THE SCIENCE AND CULTURE SERIES — ADVANCED SCIENTIFIC CULTURE Series Editor: A. Zichichi
HADRONS, NUCLEI AND APPLICATIONS PROCEEDINGS OF THE CONFERENCE: BOLOGNA 2000 STRUCTURE OFlHE NUCLEUS AT THE DAWN OF THE^ENTURY
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World Scientific
HADRONS, NUCLEI AND APPLICATIONS PROCEEDINGS OF THE CONFERENCE: BOLOGNA 2000 STRUCTURE OF THE NUCLEUS AT THE DAWN OF THE CENTURY
THE SCIENCE AND CULTURE SERIES — ADVANCED SCIENTIFIC CULTURE Series Editor: A. Zichichi, European Physical Society, Geneva, Switzerland Series Editorial Board: P. G. Bergmann, J. Collinge, V. Hughes, N. Kurti, T. D. Lee, K. M. B. Siegbahn, G. 't Hooft, P. Toubert, E. Velikhov, G. Veneziano, G. Zhou
1.
Nucleus-Nucleus Collisions Bologna 2000. Structure of the Nucleus at the Dawn of the Century
2.
Nuclear Structure Bologna 2000. Structure of the Nucleus at the Dawn of the Century
3.
Hadrons, Nuclei and Applications Bologna 2000. Structure of the Nucleus at the Dawn of the Century
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HADRONS, NUCLEI AND APPLICATIONS PROCEEDINGS OF THE CONFERENCE: BOLOGNA 2000 STRUCTURE OF THE NUCLEUS AT THE DAWN OF THE CENTURY
Bologna, Italy
29 May - 3 June 2000
Editors
Giovanni C. Bonsignori Mauro Bruno Dipartimento di Fisica dell' Universita di Bologna and INFN-Sezione di Bologna, Italy
Alberto Ventura Ente Nuove Tecnologie, Energia e Ambiente and INFN Bologna, Italy
Dario Vretenar Physics Department, University of Zagreb, Croatia
Series Editor
A. Zichichi
Vfe W o r l d Scientific « •
NewJersev Ne w Jersey • London* London • Sinaanore* Singapore • Hong Kong
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HADRONS, NUCLEI AND APPLICATIONS Proceedings of the Conference: Bologna 2000 Structure of the Nucleus at the Dawn of the Century Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
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ISBN 981-02-4733-8
Printed in Singapore.
CONTENTS
Many B o d y Methods in Nuclear Structure New Microscopic Approaches to the Physics of Nuclei with A < 12 G. Orlandini
2
Interactions, Currents and the Structure of Few-Nucleon Systems R. Schiavilla
10
Quantum Chaos and Nuclear Structure V. Zelevinsky
20
Theories and Applications beyond Mean Field with Effective Forces R. R. Rodriguez-Guzman, J. L. Egido and L. M. Robledo
28
Relativistic Theory of Pairing in Infinite Nuclear Matter M. Serra, A. Rummel and P. Ring
34
Realistic Effective Interactions and Shell-Model Calculations for Medium- and Heavy-Mass Nuclei A. Gargano
38
Derivative Coupling Model Description of Nuclear Matter in the Dirac-Hartree-Fock Approximation P. Bernardos, R. Lombard, M. Lopez-Quelle, S. Marcos and R. Niembro
44
Generator Coordinate Method including Triaxial Angular Momentum Projection K. Tanabe, K. Enami and N. Yoshinaga
48
Effect of the Triaxial Angular Momentum Projection on the Potential Energy Surface K. Enami, K. Tanabe, N. Yoshinaga and K. Higashiyama
52
v
VI
Realistic Intrinsic State Densities for Deformed Nuclei E. Mainegra and R. Capote
56
Approximate Treatment of the Centre of Mass Correction for Light Nuclei M. Grypeos, C. Koutroulos, A. Shebeko and K. Ypsilantis
60
One-Body Density Matrix and Momentum Distribution in S-P and S-D Shell Nuclei C. C. Moustakidis and S. E. Massen
64
Correlation Induced Collapse of Systems with Skyrme Forces D. V. Fedorov and A. S. Jensen
68
Hadron Dynamics Hadron Dynamics: Present Status and Future Perspective T. Bressani Section I.
