, B. J., and Zajfman, D. (1987). Rev. Sci. Instrum. 58:424. Breskin, A. and Chechik, R. (1985). IEEE Trans. Nucl. Sci. N2-32:504 and references therein. Faibis, A., Koenig, W., Kanter, E. P., and Vager, Z. (1986). Nucl. Instrum. Methods B 13:673. Gemmell, D. S. and Vager, Z. (1985). The electronic polarization induced in solids traversed by fast ions, in T reatise on Heavy-Ion Science, vol. 6, D. A. Bromley, ed., New York: Plenum, p. 243 and references therein. Graber, T., Kanter, E., Levin, J., Zajfman, D., Vager, Z., and Naaman, R. (1997). Phys. Rev. A 56:2600. Graber, T., Zajfman, D., Kanter, E. P., Vager, Z., Naaman, R., and Zabransky, B. J. (1992). Rev. Instr. 63:3569. Heber, O., Zajfman, D., and Vager, Z. (1999). Israeli patent 123747 approved 1999. Jensen, P., Brumm, M., Kraemer, W. P., and Bunker, P. R. (1995a). J. Mol. Spectrosc. 171:31. Jensen, P., Brumm, M., Kraemer, W. P., and Bunker, P. R. (1995b). J. Mol. Spectrosc. 172:194. Jensen, P. and Bunker, P. R. (1999). Private communication. Kella, D., Algranati, M., Feldman, H., Heber, O., Kovner, H., Malkin, E., Miklazky, E., Naaman, R., Zajfman, D., Zajfman, J., and Vager, Z. (1993). Nuclear Instrum. Method A 329:440. Koenig, W., Faibis, A., Kanter, E. P., Vager, Z., and Zabransky, B. (1985). Nucl. Instrum. Methods B 10:259. Kovner, H., Faibis, A., Vager, Z., and Naaman, R. (1988). Proc. Int. Workshop on the Structure of Small Molecules and Ions, R. Naaman and Z. Vager, eds., New York: Plenum Press, p. 113. Kraemer, W. P., Jensen, P., and Bunker, P. R. (1994). Can. J. Phys. 72:871. Krohn, S., Amitay, Z., Baer, A., Levin, J., Zajfman, D., Lange, M., Knoll, L., Schwalm, D., Wester, R., and Wolf, A. (2000). Accepted for publication in Phys. Rev. A. Levin, J. (1997). PhD thesis, Weizmann Inst. of Sci. Levin, J., Baer, A., Knoll, L., Scheffel, M., Schwalm, D., Vager, Z., Wester, R., Wolf, A., and Zajfman, D. (2000). Nucl. Instrum. Meth. B. 268:168. Levin, J., Feldman, H., Baer, A., Ben-Hamu, D., Heber, O., Zajfman, D., and Vager, Z. (1998). Phys. Rev. L ett. 81:3347.
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Marx, D. and Parrinello, M. (1996). Science 271:179. Oka, T. (1993). Private communication. Okumura, M., Gabrys, B. D., Jagod, M. F., and Oka, T. (1972). J. Mol. Spectrosc. 153:738. Osmann, G., Bunker, P. R., Jensen, P., and Kramer, W. P. (1997a). Chem. Phys. 225:33. Osmann, G., Bunker, P. R., Jensen, P., and Kramer, W. P. (1997b). J. Mol. Spectrosc. 186:319. Osmann, G., Bunker, P. R., Kraemer, W. P., and Jensen, P. (1999). Chem. Phys. L ett. 309:299. Ro¨sslein, M., Gabrys, C. M., Jagod, M.-F., and Oka, T. (1992). J. Mol. Spectrosc. 153:738. See, for example, Schiff, (1949). Quantum Mechanics, McGraw-Hill. Strasser, D., Urbain, X., Pedersen, H. B., Altstein, N., Heber, O., Wester, R., Bhushan, K. G., and Zajfman, D. (2000). Rev. Sci. Instruments. 71: (August). Tanabe, T. et al. (1999). Phys. Rev. L ett. 83:2163. Vager, Z. and Gemmell, D. S. (1976). Phys. Rev. L ett. 37:1352. Vager, Z., Graber, T., Kanter, E. P., and Zajfman, D. (1993). Phys. Rev. L ett. 70:3549. Vager, Z., Naaman, R., and Kanter, E. P. (1989). Science 244:426. Vager, Z., Zajfman, D., Graber, T., and Kanter, E. P. (1993). Phys. Rev. L ett. 71:4319. Wester, R., Albrecht, F., Baer, A., Grieser, M., Knoll, L., Levin, J., Repnow, R., Schwalm, D., Vager, Z., Wolf, A., and Zajfman, D. (1998). Nucl. Instrum. Methods Phys. Res A 413:739. Zajfman, D., Both, G., Kanter, E. P., and Vager, Z. (1990). Phys. Rev. A 41:2482. Zajfman, D., Kanter, E. P., Graber, T., and Vager, Z. (1992). Phys. Rev. A 46:194.
