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Nuclear Structure NATO ADVANCED STUDY INSTITUTES SERIES A series of edited volumes comprising multifaceted studies of contem porary scientific issues by some of the best scientific minds in the world, assembled in cooperation with NATO Scientific Affairs Division. Series B. Physics Recent Volumes in this Series Volume 62 - Radiationless Processes edited by Baldassare Di Bartolo Volume 63 - Characterization of Crystal Growth Defects by X-Ray Methods edited by Brian K. Tanner and D. Keith Bowen Volume 64 - Molecular Electro-optics: Electro-Optic Properties of Macromolecules and Colloids in Solution edited by Sonja Krause Volume 65 - Nonequilibrium Superconductivity, Phonons, and Kapitza Boundaries edited by Kenneth E. Gray Volume 66 - Techniques and Concepts of High-Energy Physics edited by Thomas Ferbel Volume 67- Nuclear Structure edited by K. Abrahams, K. Allaart, and A. E. L. Dieperink Volume 68 - Superconductor Materials Science: Metallurgy, Fabrication, and Applications edited by Simon Foner and Brian B. Schwartz Volume 69 - Photovoltaic and Photoelectrochemical Solar Energy Conversion edited by F. Cardon, W. P. Gomes, and W. Dekeyser Volume 70 - Current Topics in Elementary Particle Physics edited by K. H. Mutter and K. Schilling Volume 71 - Atomic and Molecular Collis~on Theory edited by Franco A. Gianturco This series is published by an international board of publishers in con junction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht, Boston, and London D Behavioral and Sijthoff & Noordhoff International Social Sciences Publishers E Applied Sciences Alphen aan den-Rijn, The Netherlands, and Germantown, U.S.A. Nuclear Structure Edited by K. Abrahams Netherlands Energy Research Foundation Petten. The Netherlands K. Allaart Free University Amsterdam, The Netherlands and A. E. L. Dieperink Nuclear Accelerator Institute Groningen, The Netherlands PLENUM PRESS. NEW YORK AND LONDON Published in cooperation with NATO Scientific Affairs Division Library of Congress Cataloging in Publication Data Netherlands Physical Society International Summer School on Nuclear Structure (1980: Dronten, The Netherlands) Nuclear structure. (NATO advanced study institutes series. Series B, Physics; v. 67) "Proceedings of the Netherlands Physical Society 1980 International Summer School on Nuclear Structure, held August 12-23, 1980, in Dronten, The Netherlands" - T.p. verso. Includes bibliographical references and index. Contents: Application of the shell model to nuclear spectroscopy/J. B. McGrory - Effective interactions/J. P. Elliott - An introduction to the interacting Boson model/ F. Iachello - [etc.) 1. Nuclear structure - Congresses. I. Abrahams, K. II. Allaart, K. III. Dieperink, A. E. L. IV. Nederlandse Natuurkundige Vereniging. V. Title. VI. Series. QC793.3.S8N47 1980 539.7'4 81-7291 AACR2 ISBN 978-1-4684-3952-6 ISBN 978-1-4684-3950-2 (eBook) DOI 10.1007/978-1-4684-3950-2 Proceedings of the Netherlands Physical Society 1980 International Summer School on Nuclear Structure, held August 12-23, 1980, in Dronten, The Netherlands © 1981 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1981 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All 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 FOREWORD After the success of the previous summer schools organized by the Nuclear Physics Division of the Netherlands' Physical Society in 1975 and 1977, we thought it worthwhile to continue this tradition. The immediate very positive reactions received from all invited speakers encouraged us to proceed with the orgaization. Although the number of students had to be restricted to about one hundred, the international character of the School was evident from about thirty nationalities which were represented. The material contained in this book covers the talks given by all speakers invited to lecture on the subject of nuclear structure research. These proceedings should therefore serve as an excellent introduction to many topics of current interest in this exciting field. We hope that the lectures and discussions as well as the many informal contacts made during the various social activities will greatly stimulate interest in nuclear structure investigations among all the participants. The organization of the summer school has been made possible by substantial support given by the Scientific Affairs Division of the North Atlantic Treaty Organization, the Netherlands' Ministry of Education and Science and the Netherlands' Physical Society. The invaluable help of the "Bureau Congressen" of the Ministry of Education and Science and the friendly assistance of the manage ment of the College of Agriculture in Dronten contributed greatly to the pleasant atmosphere during the summer school. P. W. M. Glaudemans PREFACE This book presents a review of nuclear structure research as presented during the international summer school, Dronten, the Netherlands, 12-23 August 1980. It includes not only intoductions to the shell model, to effective interactions, and to the interact ing boson model, but also a detailed treatmerit of the interactions of nuclei with electrons, muons, protons, pions and heavy ions. In addition applications are discussed in the field of exotic nuclei, fission. astrophysics and proton induced x-rays. To speed the publication, the corrected and sometimes revised manuscripts are published without consulting all authors and is the responsibility of the editors. The assistance of the secretaries of the Physics Department of the Netherlands Energy Research Foundation is gratefully ack nowledged. K. Abrahams K. Allaart A.E.L. Dieperink CONTENTS Application of the Shell Model to Nuclear Spectroscopy • • • • • • • • • • • • 1 J.B. McGrory Effective Interactions 33 J .P. Elliott An Introduction to the Interacting Boson Model. • • • • • . 