73
Strange Hadro-Dynamics
KNA and KNS Coupling Constants M. T. Jeong and I. T. Cheon
86
On The E Hypernucleus E. Satoh and M. Kimura
90
Non Mesonic Weak Decay of Hypernuclei A. Parreno
96
Study of Mesonic and Non-Mesonic Decay of A-Hypernuclei at DA3>NE L. Venturelli for the FINUDA Collaboration
100
Hypernuclear 7-Spectroscopy: Recent Results with Hyperball H. Tamura for the KEK E419, BNL E930 Collaborations
106
vii
On the Coalescence Production of Broad Resonances V. M. Kolybasov
110
Energetic Level Scheme of the Stable S = —2 Dihyperon P. Z. Aslanian and B. A. Shahbazian
114
Section II.
Mesons, Baryons and Antibaryons
Pionic Excitations of Nuclear Systems W. Weise
119
Status of Exotic Meson Searches M. Villa
127
A Study of the TT-TT Interaction in Nuclear Matter Using the 7r+ + A -+ n+ + IT* + A' Reaction P. Camerini for the CHA OS Collaboration
134
Pion-Pion Potentials by Inversion of Phase Shifts at Fixed Energy B. Bdthory, Z. Barman and B. Apagyi
140
Perspectives of the Antideuteron Physics at JHF F. Iazzi, J. Doornbos, T. Bressani and D. Calvo
146
Study of the TT+TT+ System in the Antineutron-Proton into Three Charged Pions Annihilation Reaction A. Filippi for the OBELIX Collaboration
150
Observation of an Anomalous Trend of the Antineutron-Proton Total Cross Section in the Low-Momentum Region A. Feliciello
154
A Study of the n Annihilation on Nuclei E. Botta for the OBELIX Collaboration
158
-np Scattering in the Coulomb-Nuclear Interference Region E. Fragiacomo for the CHAOS Collaboration
162
Vlli
Arguments against the Yukawa Concept of Nuclear Force at Intermediate- and Short-Ranges and the New Mechanism for NN Interaction V. I. Kukulin
166
Moving Triangle Singularities and Polarization of Fast Particles V. M. Kolybasov
170
Section III.
Hadron Structure and Electromagnetic Probes
Electron-Positron Pair Spectroscopy with HADES at GSI J. Friese for the HADES Collaboration
175
Precision Measurement of the Neutron Magnetic Form Factor from 3He(e, e') H. Gao for the E95-001 Collaboration
181
The Hypercentral Constituent Quark Model M. M. Giannini and E. Santopinto
187
Algebraic Model of Baryon Structure R. Bijker and A. Leviatan
193
Non-Perturbative vs Perturbative Nucleon Response to Electromagnetic Probes M. Traini
199
The LEGS Double Polarization Program M. Blecher for the LEGS Spin Collaboration
205
Hadrons in a Relativistic Many-Body Approach S. R. Cotanch and F. J. Llanes-Estrada
209
Light Meson Spectra and Strong Decays in a Chiral Quark Cluster Model L. A. Blanco, F. Fernandez and A. Valcarce
215
A Sketch of Two and Three Bodies H. W. Grief3hammer
219
ix
Realistic Study of the Nuclear Transparency and the Distorted Momentum Distributions in the Semi-Inclusive Process AHe{e, e'p)X H. Morita, C. Ciofi degli Atti and D. Treleani
224
Measurements of the Deuteron Elastic Structure Functions A(Q2) and B(Q2) at the Jefferson Laboratory M. Kuss for the Jefferson Lab. Hall A Collaboration
230
OZI Rule Violation in np Annihilations in Flight S. Marcello
236
Parity Violating Electron Scattering B. Mosconi and P. Ricci
240
Nuclear Astrophysics Nucleosynthesis in Supernovae and Neutron Star Mergers F.-K. Thielemann Section I.
