Interacting Bosons in Nuclear Physics

191 Pages·1979·4.946 MB·English

by  F. Iachello (auth.), F. Iachello (eds.)

Interacting Bosons
in Nuclear Physics
ETTORE MAJORANA INTERNATIONAL SCIENCE SERIES
Series Editor:
Antonino Zichichi
European Physical Society
Geneva. Switzerland
(PHYSICAL SCIENCES)
Volume 1 INTERACTING BOSONS IN NUCLEAR PHYSICS
Edited by F. lachello
Interacting Bosons
in Nuclear Physics
EdIted bv
F. lachello
University of Groningen
Groningl!n, The Netherlands
and
Yale University
New Haven, Connecticut
PIerun Press · New 'tbrk and laldon
Library of Congress Cataloging in Publication Data
Symposium on Interacting Bosons in Nuclear Physics, 1st, Erice, Italy,
1978.
Interacting bosons in nuclear physics.
(Ettore Majorana international sciences series: Physical science; v. 1)
Includes index.
1. Bosons-Congresses. I. lache"o, F. ". Title. "I. Series
OC793.5.B628S96 1978 539.7'21 79·13600
ISBN 978-1-4684-3523-8 ISBN 978-1-4684-3521-4 (eBook)
DOl 10.1007/978-1-4684-3521-4
Proceedings of the First Symposium on Interacting Bosons in Nuclear Physics,
held in Erice, Sicily, June 6-9,1978
© 1979 Plenum Press, New York
Softcover reprint of the hardcover 18t edition 1979
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
A" rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
PREFACE
During the week of June 6-9, 1978, a group of 36 physicists
from 15 countries met in Erice, Sicily, for the first specialized
seminar on "Interacting Bosons in Nuclear Physics". The countries
represented were Argentina, Belgium, Denmark, Finland, France, the
Federal Republic of Germany, Israel, Italy, Japan, the Netherlands,
Poland, Sweden, the United Kingdom, the United States of America
and Yugoslavia. The Seminar was sponsored by the Italian Ministry
of Public Education (MPI), the Italian Ministry of Scientific and
Technological Research (MRST), the North Atlantic Treaty Organiza
tion (NATO) and the Regional Sicilian Government (ERS).
The purpose of the Seminar was to discuss the present status of
the Interacting Boson Model both from the theoretical and experi
mental point of view. Some of the lectures presented in this book
summarize particular aspects of the model and are based on previously
published work (F. Iachello, R. F. Casten, Z. Sujkowski, L. Hassel
gren, H. Emling, I. Talmi, T. Otsuka, J. McGrory, A.E.L. Dieperink
and A. Arima). Others are entirely new. In particular, the lec
tures of O. Scholten and A. Gelberg and V. Kaup present the first
extensive set of calculations based on the proton-neutron boson
model, while the lecture of J.N.Ginocchio describes a fermion model
with properties identical to those of the interacting boson model.
Also new are the le~tures of D. R. Bes, R. A. Broglia and P. F.
Bortignon describing the relation of the interacting boson model
with Nuclear Field,Theory, and of J. Mayer-ter-Vehn describing the
relation of the 0(6) limit of the interacting boson model with the
y-unstable model of Wilets and Jean. Finally, the paper of V. Paar
takes a critical look at the relation between the interacting boson
model and the model of Janssen, Jolos and Donau, while the paper of H.
Feshbach makes some general remarks on the difference between the
interacting boson model and interacting boson approximation.
Since the time of the Meeting in Erice, many new developments
have occurred on the subject, among others those related to collec
tive states in odd-A nuclei. These developments are not included in
this book and hopefully will form the subject of a second Special
ized Seminar.
v
vi PREFACE
I wish to thank all the participants and contributors who made
the Seminar a very enjoyable one. I also wish to thank Professor
A. Zichichi, Director of the Center for Scientific Culture "Ettore
Majorana" who made it possible that this Seminar could take place in
Erice, and Professor G. Preparata, Director of the Seminars, for
