Advances in Nuclear Physics: Volume 1

427 Pages·1968·12.516 MB·English

by  Jorrit de Boer, Jörg Eichler (auth.), Michel Baranger, Erich Vogt (eds.)

ADVANCES IN
NUCLEAR PHYSICS
VOLUME 1
Contributors to this Volume
Jorrit de Boer Malcolm Harvey
Department of Physics Theoretical Physics
Rutgers, The State University Chalk River Nuclear Laboratories
New Brunswick, New Jersey Chalk River, Ontario, Canada
Ian Duck Georges Ripka
Department of Physics Service de Physique Theorique
Rice University Centre d'Etudes Nucleaires de Sa clay
Houston, Texas France
Jorg Eichler Erich Vogt
Hahn-Meitner Institut fOr Department of Physics
Kernforschung University of British Columbia
c.,
Berlin, Germany Vancouver, B. Canada
ADVANCES IN
NUCLEAR PHYSICS
Edited by
Michel Baranger
Department of Physics
Carnegie Institute of Technology
Pittsburgh, Pennsylvania
Erich Vogt
Department of Physics
University of British Columbia
Vancouver, B.C., Canada
VOLUME 1
~
PLENUM PRESS • NEW YORK • 1968
ISBN 978-1-4757-0105-0 ISBN 978-1-4757-0103-6 (eBook)
DOI 10.1007/978-1-4757-0103-6
Library of Congress Catalog Card Number 67-29001
© 1968 Plenum Press
Softcover reprint of the hardcover 1s t edition 1968
A Division of Plenum Publishing Corporation
227 West 17 Street, New York, N. Y. 10011
All rights reserved
No part of this publication may be reproduced in any form without
written permission from the publisher
ARTICLES PLANNED FOR
FUTURE VOLUMES
Nuclear Reactions with Polarized Beams
C. Glashausser and 1. Thirion
The Two-Nucleon Potential
P. S. Signell
The Giant Dipole Resonance
B. M. Spicer
The Pairing-Plus-Quadrupole Model
D. R. Bes and R. A. Sorensen
Muonic X-Rays
S. Devons and I. Duerdoth
The Interaction of Pions with Nuclei
D. S. Koltun
In-Beam Spectroscopy with Heavy Ions
R. M. Diamond and F. S. Stephens
Shell Model Calculations with Realistic Nuclear Forces
E. C. Halbert and T. T. S. Kuo
The i-Dependence of Stripping Reactions
C. Mayer-Boricke
Nuclear Physics with Li-Drifted Detectors
G. T. Ewan and A. E. Litherland
PREFACE
The aim of Advances in Nuclear Physics is to provide review papers which
chart the field of nuclear physics with some regularity and completeness.
We define the field of nuclear physics as that which deals with the structure
and behavior of atomic nuclei. Although many good books and reviews on
nuclear physics are available, none attempts to provide a coverage which is
at the same time continuing and reasonably complete. Many people have
felt the need for a new series to fill this gap and this is the ambition of
Advances in Nuclear Physics. The articles will be aimed at a wide audience,
from research students to active research workers. The selection of topics and
their treatment will be varied but the basic viewpoint will be pedagogical.
In the past two decades the field of nuclear physics has achieved its own
identity, occupying a central position between elementary particle physics
on one side and atomic and solid state physics on the other. Nuclear physics
is remarkable both by its unity, which it derives from its concise boundaries,
and by its amazing diversity, which stems from the multiplicity of
experimental approaches and from the complexity of the nucleon-nucleon
force. Physicists specializing in one aspect of this strongly unified, yet very
complex, field find it imperative to stay well-informed of the other aspects.
This provides a strong motivation for a comprehensive series of reviews.
Additional motivation arises from outside the community of nuclear physi
cists, through the inevitable occurrence of the nucleus as an accessory or as
a tool in other fields of physics, and through its importance for terrestrial
and stellar energy sources.
We hope to provide a varied selection of reviews in nuclear physics with a
varied approach. The topics chosen will range over the field, the emphasis
being on physics rather than on theoretical or experimental techniques.
Some effort will be made to include regularly topics of great current interest
which need to be made accessible by adequate reviews. Other reviews will
attempt to bring older topics into clearer focus. The aim will be to attract
the interest of both the active research worker and the research student.
Authors will be asked to direct their article toward the maximum number of
readers by separating clearly the technical material from the more basic
vii
viii Preface
aspects of the subject and by adopting a pedagogical point of view rather
than giving a simple recital of recent results.
Initially, the Advances are scheduled to appear about once a year with
approximately six articles per volume. To ensure rapid publication of the
papers, we shall use the "stream" technique, successfully employed for series
in other fields. A considerable number of planned future articles constitute
the source of the stream. The flow of articles from the source takes place
primarily to suit the convenience of the authors, rather than to include any
particular subset of articles in a given volume. Any attempt at a systematic
classification of the reviews would result in considerable publication delays.
Instead, each volume is published as soon as an appropriate number of