246
Theoretical Aspects of Nuclear Astrophysics
Strange Hadronic Stellar Matter within the Brueckner-Bethe-Goldstone Theory M. Baldo, G. F. Burgio and H. -J. Schulze
257
Bubble Nuclei, Neutron Stars and Quantum Billiards A. Bulgac and P. Magierski
261
Microscopic Models for Nuclear Astrophysics P. Descouvemont
267
Towards a Hartree-Fock Mass Formula J. M. Pearson, M. Onsi, S. Goriely, F. Tondeur and M. Farine
273
Nuclear Aspects of Nucleosynthesis in Massive Stars T. Rauscher, R. D. Hoffman, A. Heger and S. E. Woosley
277
X
Weak Interaction Rates of Neutron-Rich Nuclei and the R-Process Nucleosynthesis /. N. Borzov and S. Goriely
283
Systematics of Low-Lying Level Densities and Radiative Widths A. V. Ignatyuk
287
Cooling of Neutron Stars Revisited: Application of Low Energy Theorems A. E. L. Dieperink, E. N. E van Dalen, A. Korchin and R. Timmermans
293
The Role of Electron Screening Deformations in Solar Nuclear Fusion Reactions and the Solar Neutrino Puzzle T. E. Liolios
299
Nuclear Masses and Halflives: Statistical Modeling with Neural Nets E. Mavrommatis, S. Athanassopoulos, A. Dakos, K. A. Gernoth and J. W. Clark
303
Quasi-Thermal Photon Bath from Bremsstahlung P. Mohr, M. Babilon, J. Enders, T. Hartmann, C. Hutter, K. Vogt, S. Volz and A. Zilges
308
Nuclear Structure Near the Neutron Drip-Line and R-Process Calculations W. B. Walters, K.-L. Kratz and B. Pfeiffer
312
Analysis of the Neutrino Propagation in Neutron Stars in the Framework of Relativistic Nuclear Models R. Niembro, S. Marcos, P. Bernardos and M. Lopez-Quelle
315
Hyperonic Crystallization in Hadronic Matter M. A. Perez-Garcia, J. Diaz-Alonso, L. Mornas and J. P. Sudrez
319
Radioactive Witnesses of the Last Events of Nucleosynthesis in the Neighbourhood of the Nascent Solar System V. P. Chechev Section II.
323
Experimental Aspects of Nuclear Astrophysics
Bound State Beta-Decay and its Astrophysical Relevance P. Kienle
328
Searching for Signals from the Dark Universe R. Bernabei, P. Belli, R. Cerulli, F. Montecchia, M. Amato, G. Ignesti, A. Incicchitti, D. Prosperi, C. J. Dai, H. L. He, H. H. Kuang and J. M. Ma
338
Experimental Studies Related to s- and r- Process Abundances K. Wisshak, F. Voss and F. Kappeler
346
Experimental Study of the Electron Screening Effect in the d( 3 He,p) 4 He Fusion Reaction S. Zavatarelli for the L UNA Collaboration
350
The Solar Neutrino Problem: Low Energy Measurements of the 7 Be(p,7) 8 B Cross Section F. Hammache, G. Bogaert, A. Coc, M. Jacotin, J. Kiener, A. Lefebvre, V. Tatischeff, J. P. Thibaud, P. Aguer, J. F. Chemin, G. Claverie, J. N. Scheurer, E. Virassamynaiken, L. Brilliard, M. Hussonois, C. Le Naour, S. Barhoumi, S. Ouichaoui and C. Angulo
354
Determination of the Astrophysical S'-Factors Sn and S\s from 7 Be(d,n) 8 B and 8 B(d,n) 9 C Cross-Sections D. Beaumel, S. Fortier, H. Laurent, J.-M. Maison, S. Pita, T. Kubo, T. Teranishi, H. Sakurai, T. Nakamura, N. Aoi, N. Fukuda, M. Hirai, N. Imai, H. Iwasaki, H. Kumagai, S. M. Lukyanov, K. Yoneda, M. Ishihara, T. Motobayashi and H. Ohnuma
360
A Measurement of the 13 C(a,o:) Differential Cross-Section and its Application on the 1 3 C(a,n) Reaction M. Heil, A. Couture, J. Daly, R. Detwiler, J. Gorres, G. Hale, F. Kdppeler, R. Reifarth, U. Giessen, E. Stech, P. Tischhauser, C. Ugalde and M. Wiescher
364
Neutron Cross Sections Measurements for Light Elements at ORELA and their Application in Nuclear Criticality and Astrophysics K. H. Guber, L. C. Leal, R. O. Sayer, R. R. Spencer, P. E. Koehler, T. E. Valentine, H. Derrien, J. Andrzejewski, Y. M. Gledenov and J. A. Harvey
368
The Stellar Neutron Capture of 2 0 8 Pb H. Beer, W. Rochow, P. Mutti, F. Corvi, K.-L. Kratz and B. Pfeiffer
372
The r-Process as the Mirror Image of the s-Process: How Does It Work? R. Gallino, M. Busso, F. Kdppeler and G. J. Wasserburg
376
The Neutron Capture Cross Section of 1 4 7 Pm at Stellar Energies C. Arlandini, M. Heil, R. Reifarth, F. Kdppeler and P. V. Sedyshev
382
Applications of Nuclear Physics Section I.