53 F. Iachello Pion-Nuclear Many Body Problems. • • • • . • • • • • • . .• 91 W. Weise Nuclear Structure and Heavy-Ion Reactions 127 J.P. Schiffer Giant Resonances 165 A. van der Woude Multiple Coulomb Excitation of High Spin States. •••••••••.•• 207 D. Schwalm Inelastic Electron Scattering at Low Momentum Transfer and Nuclear Structure 241 A. Richter . . . . . . . . . . . ... . . . . . . . . . Exotic Nuclei. , 289 P.G. Hansen Low Energy Nuclear Fission • . • • • • • • • . . • • • • .• 309 H. Nifenecker Muon Induced Fission 355 S. Polikanov ix x CONTENTS Few Problems in Experimental Nuclear Astrophysics . . . . . . . . . 369 C. Rolfs Tritium as a Stratospheric Tracer 393 G. Hut Proton Induced X-Rays. . . . . . . . . . . . . . . . . . . . 407 R.D. Vis Participants 419 Index. . . . 429 APPLICATION OF THE SHELL MODEL TO NUCLEAR SPECTROSCOPY J. B. McGrory Oak Ridge National Laboratory* Oak Ridge, Tennessee 37830 INTRODUCTION The intent in these lectures is to present a cursory overview of existing nuclear shell model technology, to give an indication of how well nuclear phenomena can be described by the nuclear shell model, and what are possible future directions of the field. The nuclear shell model has been with us for a long time, and it is a widely used model. It is also very popular in many circles to de ride the model for its lack of elegance and sophistication. Thus, I believe it is appropriate to spend a minute at the beginning of these lectures to recall some of the reasons for our interest in the nucleus. The combination of features that make the nucleus unique are: 1) the microscopic dimensions of the nucleus are such that one must use quantum mechanics; 2) at the level we study, it is a many body system with 1 - 300 particles; and 3) of the four "fundamental" interactions (weak, strong, electromagnetic, and gravitational), only the gravitational force is generally ignorable. Beta-decay, particle transfer reactions, and electromagnetic transitions are direct manifestations of the first three of these forces, re spectively. The nucleus is the only known quantum-mechanical many body system where one can conceive of treating the constituent coordinates microscopically. There now exist volumes of nuclear data on a vast array of nuclear observables. Taken as a body, these data can be interpreted to sugges.t that the nucleus * Research sponsored by the Division of Basic Energy Sciences, U. S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corporation. 2 J. B. McGRORY sometimes behaves collectively, i.e. it rotates or vibrates, and sometimes exhibits properties of a system of independent particles. A longstanding goal of nuclear physics is to formulate one model which can give a consistent picture of all nuclear observables, and which is derivable from more-or-Iess well-known properties of the constituent protons and neutrons and. of their mutual interactions. The starting point of virtually all such models is the nuclear shell model. The model is conceptually very simple, but very tedious to implement. The model became generally accepted roughly 30 years ago, but only in the last decade or so has shell model technology evolved to the point that truly systematic studies of nuclear structure could be undertaken. Perhaps fortuitously at the same time that shell model technology evolved to a really useful level, the theory of effective interactions made considerable progress. One can, with some degree of confidence, construct the input to shell model calculations from well-known properties of interactions between free nucleons. These two 'developments mean that one can really investigate the question how do observed properties of nuclei develop from the known properties of nucleon-nucleon interactions. I will not include in this written version of the lectures the material on shell model methods, on existing shell model codes, and on the extensive calculations of nuclear properties in the sd shell. These topics are already adequately covered in existing publica tibns. 1,2 The points from those sections to note particularly here are that one can treat the entire sd shell with an (sd)A-16 model with no truncation, that a large body of nuclear data on these nuclei can be correlated with the nuclear shell model, and that shell model dimensions escalate so rapidly with increasing numbers of shell model orbits that there is/scant hope that any other major shell can be treated as completely as the sd shell. Thus, in these printed notes I will discuss some truncation methods which might be useful to ex tend the domain of applicability of the shell model. APPROXIMATIONS TO LARGE-SPACE SHELL MODEL CALCULATIONS There is now a clear case of the usefulness of the shell model where it is applicable. There are also relatively few areas of the periodic chart where the model can be applied in any completeness. The question then is: are there systematic ways to truncate the shell model spaces to viable sizes? I would now like to discuss some of the possible ways to truncate the shell model. This is a curious field in which many have nibbled, but few have moved much past the appetizer. There are many unpublished studies I have heard of but relatively few detailed studies published. A first approach would be to truncate the shell model matrix as calculated in the complete space. A first method is to calculate all diagonal elements and choose to use only the states whose
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