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Index
B
A Airspace imaging, 77—78 Alkali clusters, 180—186 Angular correlation experiments Breit-Teller effects, 123—127 Einstein-Podolsky-Rosen tests, 111— 118 Garuccio-Selleri effects, 118—119 Antihydrogen advances, 31—32 description, 28—29 4.2 K positrons, 29—30 nested penning trap, 30—31 recombination mechanisms formation processes, 35 future studies, 36 selecting processes, 30—31 Antiprotons capturing, 9—16 cooling, 9—16 decelerator, 16—17 description, 2 energy lowering, 3—4 LEAR, 7—13 lower temperature, 19 protons, comparisons cyclotron frequencies, 23—24 PCT invariance, 19—22 spinoffs, 36—37 TRAP I, 25 TRAP II, 25—26 TRAP III, 26—28 slowing, 5—9 stacking, 16 transporting, 17 TRAP duplications, 17—18 trapping, 5—9 vacuum, 16 Argonne National Laboratory set-up, 207, 211
Back projection imaging, 67—68 Bending distributions, 226—230 Binding electrons, 209—210 Bond angle distributions, 216—220 Breit-Teller effects, 123—127 C Chemical shift imaging, 70—71 Collision processes, 190—192 Coulomb explosion imaging background, 205—206 comparisons, 236—237 dectectors ANL, 211 description, 210—211 future, 212 TSR, 2112 Weizmann, 211—212 fast molecules ANL set-up, 206 future cooling method, 208 Heidelberg set-up, 208 linear molecules, 232—236 quasilinear bending distributions, 226—230 binding electron stripping, 209— 210 bond angle distributions, 216— 220 data/theory, comparison, 230— 232 description, 204—205 diatomic molecules, 222—224 framework, 212—213 molecular structure, 205 reorientation, 224—226 species, 220—222 V-space, 213—215 241
242
INDEX
Coulomb explosion imaging (Contd.) Weizmann set-up, 207—208 Cyclotron frequencies, 23—24
D Diatomic molecules, 222—224 Distributions bending, 226—230 bond angle, 216—220
E Einstein-Podolsky-Rosen tests, 111—118 Electronic states excited laser spectroscopy description, 171—172 fluorescence, 172—173 ionization, 172—173 optical double resonance, 173— 180 ground, high vibrational laser spectroscopy fluorescence, 160—167 stimulated emission pumping, 160—167 overtone spectroscopy description, 152—153 modulated absorption, 153—157 optothermal, 153—157 Electrons. see Binding electrons Emission pumping, stimulated, 167—171 Excitation, selective, 67
F Fast molecules coulomb explosion imaging ANL set-up, 206 future cooling method, 208 Heidelberg set-up, 208 Weizmann set-up, 207—208 Fluorescence, electronic states excited, 172—173 high vibrational, 160—167 Fourier spectral analysis, 127—133
G Gradient echo imaging, 68—70 Gyroscopes, nuclear spin, 48 H Heidelberg set-up, 207—208 Helium, He discovery, 45 polarization deliver systems, 62—63 description, 49—51 imaging carrier injection, 79—80 considerations, 62—63 future studies, 87—89 metastability exchange description, 60 laser, 62 methods, 48—49 next generation, 47 optical pumping description, 50—56 LDA, 57—60 spin exchange description, 50—56 LDA, 57 problems, 46 Hydrogen, atomic. see also Antihydrogen H\ ion, 26—28 role, 100 two-photon decay coherence, 127—133 correlated emissions, 133—143 fourier spectral analysis, 127—133 metastable state, 101—108 polarization correlation Breit-Teller effects, 123—127 Einstein-Podolsky-Rosen test, 101—108 three polarizers, 119—123 two polarizers, 111—118 time correlation, 133 I Invariance, PCT, 19—22 Ionization, two-photon, 172—173
243
INDEX L Laser spectroscopy advantages, 150 excited molecular states description, 171—172 fluorescence, 172—173 ionization, 172—173 optical double resonance, 173—180 high vibrational ground states fluorescence, 160—167 overtone description, 152—153 modulated absorption, 153—157 optothermal, 158—160 stimulated emission pumping, 167— 171 history, 150—151 metastability exchange, 62 optical pumping, 57—60 polarization in vivo, 86—87 sub-doppler, 180—186 time-resolved coherent control, 194—196 collision processes, 190—192 lifetime measurements, 187—190 photodissociation processes, 192— 193 LEAR, 7—13 Lifetime measurements, 187—190 Linear molecules, 232—236 Lung function, 83—84
M Magnetic resonance images basic techniques contrast, 71—72 -space, 65—66 low field, 72—73 NMR, 63—64 one-dimensional, 64—65 sequences back projection, 67—68 chemical shift, 70—71 gradient echo, 68—70 selective excitation, 67 description, 42—43 development, 43—44
future possibilities, 87—89 history, 44—49 polarized gas, 75—77 Xe framework, 80 lung function, 83—84 time dependence, 84—86 tracer techniques, 84—86 in vivo, 81—83 Magnetic tracer techniques, 84—86 Magnetization, sampling, 75—76 MRI. see Magnetic resonance images N Nested penning trap demonstrating, 30—31 selecting process, 32—34 NMR. see Nuclear magnetic resonance Nuclear magnetic resonance description, 63—64 Xe framework, 80 lung function, 83—84 time dependence, 84—86 tracer techniques, 84—86 in vivo, 81—83 Nuclear polarization airspace imaging, 77—78 He deliver systems, 62—63 description, 49—51 imaging carrier injection, 79—80 considerations, 74—75 future studies, 87—89 metastability exchange description, 60—62 laser, 62 methods, 48—49 next generation, 47 optical pumping description, 50—56 LDA, 57—60 spin exchange description, 50—56 LDA, 57 MRI imaging, 75—76 Xe deliver systems, 62—63
244
INDEX