Fission, Spallation and Transmutation
The ENEA ADS Project G. Gherardi for the ENEA ADS Project
387
Heat Deposit Calculation in Spallation Unit F. I. Karmanov, A. A. Travleev, L. N. Latysheva and M. Vecchi
393
xiii
Nuclide Composition of Pb-Bi Heat Transfer Irradiated in 80MW Sub-Critical Reactor A. Y. Konobeyev and M. Vecchi
397
Radiological Aspects of Heavy Metal Liquid Targets for Accelerator-Driven System as Intense Neutron Sources E. V. Gai, A. V. Ignatyuk, V. P. Lunev and Yu. N. Shubin
401
Intermediate-Energy Nuclear Data for Radioactive Ion Beams and Accelerator-Driven Systems M. V. Ricciardi, P. Armbruster, T. Enqvist, F. Rejmund, K.-H. Schmidt, J. Taieb, J. Benlliure, E. Casarejos, M. Bernas, B. Mustapha, L. Tassan-Got, A. Boudard, R. Legrain, S. Leray, C. Stephan, C. Volant, W. Wlazlo, S. Czajkowski, J. P. Dufour and M. Pravikoff
407
Actinide Nucleon-Induced Fission Reactions up to 150 MeV V. M. Maslov and A. Hasegawa
413
The AUSTRON Spallation Source Project G. Badurek, E. Jericha, H. Weber and E. Griesmayer
418
Section II.
Other Applications of Nuclear Physics
Recent Model Developments for Nucleon Induced Reactions up to 200 MeV E. Bauge, J. P. Delaroche, M. Girod, S. Hilaire, J. Libert, B. Morillon and P. Romain
425
Multistep Description of Nucleon Production Spectra in Nucleon-Induced Reactions at Intermediate Energy E. Ramstrom, H. Lenske and H. H. Wolter
431
Hadron Cancer Therapy: Role of Nuclear Reactions M. B. Chadwick
437
XIV
Accelerator-Based Sources of Epithermal Neutrons for BNCT E. Bisceglie, P. Colangelo, N. Colonna, V. Variale and P. Santorelli
443
Study of the Light Ion Beam Fragmentation in Thick Tissue-Like Matters Using Tissue-Like Track Detector S. P. Tretyakova, A. N. Golovchenko, R. Ilic and J. Skvarc
447
Anisotropy Functions for Palladium Model 200 Interstitial Brachyterapy Source R. Capote, E. Mainegra and E. Lopez
451
Production of Radiopharmaceuticals Based on the 199 T7 and 2uAt for Myocardium Diagnostic and Cancer Therapy O. V. Fotina, D. 0. Eremenko, V. O. Kordyukevich, S. Yu. Platonov, E. I. Sirotinin, A. V. Tultaev and O. A. Yuminov
455
Horizontal Compilations of Nuclear Data Z. N. Soroko, S. I. Sukhoruchkin and D. S. Sukhoruchkin
459
Tuning Effect in Nuclear Data S. I. Sukhoruchkin
463
List of Participants
468
Author Index
495
Many Body Methods in Nuclear Structure
N E W M I C R O S C O P I C A P P R O A C H E S TO T H E P H Y S I C S OF N U C L E I W I T H A < 12
Dipartimento
G. O R L A N D I N I di Fisica, Universita di Trento, 1-38050 Povo (Trento) and I.N.F.N. Gruppo Collegato di Trento E-mail:
[email protected] Italy
The important progresses achieved in recent years in describing nuclei with A < 12 within microscopic theories are reviewed. In particular both results for bound states and for continuum states are presented. It is inferred that, because of these progresses, few-body physics is playing an increasingly important role in modern nuclear physics. The microscopic knowledge of light systems represents in fact the necessary bridge between our understanding of nuclear structure and QCD, the fundamental theory of strong interaction.
1
Introduction
Few-body systems are playing an increasingly i m p o r t a n t role in modern nuclear physics to the extent t h a t ab initio calculations performed within different approaches are able to produce very accurate results. T h e possibility of comparing these results with experimental d a t a unambiguously gives valuable information about the properties of the forces governing nuclear dynamics, challenges to a more fundamental comprehension of their origin and sheds some light on the many-body mechanisms generating typical properties of heavier systems. In this talk I intend to review briefly the recent progresses m a d e in treating both static and dynamical properties of few-nucleon systems.