articles have been completed; but some effort is made to achieve simultaneity,
so that the spread in completion dates of the articles in a given volume is
much less than the interval between volumes.
A list of articles planned for future volumes is given on page v. The
prospective articles together with those in this first volume still fall far short
of our long-range aims for coverage of the field of nuclear physics. In partic
ular, we definitely intend to present more articles on experimental topics.
We shall eagerly receive and discuss outside suggestions of topics for
additional papers, and especially suggestions of suitable authors to write
them.
The editors owe a great deal to the authors of the present volume for their
cooperation in its rapid completion, and to many colleagues who have already
given advice about the series. In embarking on this venture, we have had the
support of Plenum Press, a relatively new publisher in the field of physics,
and of its vice-president, Alan Liss, who has an almost unmatched back
ground in physics publications.
M. BARANGER
E. VOGT
October 15, 1967
CONTENTS
Chapter 1
THE REORIENTATION EFFECT
Jorrit de Boer and Jorg Eichler
1. Introduction . . . . . . . . 1
2. Classical Estimates of Effects . 3
2.1 External Field Gradients . 4
2.2 Electronic Field Gradient 4
2.3 Muonic X Rays 4
2.4 Coulomb Excitation. . . 5
3. Theory of Coulomb Excitation 5
3.1 Approximations. . . . . 6
3.2 First-Order Perturbation Theory 6
3.3 Second-Order Perturbation Theory as a Guide to the Exact
Solution . . . . . . . . . . . . . . . 9
3.4 Symmetrization of the Excitation Process 13
4. Theory of the Reorientation Effect. . . . . . 14
4.1 The Amplitude for the Excitation 0+ 2-t- 14
-40
4.2 The Excitation Probability . . . . . . . 15
4.3 The Angular Distribution of the De-excitation Gamma
Rays. . . . . . . . . . . . . . . . 16
4.4 Magnetic Dipole Reorientation . . . . 19
4.5 Corrections for Multiple £2 Transitions 20
5. Excitation via the Giant Dipole Resonance 21
5.1 The Transition Probability . . . . 22
5.2 Interpretation as Polarization Effect 24
6. Experimental Methods . . . . . . 28
6.1 Bombarding Conditions . . . . . 28
6.2 Measurement of Cross Sections . . 32
6.3 Measurement of the Gamma-Ray Angular Distribution 39
6.4 Measurement of the Excitation of the Projectile. . .. 43
ix
x Contents
7. Reorientation Experiments . . . 44
7.1 Experimental Methods Used 44
7.2 Results. . 46
7.3 Discussion 48
Acknowledgments. 49
Appendix I. Numerical Expressions. 49
Appendix II. Tables of Orbital Integrals 51
Appendix III. Approximate Formula for the Reorientation Effect. 51
References 64
Chapter 2
THE NUCLEAR SU MODEL
J
Malcolm Harvey
1. Introduction . . . 67
2. Basic Shell Model . 69
2.1 General Theory . 69
2.2 Invariance Properties 73
2.3 Approximate- and Broken-Symmetry Groups . 76
2.4 Rotational Features in the Ip Shell . . . . . 77
3. Symmetry of Oscillator Quanta - The Groups Ua and SUa 79
3.1 Problems ............. 79
3.2 Formal Properties of Ua and SUa . . . . . . . . . 79
3.3 Classification According to Ua and SUa . . . . . . 83
3.4 Simultaneous Classification According to SA and SUa 85
3.5 Classification According to SUa and Ra. . . . . . . 89
3.6 Classification According to SUa and SU2 X Ul • • • 90
3.7 Construction of States Classified According to SUa and Ra 94
4. The Effective Interaction . . . . . . . 99
4.1 General Principles. . . . . . . . 99
4.2 The Quadrupole-Quadrupole Force 100
4.3 The Casimir Operator of SUa. . . 103
5. Application of the SUa-Coupling Scheme to Light Nuclei 105
5.1 General Remarks . . . . . . . . . . . . . . 105
5.2 Accuracy of the SUa Classification Scheme in the
(2s, 1d ) Shell . . . . . . . . . . . . . . . . 106
5.3 Positive-Parity States of Doubly Even Nuclei in the
(2s, Id) Shell . . . . . . . . . . . . . . . . . 109
Contents xi
5.4 Positive-Parity States of Odd A and Doubly Odd Nuclei in
the (2s, Id) Shell . . . . . . . . . . . . 123
5.5 Negative-Parity States in the (2s, Id) Shell . 128
5.6 Multi-Excitation States in the (2s, Id) Shell. 139
5.7 Multi-Excitation States in the Ip Shell 142
6. Summary and Developments 142
Acknowledgments . . . . . . . 148
References 148
Appendix A. Harmonic Oscillator 152
Appendix B. Use of Groups in Quantum Mechanics 154
Appendix C. The Symmetric and Unitary Groups . 157
Appendix D. Generating Operators of Us 162
Appendix E. Classification According to SUa without the
Harmonic Oscillator . . . . . . . . . . 165
Appendix F. Raising and Lowering Operators of the Group SUa. 166
Appendix G. Calculation of Matrix Elements . . . . . . 170
Appendix H. The Normalization Coefficients and Overlaps 177
Appendix I. Use of the Group SUa in the Classification of
Elementary Particles . . . . . . . . . . . 180
Chapter 3
THE HARTREE-FOCK THEORY OF
DEFORMED LIGHT NUCLEI
Georges Ripka
1. Introduction . . . . . . . . . . . . 183
2. The Hartree-Fock Equations ..... 187
3. Symmetries of the Hartree-Fock Hamiltonian. 189
3.1 Time-Reversal Symmetry 190
3.2 Parity and Axial Symmetry . 191
3.3 Isospin Invariance 191
3.4 Spherical Symmetry . . . . 191
3.5 Spin and Isospin Invariance . 192
4. The Choice of an Expansion for the Orbits 192
4.1 Spherical Symmetry 194
4.2 Axial Symmetry ........ . 194