his help and collaboration. A final thank you to all those who
in Erice, Groningen and Yale have helped me on many occasions.
Without them, the preparation of this book would not have been
possible.
F. Iachello
February 1979
New Haven, Conn.
TABLE OF CONTENTS
1. INTRODUCTION
l.a. Present Status of the Interacting Boson Model. . •. 1
F. Iachello
2. PHENOMENOLOGY AND SYMMETRIES OF THE INTERACTING BOSON MODEL
2.a. A Phenomenological Study of Even-Even Nuclei
in the Neutron-Proton IBA • • • • • 17
o. Scholten
2.b. The IBA in the Os-Pt Region. • • • • • • • • • • •• 37
R. F. Casten
2.c. Transitional Region and the Interacting
A~150
Boson Model • • • • • • • • • • • • • 55
z.
Sujkowski
2.d. Collective States in Some Transitional Nuclei
with 28~Z, N~50 • • • . • • . • • • 59
A. Gelberg and V. Kaup
2.e. Systematics of Experimental Properties of Low-Lying
States in Even Ru and Pd Nuclei • • • • •• 67
L. Hasselgren
2.f. B(E2)-Values of High Spin States in lS8Dy• 75
H. Emling
3. MICROSCOPIC THEORY OF THE INTERACTING BOSON MODEL
3.a. Shell Model Description of Interacting Bosons. 79
1. Talmi
vii
viii CONTENTS
3.b. Nuclear Shell Model and Interacting Bosons • • • •• 93
T. Otsuka
3.c. Fermion Hamiltonians with Monopole and
Quadrupole Pairing. • • • III
J. N. Ginocchio
3.d. Shell Model Tests of the Interacting Boson Model
Description of Nuclear Collective
Motion • • • • • • • • • • • • • • • • 121
J. B. McGrory
4. APPLICATIONS TO REACTIONS
4.a. Electron Scattering in the Interacting
Boson Model • •••••• 129
A. E. L. Dieperink
5. RELATION TO OTHER MODELS
S.a. Nuclear Field Theory Treatment of the
Interacting Boson Model 143
D. R. Bes and R. A. Broglia
S.b. On the Interaction of Many-Phonon Monopole
Pairing Vibrations •••••• 151
P. F. Bortignon and R. A. Broglia
S.c. On the Relation Between the 0(6) Limit of the
Interacting Boson Model and Triaxial
Nuclear Models. • • • • • • • • • • • 157
J. Meyer-ter-Vehn
S.d. IBM Versus Quadrupole Phonons. • • • • • • • • • • • 163
V. Paar
6. CONCLUSIONS
6.a. General Remarks Regarding the Interacting
Boson Model and Approximation • • 173
H. Feshbach
6.b. Concluding Remarks. • • • • • • • • • • • • • • •• 179
A. Arima
CONTENTS ix
Participants 185
Index. 189
PRESENT STATUS OF THE INTERACTING BOSON MODEL
F. Iachello
Kernfysisch Vernsneller Instituut
University of Groningen, Groningen, The Netherlands
1. INTRODUCTION
The purpose of this meeting is to yiscuss the scope and lim
itations of the interacting boson model which has been intro
duced recently in order to describe collective low-lying states
in medium and heavy-mass nuclei. In my talk, I will summarize
the present status of the model referring to the following talks
for more detailed and complete expositions. It seems appropri
ate to divide the talk in two parts in the first part, I will
discuss the interacting boson model, as a tool to classify and
describe collective states in nuclei; in the second part, I will
discuss the interacting boson approximation in which one tries
to derive the model as an approximation scheme to the shell model,
thus providing a microscopic description of the collective states.
While at present the first part may be, to a good extent, con
sidered concluded, in the sense that all possible solutions have
been investigated, the second part is still in its infant stage,.
and it may require several years before a fully microscopic
theory will be preserved.
2. THE MODEL
I begin with a short summary of the model. In its simplest
form, we assume that an even-even nucleus consists of an inert
core plus some valence particles. Furthermore, we assume that
the valence particles, which are those outside the major closed
shells at 50, 82, 126°, tend to pair together in states with
angular momentum L = and 2, and we °t reat these pairs as bosons.
The pairs with angular momentum L = are called s-bosons, those