2
Few-body bound states
Various methods are used to calculate binding energies and low lying spectra of light nuclei. They can be grouped as follows: l)Montecarlo (stochastic) methods. T h e Green Function Montecarlo Method ( G F M C ) 1 is based on the use of the evolution propagator in imaginary time and is designed to calculate expectation values of the Hamiltonian and other operators. Combined with the Variational Montecarlo ( V M C ) l technique G F M C is able to give very accurate results for nuclei with A = 3 and 4 and has been extended up to systems with A = 8. T h e accuracy of this m e t h o d is governed by the "statistical" errors. T h e Stochastic Variational Method (SVM) 2 is based on expansions of the variational wave functions on correlated gaussians basis and subsequent stochastic selection of the most important components. 2
3
Because of the "statistical sampling" also the SVM is able to treat a large number of variables and therefore to treat systems with A > 4.
Figure 1: VMC, GFMC and experimental energies of nuclear states for A < 4 < 8. From Ref. 3 .
2)The Faddeev-Yakubosky (FY)4 or equivalently the Alt-Grassberger-Sandhas5 (AGS) methods. They are based on solutions of coupled integral equations. The A-body wave function is obtained. Up to now A is limited to 3 and 4. They are naturally formulated in momentum space, but also treated in configuration space 6 . The accuracy of these methods is driven by the numerical errors in the solutions of the integral equations. $)The no core shell model (NCSM) method7. The Hamiltonian is diagonalized on the harmonic oscillator basis. Effective interaction operators calculated within either the Bloch-Horowitz 8 or the Lee-Suzuki unitary transformation methods 9 are used. The accuracy is driven by the size of the model space and by the number of particles in the subsystems where the effective interaction is built. This method has been applied to systems up to A=12. 4)The Hyperspherical Harmonics (HH) methods. They are based on expansions of the wave functions over the HH basis. They are formulated in configuration
4
space. The accuracy is driven by the number of basis functions one is able to treat and therefore by the rate of convergence. Two methods exist to improve the convergence rate. One of them, known as the Correlated Hyperspherical Harmonics method (CHH) 10 introduces correlation functions in the HH basis. The other very recent one, which will be called the Effective Interaction Hyperspherical Harmonics (EIHH) method 1 1 , makes use of the effective interaction operator built with the unitary transformation method 9 . While the CHH approach has been used only for A=3,4 the EIHH has extended calculations to A=5,6 nuclei. In Fig.l VMC and GFMC results for the energies of the low-lying nuclear states of nuclei with A = 4 -r- 8 3 are reported together with experimental values. In Fig.2 the spectrum of positive parity states of 12 C obtained within the NCSM approach 12 is shown. From the quality of the agreement between theory and experiment, and considering that these are ab initio calculations with realistic NN interactions (in some cases even with inclusion of three-body forces) one can probably conclude that we are close to understanding the microscopic origin of those spectra. If on the one hand the remaining disagreement challenges us to get a better control on the few- (many-)body techniques, especially for the heavier systems, on the other hand it focuses our interest on the off shell properties of the NN potential and/or on the origin and role of the many-body forces. Of course the issue of a better and better control on the
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few (many) - body techniques is an important one, before definite statements can be made about the origin of the dynamics. In this respect the continuous improvements of computational facilities will continue to have a major impact. But also the progresses in finding new algorithms and new ideas how to generalize or combine different methods are going to be very important. In this respect I would like to mention an example of how one can make important progresses by combining ideas originated in the many body field with a technique typical of few-body physics. I refer to the results obtained in Ref. n . As it was said in the previous subsection the limits of the HH expansion approach lies in the rate of convergence to the exact eigenvalue as more and more HH functions are considered. The problems of convergence may become serious especially when one has to do with strong core potentials like the NN potential. In fact this generates high momentum components in the wave function which then require HH functions of high order to be described. The CHH approach tries to incorporate those high momentum components in the basis functions by modifying them in a "physically" sensible, though rather arbitrary, way. This is done by multiplying the basis functions by a product of "correlation" functions. An alternative way (well known in the many body field as well as
Figure 3: Binding energies and r.m.s. radii of nuclei with A = 4 4- 6 systems as a function of the hyperangular quantum number K. For A = 4 (right) EIHH results (full thick line) are compared to NCSM results and to bare interaction results (full light line). From Ref. x l .