Nuclear polarization (Contd.) imaging carrier injection, 79—80 considerations, 74—75 future studies, 87—89 in vivo, 86 metastability exchange description, 60 laser, 62 methods, 48—49 optical pumping description, 50—56 LDA, 57—60 spin exchange description, 50—56 LDA, 57 Nuclear spin gyroscopes, 48 O One-dimensional imaging, 64—65 Optical double resonance techniques, 173—180 Optical pumping description, 50—56 LDA, 57—60 Overtone spectroscopy, 152—153 P PCT invariance, 19—22 Penning trap, 37 Photodissociation processes, 192—193 Polarization correlation experiments Breit-Teller effects, 123—127 Einstein-Podolsky-Rosen tests, 111—118 Garuccio-Selleri effects, 118—119 three polarizers, 119—123 two polarizers, 111—118 nuclear (see Nuclear polarization) Positrons, 4.2K, 29—30 Protons antiprotons, comparisons cyclotron frequencies, 23—24 PCT invariance, 19—22 spinoffs, 36—37 TRAP I, 25
TRAP II, 25—26 TRAP III, 26—28 Q Quasilinear molecules, XH> bond angle distributions, 216—220 production, 212—213 species, 220—222 V-space bending information, 214—215 conversion, 212—213 R Radiation, two-photon atomic hydrogen, 101—108 coherence, 127—133 correlation experiments Breit-Teller effects, 123—127 Einstein-Podolsky-Rosen tests, 111—118 emissions, 133—143 Garuccio-Selleri effects, 118—119 three polarizers, 119—123 two polarizers, 111—118 fourier spectral analysis, 127—133 function, 100—101 stirling apparatus, 109—110 time correlation, 133 Resonance optical double, 173—180 two-photon, 173—180 S Small molecules alkali clusters, 180—186 electronically excited description, 171—172 fluorescence, 172—173 ionization, 172—173 optical double resonance, 173—180 properties, 149—150 high vibrational states fluorescence spectroscopy, 160—167 overtone spectroscopy description, 152—153 modulated absorption, 153—157
245
INDEX optothermal, 158—160 sub-doppler spectroscopy, 180—186 time-resolved coherent control, 194—196 collision processes, 190—192 lifetime measurements, 187—190 photodissociation processes, 192— 193 Spin exchange description, 50—56 laser, 57 Sub-doppler spectroscopy, 180—186 T Time depencence, 84—86 TRAP duplications, 17—18 proton/antiproton, 25—28 type I, 25 type II, 25—26 type III, 26—28 W Wake effects diatomic molecules, 222—224 quasilinear molecules, 216—220 Wave functions, 232—236 Weizmann set-up, 207—208, 212
X Xenon, Xe dissolved imaging framework, 80 lung function, 83—84 time dependence, 84—86 tracer techniques, 84—86 in vivo, 81—83 polarization delivery systems, 62—63 description, 49—51 imaging carrier injection, 79—80 considerations, 62—63 future studies, 87—89 in vivo, 86—87 metastability exchange description, 60 laser, 62 optical pumping description, 49—51 LDA, 57—60 spin exchange description, 50—56 LDA, 57
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Contents of Volumes in This Serial Volume 1 Molecular Orbital Theory of the Spin Properties of Conjugated Molecules, G. G. Hall and A. T. Amos
Volume 3 The Quantal Calculation of Photoionization Cross Sections, A. L . Stewart Radiofrequency Spectroscopy of Stored Ions I: Storage, H. G. Dehmelt
Electron Affinities of Atoms and Molecules, B. L. Moiseiwitsch
Optical Pumping Methods in Atomic Spectroscopy, B. Budick
Atomic Rearrangement Collisions, B. H. Bransden
Energy Transfer in Organic Molecular Crystals: A Survey of Experiments, H. C. Wolf
The Production of Rotational and Vibrational Transitions in Encounters between Molecules, K. Takayanagi
Atomic and Molecular Scattering from Solid Surfaces, Robert E. Stickney
The Study of Intermolecular Potentials with Molecular Beams at Thermal Energies, H. Pauly and J. P. Toennies
Quantum Mechanics in Gas Crystal-Surface van der Waals Scattering, E. Chanoch Beder
High-Intensity and High-Energy Molecular Beams, J. B. Anderson, R. P. Andres, and J. B. Fen
Reactive Collisions between Gas and Surface Atoms, Henry Wise and Bernard J. Wood
Volume 2 The Calculation of van der Waals Interactions, A. Dalgarno and W. D. Davison Thermal Diffusion in Gases, E. A. Mason, R. J. Munn, and Francis J. Smith Spectroscopy in the Vacuum Ultraviolet, W. R. S. Garton The Measurement of the Photoionization Cross Sections of the Atomic Gases, James A. R. Samson The Theory of Electron-Atom Collisions, R. Peterkop and V. Veldre Experimental Studies of Excitation in Collisions between Atomic and Ionic Systems, F. J. de Heer Mass Spectrometry of Free Radicals, S. N. Foner
Volume 4 H. S. W. Massey — A Sixtieth Birthday Tribute, E. H. S. Burhop Electronic Eigenenergies of the Hydrogen Molecular Ion, D. R. Bates and R. H. G. Reid Applications of Quantum Theory to the Viscosity of Dilute Gases, R. A. Buckingham and E. Gal Positrons and Positronium in Gases, P. A. Fraser Classical Theory of Atomic Scattering, A. Burgess and I. C. Percival Born Expansions, A. R. Holt and B. L . Moiselwitsch Resonances in Electron Scattering by Atoms and Molecules, P. G. Burke Relativistic Inner Shell Ionizations, C. B. O. Mohr 247
248
CONTENTS OF VOLUMES IN THIS SERIAL
Recent Measurements on Charge Transfer, J. B. Hasted Measurements of Electron Excitation Functions, D. W. O. Heddle and R. G. W. Keesing Some New Experimental Methods in Collision Physics, R. F. Stebbings Atomic Collision Processes in Gaseous Nebulae, M. J. Seaton