6
in field theory) of incorporating in the model space effects coming from the neglected space is the "effective operator" approach. In this framework one is able to build systematically the " effective interaction" to use in the Schrodinger equation instead of the bare interaction. The effective interaction generates in the wave functions large parts of those effects which would otherwise be left in the neglected basis states. The NCSM method 7 makes large use of this concept within the harmonic oscillator basis. The EIHH method n instead uses it within the HH expansion. The convergence is improved considerably and at the same time some of the well known drawbacks of the h.o. basis are cured. In Fig. 3 (left) the rate of convergence of ground state energy and radius of the A=4 system are plotted in function of the hyperspherical quantum number K and compared to NCSM results. One notices the striking improvement in the convergence rate due to the use of the effective interaction. The comparison with NCSM results puts in evidence the additional advantage of the HH formalism in that it does not require any additional parameter (like the h.o. frequency) affecting the rate of convergence. In Fig. 3 (right) rate of convergences of energies and radii of A=5,6 systems are also shown. From these results one can conclude that the EIHH is a very promising alternative method to study bound state properties of light systems and allows the HH formalism to be applied beyond A=4.
3
Few-body problem in the continuum
Finding exact solutions of the Schrodinger equation in the continuum is a very difficult task, even if the number of degrees of freedom is small. The difficulty lies in the definition and treatment of the boundary conditions. While solutions are easily obtained in the two-body case the problem alread becomes very involved going to A=3. It is clear that when A > 2 an increasing number of break up channels opens up, each of them requiring different boundary conditions. At present only few groups are able to comply with this difficult task. This is done within two different approaches: in one case the continuum Faddeev-Yakubosky integral equations are solved 4 ' 5 ' 6 ' 13 , in the other the HH expansion method is coupled to the use of the complex form of the Kohn variational principle 14 . A third unconventional, but very powerful approach, the Lorentz Integral Transform Method 17 , which is able to reduce the problem of calculating transition matrix elements to continuum states into bound state problems, will be the topics of the next section. In Figs. 4 and 5 results for n-d and p-d scattering cross sections are shown. One notices the remarkable agreement between theory and experiment for differential cross sections at different energies. This might imply that the
7
three-body problem is very well understood within a non relativistic framework with realistic potentials. However, the properties and origin of these potentials is just the i m p o r t a n t issue opened by this comparison. In fact, as it is shown in Fig. 4, it is the inclusion of three-body forces t h a t brings theory t o agree with data. O n the other hand the vector analyzing powers of b o t h p-d and
E„
90
120
150
160
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60
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120
150
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Figure 4: n-d differential cross sections at two different neutron energies. Long dashed curves: results with only Vjyjv- Solid curve: Vjvw + VNNN results. From Ref.13.
90 135 180
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45 90 135 180
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Figure 5: p-d (solid) and n-d (dashed) differential cross sections, nucleon analyzing power, deuteron analyzing power and tensor analyzingpowers at two different energies. From Ref. l i .
n-d scattering are not reproduced by the same two and three-body potentials. This fact brings u p the issue of our understanding of the three-body force. It is clear t h a t it is i m p o r t a n t t o find more observables which are sensitive t o it and can serve as test ground for the construction of this force in the same way as NN scattering d a t a have been determining the two-body force.
4
Calculation of inclusive reactions and the role of N N N interaction
In this section it will be shown that total photonuclear cross sections are sensitive to the NNN interaction and can serve to study its properties. From what has been said in the previous section one could infer that such inclusive observables are tremendously difficult to calculate. In fact they require the knowledge of continuum states in all break up channels. It turns out, however, that this is not the case if one uses the LITM. The LITM can be listed among the most t\
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powerful methods to treat problems involving the knowledge of continuum states since it reduces the problem of calculating transition matrix elements to continuum states into bound state problems. It can be formulated and tested both for inclusive as well as for exclusive reactions. In Ref. 16 the inclusive version of the method has been used to calculate the total photodisintegration cross section of three body systems. The results are shown in Fig.6. One can notice the important role that NNN interaction plays in lowering the resonance peak towards experimental results. This effect is very promising in view of explaining the origin of the strong disagreement between theory and experiment in 4 H e ? . Even more interesting effects of the three body force are found in the higher energy tail of the cross section 16 . Unfortunately this energy range
9
is poorly known experimentally. We hope that these results will create some interest for modern experimental investigations of such observables having as principal aim the better knowledge of three body forces. Acknowledgment s An important part of the results shown here have been obtained in fruitful collaborations with N. Barnea, V.D. Efros, W. Leidemann and E.L. Tomusiak. References 1. J. Carlson and R. Schiavilla, Rev. Mod. Phys.70 ,743 (1998) and references therein. 2. V.I. Kukulin and V.M. Krasnapol'sky, /. Phys. G3, 795 (1977); K. Varga and Y. Suzuki, Phys. Rev. C 52, 2885 (1995). 3. R. B. Wiringaet al., Phys. Rev. C 62, 014001 (2000). 4. A. Nogga, H. Kamadaand W. Gloeckle, Phys. Rev. Lett. 85, 944 (2000) and references therein. 5. W. Sandhas et al.,iVttc/. Phys. A 631, 210c (1998) and references therein; A.C. Fonseca, Phys. Rev. Lett. 83, 4021 (1999). 6. F. Ciesielski and J. Carbonell, Phys. Rev. C 58, 58 (1998). 7. P. Navratil, G. P. Kamuntavicius, B. R. Barrett, Phys. Rev. C 61, 044001 (2000) and references therein; W. C. Haxton and C.-L. Song, Phys. Rev. Lett 84, 5454 (2000). 8. C. Bloch and J. Horowitz, Nucl. Phys.8, 91 (1958). 9. K. Suzuki and S.Y. Lee, Progr. Theor. Phys. 64,2091, (1980). 10. Yu.I Fenin and V. Efros, Sov. J. Nucl Phys. 15, 497 (1972); A. Kievsky, M. Viviani and S. Rosati,iVue/. Phys. A 577, 511 (1994). 11. N. Barnea, W. Leidemann and G. Orlandini, Phys. Rev. C 61, 054001 (2000). 12. P. Navratil, J. P. Vary and B. R. Barrett, Phys. Rev. Lett. 84, 5728 (2000). 13. H. Witalaet al. Phys. Rev. Lett. 81, 1183 (1998). 14. A. Kievsky, S. Rosati, M. Viviani, Phys. Rev. Lett. 82, 3759 (1999). 15. V.D Efros, W. Leidemann and G. Orlandini, Phys. Lett. B 338, 130 (1994). 16. V.D Efros et al., Phys. Lett. B 484, 223 (2000). 17. V.D Efros, W. Leidemann and G. Orlandini, Phys. Rev. Lett. 78, 4015 (1997).
INTERACTIONS, CURRENTS, A N D THE STRUCTURE OF FEW-NUCLEON SYSTEMS
R. S C H I A V I L L A Jefferson
Lab, Newport and Old Dominion University,
News, Norfolk,
VA
23606 VA
23529
Our current understanding of the structure of nuclei with A < 8, including energy spectra, electromagnetic form factors, and weak transitions, is reviewed within the context of a realistic approach t o nuclear dynamics based on two- and threenucleon interactions and associated electro-weak currents. Low-energy radiative and weak capture reactions of astrophysical relevance involving these light systems are also discussed.
1
Introduction
Few-nucleon systems provide a unique opportunity for testing the simple, traditional picture of the nucleus as a system of point-like nucleons interacting among themselves via effective many-body potentials, and with external electro-weak probes via effective many-body currents. Through advances in computational techniques and facilities, the last few years have witnessed dramatic progress in numerically exact studies of the structure and dynamics of systems with mass number A < 8, including energy spectra of low-lying states, momentum distributions and cluster amplitudes, elastic and inelastic electromagnetic form factors, /3-decays, radiative and weak capture reactions at low energies, inclusive response to hadronic and electro-weak probes at intermediate energies. In the present talk, I will review the "nuclear standard model" outlined above, and present the extent to which it is successful in predicting some of the nuclear properties alluded to earlier. Of course, given the limited time, some of the theoretical and experimental developments will be treated cursorily. Nevertheless, I still hope to be able to convey a broad view of the intriguing and important studies in few-nucleon physics today.