The Diffusion of Atoms and Molecules, E. A. Mason and T. R. Marrero Theory and Application of Sturmian Functions, Manuel Rotenberg Use of Classical Mechanics in the Treatment of Collisions between Massive Systems, D. R. Bates and A. E. Kingston
Collisions in the Ionosphere, A. Dalgarno
Volume 7
The Direct Study of lonization in Space, R. L. F. Boyd
Physics of the Hydrogen Master, C. Audoin, J. P. Schermann, and P. Grivet Molecular Wave Functions: Calculations and Use in Atomic and Molecular Processes, J. C. Browne Localized Molecular Orbitals, Harel Weinstein, Ruben Pauncz, and Maurice Cohen General Theory of Spin-Coupled Wave Functions for Atoms and Molecules, J. Gerratt Diabatic States of Molecules — QuasiStationary Electronic States, Thomas F. O’Malley Selection Rules within Atomic Shells, B. R. Judd Green’s Function Technique in Atomic and Molecular Physics, Gy. Csanak, H. S. Taylor, and Robert Yaris A Review of Pseudo-Potentials with Emphasis on Their Application to Liquid Metals, Nathan Wiser and A. J. Greenfield
Volume 5 Flowing Afterglow Measurements of IonNeutral Reactions, E. E. Ferguson, F. C. Fehsenfeld, and A. L. Schmeltekopf Experiments with Merging Beams, Roy H. Neynaber Radiofrequency Spectroscopy of Stored Ions II: Spectroscopy, H. G. Dehmelt The Spectra of Molecular Solids, O. Schnepp The Meaning of Collision Broadening of Spectral Lines: The Classical Oscillator Analog, A. Ben-Reuven The Calculation of Atomic Transition Probabilities, R. J. S. Crossley Tables of One- and Two-Particle Coefficients of Fractional Parentage for Configurations s s p , C. D. H. Chisholm, A. Dalgarno, N and E. R. Innes Relativistic Z-Dependent Corrections to Atomic Energy Levels, Holly Thomis Doyle
Volume 6 Dissociative Recombination, J. N. Bardsley and M. A. Biondi Analysis of the Velocity Field in Plasmas from the Doppler Broadening of Spectral Emission Lines, A. S. Kaufman The Rotational Excitation of Molecules by Slow Electrons, Kazuo Takayanagi and Yukikazu Itikawa
Volume 8 Interstellar Molecules: Their Formation and Destruction, D. McNally Monte Carlo Trajectory Calculations of Atomic and Molecular Excitation in Thermal Systems, James C. Keck Nonrelativistic Off-Shell Two-Body Coulomb Amplitudes, Joseph C. Y. Chen and Augustine C. Chen Photoionization with Molecular Beams, R. B. Cairns, Halstead Harrison, and R. I. Schoen
CONTENTS OF VOLUMES IN THIS SERIAL The Auger Effect, E. H. S. Burhop and W. N. Asaad
Volume 9 Correlation in Excited States of Atoms, A. W. Weiss The Calculation of Electron—Atom Excitation Cross Sections, M. R. H. Rudge Collision-Induced Transitions between Rotational Levels, Takeshi Oka The Differential Cross Section of Low-Energy Electron—Atom Collisions, D. Andrick Molecular Beam Electric Resonance Spectroscopy, Jens C. Zorn and Thomas C. English Atomic and Molecular Processes in the Martian Atmosphere, Michael B. McElroy
Volume 10 Relativistic Effects in the Many-Electron Atom, Lloyd Annstrong, Jr. and Serge Feneuille The First Born Approximation, K. L. Bell and A. K. Kingston Photoelectron Spectroscopy, W. C. Price Dye Lasers in Atomic Spectroscopy, W. Lange, J. Luther, and A. Steudel Recent Progress in the Classification of the Spectra of Highly Ionized Atoms, B. C. Fawcett A Review of Jovian Ionospheric Chemistry, Wesley T. Huntress, Jr.
Volume 11 The Theory of Collisions between Charged Particles and Highly Excited Atoms, I. C. Percival and D. Richards Electron Impact Excitation of Positive Ions, M. J. Seaton The R-Matrix Theory of Atomic Process, P. G. Burke and W. D. Robb Role of Energy in Reactive Molecular
249
Scattering: An Information-Theoretic Approach, R. B. Bernstein and R. D. Levine Inner Shell Ionization by Incident Nuclei, Johannes M. Hansteen Stark Broadening, Hans R. Griem Chemiluminescence in Gases, M. F. Golde and B. A. Thrush
Volume 12 Nonadiabatic Transitions between Ionic and Covalent States, R. K. Janev Recent Progress in the Theory of Atomic Isotope Shift, J. Bauche and R.-J. Champeau Topics on Multiphoton Processes in Atoms, P. Lambropoulos Optical Pumping of Molecules, M. Broyer, G. Goudedard, J. C. Lehmann, and J. Vigué Highly Ionized Ions, Ivan A. Sellin Time-of-Flight Scattering Spectroscopy, Wilhelm Raith Ion Chemistry in the D Region, George C. Reid
Volume 13 Atomic and Molecular Polarizabilities — A Review of Recent Advances, Thomas M. Miller and Benjamin Bederson Study of Collisions by Laser Spectroscopy, Paul R. Berman Collision Experiments with Laser-Excited Atoms in Crossed Beams, I.V. Hertel and W. Stoll Scattering Studies of Rotational and Vibrational Excitation of Molecules, Manfred Faubel and J. Peter Toennies Low-Energy Electron Scattering by Complex Atoms: Theory and Calculations, R. K. Nesbet Microwave Transitions of Interstellar Atoms and Molecules, W. B. Somerville
250
CONTENTS OF VOLUMES IN THIS SERIAL
Volume 14 Resonances in Electron Atom and Molecule Scattering, D. E. Golden The Accurate Calculation of Atomic Properties by Numerical Methods, Brian C. Webster, Michael J. Jamieson, and Ronald E. Stewart (e, 2e) Collisions, Erich Weigold and Ian E. McCarthy Forbidden Transitions in One- and TwoElectron Atoms, Richard Marrus and Peter J. Mohr Semiclassical Effects in Heavy-Particle Collisions, M. S. Child Atomic Physics Tests of the Basic Concepts in Quantum Mechanics, Francis M. Pipkin Quasi-Molecular Interference Effects in Ion— Atom Collisions, S. V. Bobashev Rydberg Atoms, S. A. Edelstein and T. F. Gallagher UV and X-Ray Spectroscopy in Astrophysics, A. K. Dupree
Volume 15 Negative Ions, H. S. W. Massey
Inner-Shell Ionization, E. H. S. Burhop Excitation of Atoms by Electron Impact, D. W. O. Heddle Coherence and Correlation in Atomic Collisions, H. Kleinpoppen Theory of Low Energy Electron-Molecule Collisions, P. G. Burke
Volume 16 Atomic Hartree—Fock Theory, M. Cohen and R. P. McEachran Experiments and Model Calculations to Determine Interatomic Potentials, R. Düren Sources of Polarized Electrons, R. J. Celotta and D. T. Pierce Theory of Atomic Processes in Strong Resonant Electromagnetic Fields, S. Swain Spectroscopy of Laser-Produced Plasmas, M. H. Key and R. J. Hutcheon Relativistic Effects in Atomic Collisions Theory, B. L. Moiseiwitsch Parity Nonconservation in Atoms: Status of Theory and Experiment, E. N. Fortson and L. Wilets
Atomic Physics from Atmospheric and Astrophysical Studies, A. Dalgarno Collisions of Highly Excited Atoms, R. F. Stebbings
Volume 17
Theoretical Aspects of Positron Collisions in Gases, J. W. Humberston
Collective Effects in Photoionization of Atoms, M. Ya. Amusia
Experimental Aspects of Positron Collisions in Gases, T. C. Griffith
Nonadiabatic Charge Transfer, D. S. F. Crothers
Reactive Scattering: Recent Advances in Theory and Experiment, Richard B. Bernstein
Atomic Rydberg States, Serge Feneuille and Pierre Jacquinot
Ion—Atom Charge Transfer Collisions at Low Energies, J. B. Hasted Aspects of Recombination, D. R. Bates The Theory of Fast Heavy Particle Collisions, B. H. Bransden Atomic Collision Processes in Controlled Thermonuclear Fusion Research, H. B. Gilbody
Superfluorescence, M. F. H. Schuurmans, Q. H. F. Vrehen, D. Polder, and H. M. Gibbs Applications of Resonance Ionization Spectroscopy in Atomic and Molecular Physics, M. G. Payne, C. H. Chen, G. S. Hurst, and G. W. Foltz Inner-Shell Vacancy Production in Ion— Atom Collisions, C. D. Lin and Patrick Richard
CONTENTS OF VOLUMES IN THIS SERIAL Atomic Processes in the Sun, P. L. Dufton and A. E. Kingston
Volume 18 Theory of Electron—Atom Scattering in a Radiation Field, Leonard Rosenberg Positron—Gas Scattering Experiments, Talbert S. Stein and Walter E. Kauppila Nonresonant Multiphoton Ionization of Atoms, J. Morellec, D. Normand, and G. Petite Classical and Semiclassical Methods in Inelastic Heavy-Particle Collisions, A. S. Dickinson and D. Richards Recent Computational Developments in the Use of Complex Scaling in Resonance Phenomena, B. R. Junker Direct Excitation in Atomic Collisions: Studies of Quasi-One-Electron Systems, N. Anderson and S. E. Nielsen Model Potentials in Atomic Structure, A. Hibbert Recent Developments in the Theory of Electron Scattering by Highly Polar Molecules, D. W. Norcross and L. A. Collins Quantum Electrodynamic Effects in FewElectron Atomic Systems, G. W. F. Drake
Volume 19 Electron Capture in Collisions of Hydrogen Atoms with Fully Stripped Ions, B. H. Bransden and R. K. Janev Interactions of Simple Ion—Atom Systems, J. T. Park High-Resolution Spectroscopy of Stored Ions, D. J. Wineland, Wayne M. Itano, and R. S. Van Dyck, Jr. Spin-Dependent Phenomena in Inelastic Electron—Atom Collisions, K. Blum and H. Kleinpoppen The Reduced Potential Curve Method for Diatomic Molecules and Its Applications, E. Jenc
251
The Vibrational Excitation of Molecules by Electron Impact, D. G. Thompson Vibrational and Rotational Excitation in Molecular Collisions, Manfred Faubel Spin Polarization of Atomic and Molecular Photoelectrons, N. A. Cherepkov
Volume 20 Ion—Ion Recombination in an Ambient Gas, D. R. Bates Atomic Charges within Molecules, G. G. Hall Experimental Studies on Cluster Ions, T. D. Mark and A. W. Castleman, Jr. Nuclear Reaction Effects on Atomic InnerShell Ionization, W. E. Meyerhof and J.-F. Chemin Numerical Calculations on Electron-Impact Ionization, Christopher Bottcher Electron and Ion Mobilities, Gordon R. Freeman and David A. Armstrong On the Problem of Extreme UV and X-Ray Lasers, I. L. Sobel’man and A. V. Vinogradov Radiative Properties of Rydberg State, in Resonant Cavities, S. Haroche and J. M. Ralmond Rydberg Atoms: High-Resolution Spectroscopy and Radiation Interaction — Rydberg Molecules, J. A. C. Gallas, G. Leuchs, H. Walther, and H. Figger
Volume 21 Subnatural Linewidths in Atomic Spectroscopy, Dennis P. O’Brien, Pierre Meystre, and Herbert Walther Molecular Applications of Quantum Defect Theory, Chris H. Greene and Ch. Jungen Theory of Dielectronic Recombination, Yukap Hahn Recent Developments in Semiclassical Floquet Theories for Intense-Field Multiphoton Processes, Shih-I Chu
252
CONTENTS OF VOLUMES IN THIS SERIAL
Scattering in Strong Magnetic Fields, M. R. C. McDowell and M. Zarcone
Volume 24
Pressure Ionization, Resonances, and the Continuity of Bound and Free States, R. M. More
The Selected Ion Flow Tube (SIDT): Studies of Ion—Neutral Reactions, D. Smith and N. G. Adams Near-Threshold Electron—Molecule Scattering, Michael A. Morrison
Volume 22 Positronium — Its Formation and Interaction with Simple Systems, J. W. Humberston Experimental Aspects of Positron and Positronium Physics, T. C. Griffith