2
Potentials and Energy Spectra
The Hamiltonian in the nuclear standard model is written as
10
11
i
i<j
i<j 1 basis states. The web of energy terms drawn as a function of the interaction strength is the first qualitative manifestation of quantum chaos. Quantitatively, the spectral statistics very fast go to the limit of random matrix theory (RMT) with the Wigner spacing distribution and high spectral rigidity 1,2 . The structure of eigenfunctions continues to evolve even after that being much more sensitive to the strength of the residual interaction 3 ' 4 . The emerging complexity can be measured by the number N of significant basis components, or by information entropy
S? = -5>£ln
-5
5
NJ
Figure 2: Energy of the ground states for Jo = 0, left, and Jo = Jmax, right, vs statistical theory; dots correspond to simulations for different sets of random interaction parameters. The straight line on the left panel shows a constant shift.
unique and the dynamical mixing plays no role. The random character of the wave function for Jo = 0 is confirmed by the direct analysis of the distribution of its components in the seniority basis. The fully paired component of seniority zero is distributed according to the RMT predictions. We come to the conclusion that elements of the ordered spectra of finite Fermi-systems are in fact stipulated by the rotational invariance and the presence of many competing quasi-random paths of angular momentum coupling. The geometrical chaoticity should be included as an important ingredient in microscopic nuclear models of collective phenomena. In particular, it can serve as a criterion for the selection of the coherent contributions to large amplitude collective motion. Another interesting area is the study of quantum chaos in a rotationally invariant mesoscopic system. One can envisage new applications to nuclei, atoms, atomic aggregates and traps. Acknowledgments The author is indebted to B.A. Brown, P. Cejnar, M. Horoi, D. Mulhall, V. Sokolov and A. Volya for fruitful collaboration. The work was supported by the NSF grants 96-05207 and 0070911.
27
References 1. T.A. Brody et. ah, Rev. Mod. Phys. 53, 385 (1981). 2. T. Guhr, A. Miiller-Groeling and H.A. Weidenmuller, Phys. Rep. 299, 189 (1998). 3. V. Zelevinsky et ai., Phys. Rep. 276, 85 (1996). 4. V. Zelevinsky, Ann. Rev. Nucl. Part. Sci. 46, 237 (1996). 5. I.C. Percival, J. Phys. B6, L229 (1973). 6. V.G. Zelevinsky, Nucl. Phys. A555, 109 (1993). 7. O.P. Sushkov and V.V. Flambaum, Sov. Phys. Usp. 25, 1 (1982). 8. L. Van Hove, Physica 2 1 , 517 (1955); 23, 441 (1957); 25, 268 (1959). 9. M. Srednicki, Phys. Rev. E 50, 888 (1994). 10. M. Horoi, V. Zelevinsky and B.A. Brown, Phys. Rev. Lett. 74, 231 (1995). 11. V.V. Flambaum and F.M. Izrailev, Phys. Rev. E55, R13 (1997); 56, 5144 (1997). 12. B. Lauritzen et ai., Phys. Rev. Lett. 74, 5190 (1995). 13. N. Frazier, B.A. Brown and V. Zelevinsky, Phys. Rev. C54, 1665 (1996). 14. M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer, Berlin, 1993). 15. V.V. Sokolov, B.A. Brown, and V. Zelevinsky, Phys. Rev. E58, 56 (1998). 16. P. Cejnar, V. Zelevinsky and V. Sokolov, to be published. 17. M. Horoi and V. Zelevinsky, BAPS 44, No. 1, 397 (1999). 18. V. Zelevinsky, in Recent Progress in Many-Body Theories, Eds. D. Neilson and R.F. Bishop (World Scientific, Singapore, 1998) p. 225. 19. V.V. Flambaum, in Parity and Time Reversal Violation in Compound Nuclear States and Related Topics, eds. N. Auerbach and J.D. Bowman (World Scientific, Singapore, 1996) p. 41. 20. C.W. Johnson, G.F. Bertsch, and D.J. Dean, Phys. Rev. Lett. 80, 2749 (1998); C.W. Johnson et ai., Phys. Rev. C 6 1 , 014311 (2000). 21. M. Horoi et ai. BAPS 44 No. 5, 45 (1999). 22. D. Mulhall, A. Volya and V. Zelevinsky, to be published. 23. R. Bijker, A. Frank and S. Pittel, Phys. Rev. C 60, 021302 (1999).
THEORIES A N D A P P L I C A T I O N S B E Y O N D M E A N FIELD W I T H EFFECTIVE FORCES R.R. RODRIGUEZ-GUZMAN, J.L. EGIDO AND L.M. ROBLEDO Departamento de Fisica Tedrica C-XI, Universidad Autonoma de Madrid, 28049-Madrid, Spam. Techniques beyond the mean field are used to describe the properties of the lowlying states of the light nuclei 30