Angular Correlation in Multiphoton Ionization of Atoms, S. J. Smith and G. Leuchs Optical Pumping and Spin Exchange in Gas Cells, R. J. Knize, Z. Wu, and W. Happer Correlations in Electron—Atom Scattering, A. Crowe
Doubly Excited States, Including New Classification Schemes, C. D. Lin Measurements of Charge Transfer and Ionization in Collisions Involving Hydrogen Atoms, H. B. Gilbody Electron—Ion and Ion—Ion Collisions with Intersecting Beams, K. Dolder and B. Pearl Electron Capture by Simple Ions, Edward Pollack and Yukap Hahn Relativistic Heavy-Ion—Atom Collisions, R. Anholt and Harvey Gould Continued-Fraction Methods in Atomic Physics, S. Swain
Volume 23 Vacuum Ultraviolet Laser Spectroscopy of Small Molecules, C. R. Vidal Foundations of the Relativistic Theory of Atomic and Molecular Structure, Ian P. Grant and Harry M. Quiney Point-Charge Models for Molecules Derived from Least-Squares Fitting of the Electric Potential, D. E. Williams and Ji-Min Yan Transition Arrays in the Spectra of Ionized Atoms, J. Bauche, C. Bauche-Arnoult, and M. Klapisch Photoionization and Collisional Ionization of Excited Atoms Using Synchroton and Laser Radiation, E. J. Wuilleumier; D. L. Ederer, and J. L. Picqué
Volume 25 Alexander Dalgarno: Life and Personality, David R. Bates and George A. Victor Alexander Dalgarno: Contributions to Atomic and Molecular Physics, Neal Lane Alexander Dalgarno: Contributions to Aeronomy, Michael B. McElroy Alexander Dalgarno: Contributions to Astrophysics, David A. Williams Dipole Polarizability Measurements, Thomas M. Miller and Benjamin Bederson Flow Tube Studies of Ion—Molecule Reactions, Eldon Ferguson Differential Scattering in He—He and He>— He Collisions at KeV Energies, R. F. Stebbings Atomic Excitation in Dense Plasmas, Jon C. Weisheit Pressure Broadening and Laser-Induced Spectral Line Shapes, Kenneth M. Sando and Shih-I Chu Model-Potential Methods, G. Laughlin and G. A. Victor Z-Expansion Methods, M. Cohen Schwinger Variational Methods, Deborah Kay Watson Fine-Structure Transitions in Proton-Ion Collisions, R. H. G. Reid
CONTENTS OF VOLUMES IN THIS SERIAL
253
Electron Impact Excitation, R. J. W. Henry and A. E. Kingston
Volume 27
Recent Advances in the Numerical Calculation of Ionization Amplitudes, Christopher Bottcher
Negative Ions: Structure and Spectra, David R. Bates
The Numerical Solution of the Equations of Molecular Scattering, A. C. Allison High Energy Charge Transfer, B. H. Bransden and D. P. Dewangan Relativistic Random-Phase Approximation, W. R. Johnson Relativistic Sturmian and Finite Basis Set Methods in Atomic Physics, G. W. F. Drake and S. P. Goldman Dissociation Dynamics of Polyatomic Molecules, T. Uzer
Electron Polarization Phenomena in Electron—Atom Collisions, Joachim Kessler Electron—Atom Scattering, I. E. McCarthy and E. Weigold Electron—Atom Ionization, I. E. McCarthy and E. Weigold Role of Autoionizing States in Multiphoton Ionization of Complex Atoms, V. I. Lengyel and M. I. Haysak Multiphoton Ionization of Atomic Hydrogen Using Perturbation Theory, E. Karule
Photodissociation Processes in Diatomic Molecules of Astrophysical Interest, Kate P. Kirby and Ewine F. van Dishoeck
Volume 28
The Abundances and Excitation of Interstellar Molecules, John. H. Black
The Theory of Fast Ion-Atom Collisions, J. S. Briggs and J. H. Macek
Volume 26 Comparisons of Positrons and Electron Scattering by Gases, Walter E. Kauppila and Talbert S. Stein
Some Recent Developments in the Fundamental Theory of Light, Peter W. Milonni and Surendra Singh Squeezed States of the Radiation Field, Khalid Zaheer and M. Suhail Zubairy Cavity Quantum, Electrodynamics, E. A. Hinds
Electron Capture at Relativistic Energies, B. L. Moiseiwitsch The Low-Energy, Heavy Particle Collisions — A Close-Coupling Treatment, Mineo Kimura and Neal F. Lane Vibronic Phenomena in Collisions of Atomic and Molecular Species, V. Sidis Associative Ionization: Experiments, Potentials, and Dynamics, John Weiner, Françoise Masnou-Sweeuws, and Annick Giusti-Suzor On the Decay of Re: An Interface of Atomic and Nuclear Physics and Cosmochronology, Zonghau Chen, Leonard Rosenberg, and Larry Spruch Progress in Low Pressure Mercury-Rare Gas Discharge Research, J. Maya and R. Lagushenko
Volume 29 Studies of Electron Excitation of Rare-Gas Atoms into and out of Metastable Levels Using Optical and Laser Techniques, Chun C. Lin and L. W. Anderson Cross Sections for Direct Multiphoton Ionization of Atoms, M. V. Ammosov, N. B. Delone, M. Yu. Ivanov, I. I. Bondar, and A. V. Masalov Collision-Induced Coherences in Optical Physics, G. S. Agarwal Muon-Catalyzed Fusion, Johann Rafelski and Helga E Rafelski Cooperative Effects in Atomic Physics, J. P. Connerade
254
CONTENTS OF VOLUMES IN THIS SERIAL
Multiple Electron Excitation, Ionization, and Transfer in High-Velocity Atomic and Molecular Collisions, J. H. McGuire
Volume 30 Differential Cross Sections for Excitation of Helium Atoms and Helium-Like Ions by Electron Impact, Shinobu Nakazaki Cross-Section Measurements for Electron Impact on Excited Atomic Species, S. Trajmar and J. C. Nickel The Dissociative Ionization of Simple Molecules by Fast Ions, Colin J. Latimer Theory of Collisions between Laser Cooled Atoms, P. S. Julienne, A. M. Smith, and K. Burnett Light-Induced Drift, E. R. Eliel Continuum Distorted Wave Methods in Ion— Atom Collisions, Derrick S. F. Crothers and Louis J. Dubé
Volume 31 Energies and Asymptotic Analysis for Helium Rydberg States, G. W. F. Drake Spectroscopy of Trapped Ions, R. C. Thompson Phase Transitions of Stored Laser-Cooled Ions, H. Walther Selection of Electronic States in Atomic Beams with Lasers, Jacques Baudon, Rudolf Düren, and Jacques Robert Atomic Physics and Non-Maxwellian Plasmas, Michèle Lamoureux
Volume 32 Photoionization of Atomic Oxygen and Atomic Nitrogen, K. L. Bell and A. E. Kingston Positronium Formation by Positron Impact on Atoms at Intermediate Energies, B. H. Bransden and C. J. Noble
Electron—Atom Scattering Theory and Calculations, P. G. Burke Terrestrial and Extraterrestrial H >, Alexander Dalgarno Indirect Ionization of Positive Atomic Ions, K Dolder Quantum Defect Theory and Analysis of High-Precision Helium Term Energies, G. W. F. Drake Electron—lon and Ion—Ion Recombination Processes, M. R. Flannery Studies of State-Selective Electron Capture in Atomic Hydrogen by Translational Energy Spectroscopy, H. B. Gilbody Relativistic Electronic Structure of Atoms and Molecules, I. P. Grant The Chemistry of Stellar Environments, D. A. Howe, J. M. C. Rawlings, and D. A. Williams Positron and Positronium Scattering at Low Energies, J. W. Humberston How Perfect are Complete Atomic Collision Experiments?, H. Kleinpoppen and H. Handy Adiabatic Expansions and Nonadiabatic Effects, R. McCarroll and D. S. F. Crothers Electron Capture to the Continuum, B. L Moiseiwitsch How Opaque Is a Star? M. J. Seaton Studies of Electron Attachment at Thermal Energies Using the Flowing Afterglow— Langmuir Technique, David Smith and Patrik Spanel Exact and Approximate Rate Equations in Atom-Field Interactions, S. Swain Atoms in Cavities and Traps, H. Walther Some Recent Advances in Electron-Impact Excitation of n : 3 States of Atomic Hydrogen and Helium, J. F. Williams and J. B. Wang
Volume 33 Principles and Methods for Measurement of Electron Impact Excitation Cross Sections for Atoms and Molecules by Optical
CONTENTS OF VOLUMES IN THIS SERIAL Techniques, A. R. Filippelli, Chun C. Lin, L. W. Andersen, and J. W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Analysis of Scattered Electrons, S. Trajmar and J. W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Electron Swarm Methods, R. W. Crompton
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Polarization and Orientation Phenomena in Photoionization of Molecules, N. A. Cherepkov Role of Two-Center Electron—Electron Interaction in Projectile Electron Excitation and Loss, E. C. Montenegro, W. E. Meyerhof, and J. H. McGuire Indirect Processes in Electron Impact Ionization of Positive Ions, D. L. Moores and K. J. Reed
Some Benchmark Measurements of Cross Sections for Collisions of Simple Heavy Particles, H. B. Gilbody
Dissociative Recombination: Crossing and Tunneling Modes, David R. Bates
The Role of Theory in the Evaluation and Interpretation of Cross-Section Data, Barry I. Schneider
Volume 35
Analytic Representation of Cross-Section Data, Mitio Inokuti, Mineo Kimura, M. A. Dillon, and Isao Shimamura
Laser Manipulation of Atoms, K. Sengstock and W. Ertmer
Electron Collisions with N , O and O: What We Do and Do Not Know, Yukikazu Itikawa
Advances in Ultracold Collisions: Experiment and Theory, J. Weiner Ionization Dynamics in Strong Laser Fields, L. F. DiMauro and P. Agostini
Need for Cross Sections in Fusion Plasma Research, Hugh P. Summers
Infrared Spectroscopy of Size Selected Molecular Clusters, U. Buck
Need for Cross Sections in Plasma Chemistry, M. Capitelli, R. Celiberto, and M. Cacciatore
Femtosecond Spectroscopy of Molecules and Clusters, T. Baumer and G. Gerber
Guide for Users of Data Resources, Jean W. Gallagher
Calculation of Electron Scattering on Hydrogenic Targets, I. Bray and A. T. Stelbovics
Guide to Bibliographies, Books, Reviews, and Compendia of Data on Atomic Collisions, E. W. McDaniel and E. J. Mansky
Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence, W. R. Johnson, D. R. Plante, and J. Sapirstein
Volume 34 Atom Interferometry, C. S. Adams, O. Carnal, and J. Mlynek
Rotational Energy Transfer in Small Polyatomic Molecules, H. O. Everitt and F. C. De Lucia
Optical Tests of Quantum Mechanics, R. Y. Chiao, P G. Kwiat, and A. M. Steinberg
Volume 36
Classical and Quantum Chaos in Atomic Systems, Dominique Delande and Andreas Buchleitner
Complete Experiments in Electron—Atom Collisions, Nils Overgaard Andersen and Klaus Bartschat
Measurements of Collisions between LaserCooled Atoms, Thad Walker and Paul Feng
Stimulated Rayleigh Resonances and RecoilInduced Effects, J.-Y. Courtois and G. Grynberg
The Measurement and Analysis of Electric Fields in Glow Discharge Plasmas, J. E. Lawler and D. A. Doughty
Precision Laser Spectroscopy Using AcoustoOptic Modulators, W. A. van Wijngaarden
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CONTENTS OF VOLUMES IN THIS SERIAL
Highly Parallel Computational Techniques for Electron—Molecule Collisions, Carl Winstead and Vincent McKoy Quantum Field Theory of Atoms and Photons, Maciej Lewenstein and Li You
Volume 37 Evanescent Light-Wave Atom Mirrors, Resonators, Waveguides, and Traps, Jonathan P. Dowling and Julio GeaBanacloche Optical Lattices, P. S. Jessen and I. H. Deutsch Channeling Heavy Ions through Crystalline Lattices, Herbert F. Krause and Sheldon Datz Evaporative Cooling of Trapped Atoms, Wolfgang Ketterle and N. J. van Druten Nonclassical States of Motion in Ion Traps, J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller The Physics of Highly-Charged Heavy Ions Revealed by Storage/Cooler Rings, P. H. Mokler and Th. Stöhlker
Volume 38 Electronic Wavepackets, Robert R. Jones and L. D. Noordam Chiral Effects in Electron Scattering by Molecules, K. Blum and D. G. Thompson Optical and Magneto-Optical Spectroscopy of Point Defects in Condensed Helium, Serguei I. Kanorsky and Antoine Weis Rydberg Ionization: From Field to Photon, G. M. Lankhuijzen and L. D. Noordam Studies of Negative Ions in Storage Rings, L. H. Andersen, T. Andersen, and P. Hvelplund Single-Molecule Spectroscopy and Quantum Optics in Solids, W. E. Moerner, R. M. Dickson, and D. J. Norris
Volume 39 Author and Subject Cumulative Index Volumes 1—38 Author Index Subject Index Appendix: Tables of Contents of Volumes 1—38 and Supplements
Volume 40 Electric Dipole Moments of Leptons, Eugene D. Commins High-Precision Calculations for the Ground and Excited States of the Lithium Atom, Frederick W. King Storage Ring Laser Spectroscopy, Thomas U. Kühl Laser Cooling of Solids, Carl E. Mungan and Timothy R. Gosnell Optical Pattern Formation, L. A. Lugiato, M. Brambilla, and A. Gatti
Volume 41 Two-Photon Entanglement and Quantum Reality, Yanhua Shih Quantum Chaos with Cold Atoms, Mark G. Raizen Study of the Spatial and Temporal Coherence of High-Order Harmonics, Pascal Salie`res, Ann L’Huiller Philippe Antoine, and Maciej Lewenstein Atom Optics in Quantized Light Fields, Matthias Freyburger, Alois M. Herkommer, Daniel S. Krähmer, Erwin Mayr, and Wolfgang P. Schleich Atom Waveguides, Victor I. Balykin Atomic Matter Wave Amplification by Optical Pumping, Ulf Janicke and Martin Wilkens
Volume 42 Fundamental Tests of Quantum Mechanics, Edward S. Fry and Thomas Walther
CONTENTS OF VOLUMES IN THIS SERIAL Wave-Particle Duality in an Atom Interferometer, Stephan Dürr and Gerhard Rempe Atom Holography, Fujio Shimizu Optical Dipole Traps for Neutral Atoms, Rudolf Grimm, Matthias Weidemüller, and Yurii B. Ovchinnikov Formation of Cold (T1K) Molecules, J. T. Bahns, P. L. Gould, and W. C. Stwalley High-Intensity Laser-Atom Physics, C. J. Joachain, M. Dorr, and N. J. Kylstra Coherent Control of Atomic, Molecular, and Electronic Processes, Moshe Shapiro and Paul Brumer
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Molecular Processes in Reactive Plasmas, Yoshihiko Hatano Ion—Molecule Reactions, Werner L indinger, Armin Hansel, and Zdenek Herman Uses of High-Sensitivity White-Light Absorption Spectroscopy in Chemical Vapor Deposition and Plasma Processing, L. W. Anderson, A. N. Goyette, and J. E. L awler Fundamental Processes of Plasma—Surface Interactions, Rainer Hippler Recent Applications of Gaseous Discharges: Dusty Plasmas and Upward-Directed Lightning, Ara Chutjian
Resonant Nonlinear Optics in Phase Coherent Media, M. D. Lukin, P. Hemmer, and M. O. Scully
Opportunities and Challenges for Atomic, Molecular, and Optical Physics in Plasma Chemistry, Kurt Becker, Hans Deutsch, and Mitio Inokuti
The Characterization of Liquid and Solid Surfaces with Metastable Helium Atoms, H. Morgner
Volume 44
Quantum Communication with Entangled Photons, Harald Weinfurter
Volume 43 Plasma Processing of Materials and Atomic, Molecular, and Optical Physics: An Introduction, Hiroshi Tanaka and Mitio Inokuti The Boltzmann Equation and Transport Coefficients of Electrons in Weakly Ionized Plasmas, R. W inkler
Mechanisms of Electron Transport in Electrical Discharges and Electron Collision Cross Sections, Hiroshi Tanaka and Osamu Sueoka Theoretical Consideration of PlasmaProcessing Processes, Mineo Kimura Electron Collision Data for PlasmaProcessing Gases, L oucas G. Christophorou and James K. Olthoff Radical Measurements in Plasma Processing, Toshio Goto
Electron Collision Data for Plasma Chemistry Modeling, W. L . Morgan
Radio-Frequency Plasma Modeling for Low-Temperature Processing, Toshiaki Makabe
Electron—Molecule Collisions in LowTemperature Plasmas: The Role of Theory, Carl W instead and V incent McKoy
Electron Interactions with Excited Atoms and Molecules, L oucas G. Christophorou and James K. Olthoff
Electron Impact Ionization of Organic Silicon Compounds, Ralf Basner, Kurt Becker, Hans Deutsch, and Martin Schmidt Kinetic Energy Dependence of Ion—Molecule Reactions Related to Plasma Chemistry, P. B. Armentrout Physicochemical Aspects of Atomic and
Volume 45 Comparing the Antiproton and Proton, and Opening the Way to Cold Antihydrogen, G. Gabrielse
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CONTENTS OF VOLUMES IN THIS SERIAL
Medical Imaging with Laser-Polarized Noble Gases, T imothy Chupp and Scott Swanson Polarization and Coherence Analysis of the Optical Two-Photon Radiation from the Metastable 2S State of Atomic Hydrogen, Alan J. Duncan, Hans Kleinpoppen, and Marlan O. Scully
Laser Spectroscopy of Small Molecules, W. Demtro¨der, M. Keil, and H. Wenz Coulomb Explosion Imaging of Molecules, Z. Vager