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Problems and Solutions on Atomic, Nuclear and Particle Physics This Page Intentionally Left Blank Major American Universities Ph.D. Qualifying Questions and Solutions Problems and Solutions on Atomic, Nuclear and Particle Physics Compiled by The Physics Coaching Class University of Science and Technology of China Edited by Yung-Kuo Lim National University of Singapore World Scientific Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P 0 Box 128, Farrer Road, Singapore 912805 USA office: Suite lB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the BritishLibrary. Major American Universities Ph.D. Qualifying Questions and Solutions PROBLEMS AND SOLUTIONS ON ATOMIC, NUCLEAR AND PARTICLE PHYSICS Copyright © 2000 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. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-02-3917-3 981-02-3918-l (pbk) This book is printed on acid-free paper. Printed in Singapore by Uto-Print PREFACE This series of physics problems and solutions, which consists of seven volumes — Mechanics, Electromagnetism, Optics, Atomic, Nuclear and Particle Physics, Thermodynamics and Statistical Physics, Quantum Me- chanics, Solid State Physics and Relativity, contains a selection of 2550 problems from the graduate-school entrance and qualifying examination papers of seven U.S. universities — California University Berkeley Cam- pus, Columbia University, Chicago University, Massachusetts Institute of Technology, New York State University Buffalo Campus, Princeton Uni- versity, Wisconsin University — as well as the CUSPEA and C.C. Ting’s papers for selection of Chinese students for further studies in U.S.A., and theirsolutionswhichrepresenttheeffortofmorethan70Chinesephysicists, plus some 20 more who checked the solutions. The series is remarkable for its comprehensive coverage. In each area theproblemsspanawidespectrumoftopics,whilemanyproblemsoverlap several areas. The problems themselves are remarkable for their versatil- ity in applying the physical laws and principles, their uptodate realistic situations, and their scanty demand on mathematical skills. Many of the problems involve order-of-magnitude calculations which one often requires inanexperimentalsituationforestimatingaquantityfromasimplemodel. Inshort,theexercisesblendtogethertheobjectivesofenhancementofone’s understanding of physical principles and ability of practical application. The solutions as presented generally just provide a guidance to solving the problems, rather than step-by-step manipulation, and leave much to thestudentstoworkoutforthemselves,ofwhommuchisdemandedofthe basic knowledge in physics. Thus the series would provide an invaluable complement to the textbooks. The present volume consists of 483 problems. It covers practically the whole of the usual undergraduate syllabus in atomic, nuclear and particle physics, but in substance and sophistication goes much beyond. Some problems on experimental methodology have also been included. Inediting, noattempthasbeenmadetounifythephysicalterms,units and symbols. Rather, they are left to the setters’ and solvers’ own prefer- ence so as to reflect the realistic situation of the usage today. Great pains has been taken to trace the logical steps from the first principles to the finalsolution,frequentlyeventotheextentofrewritingtheentiresolution. v vi Preface Inaddition, a subjectindexto problemshas beenincluded to facilitatethe location of topics. These editorial efforts hopefully will enhance the value of the volume to the students and teachers alike. Yung-Kuo Lim Editor INTRODUCTION Solving problems in course work is an exercise of the mental facilities, and examination problems are usually chosen, or set similar to such problems. Working out problems is thus an essential and important aspect of the study of physics. The series Major American University Ph.D. Qualifying Questions and Solutions comprises seven volumes and is the result of months of work of a number of Chinese physicists. The subjects of the volumes and the respective coordinators are as follows: 1. Mechanics (Qiang Yan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua, Yang De-tian) 2. Electromagnetism (Zhao Shu-ping, You Jun-han, Zhu Jun-jie) 3. Optics (Bai Gui-ru, Guo Guang-can) 4. Atomic, Nuclear and Particle Physics (Jin Huai-cheng, Yang Bao- zhong, Fan Yang-mei) 5. Thermodynamics and Statistical Physics (Zheng Jiu-ren) 6. Quantum Mechanics (Zhang Yong-de, Zhu Dong-pei, Fan Hong-yi) 7. Solid State Physics and Miscellaneous Topics (Zhang Jia-lu, Zhou You-yuan, Zhang Shi-ling). These volumes, which cover almost all aspects of university physics, contain 2550 problems, mostly solved in detail. The problems have been carefully chosen from a total of 3100 problems, collected from the China-U.S.A. Physics Examination and Applica- tion Program, the Ph.D. Qualifying Examination on Experimental High EnergyPhysics sponsoredby Chao-ChongTing, and the graduatequalify- ingexaminationsofsevenworld-renownedAmericanuniversities: Columbia University, the University of California at Berkeley, Massachusetts Insti- tute ofTechnology,theUniversityofWisconsin,theUniversityofChicago, Princeton University, and the State University of New York at Buffalo. Generally speaking, examination problems in physics in American universities do not require too much mathematics. They can be character- ized to a large extent as follows. Many problems are concerned with the various frontier subjects and overlapping domains of topics, having been selected from the setters own research encounters. These problems show a “modern” flavor. Some problems involve a wide field and require a sharp mind for their analysis, while others require simple and practical methods vii viii Introduction demanding a fine “touch of physics”. Indeed, we believe that these problems, as a whole, reflect to some extent the characteristics of American science and culture, as well as give a glimpse of the philosophy underlying American education. That being so, we considered it worthwhile to collect and solve these problems, and introduce them to students and teachers everywhere, even thoughtheworkwasbothtediousandstrenuous. Aboutahundredteachers and graduate students took part in this time-consuming task. This volume on Atomic, Nuclear and Particle Physics which contains 483 problems is divided into four parts: Atomic and Molecular Physics (142),Nuclear Physics(120),ParticlePhysics(90), ExperimentalMethods and Miscellaneous topics (131). In scope and depth, most of the problems conform to the usual undergraduate syllabi for atomic, nuclear and particle physics in most universities. Some of them, however, are rather profound, sophisticated, and broad-based. In particular they demonstrate the use of fundamental principles in the latest researchactivities. It is hoped that the problems would helpthereadernotonlyinenhancingunderstandingofthebasicprinciples, but also in cultivating the ability to solve practical problems in a realistic environment. This volume was the result of the collective efforts of forty physicists involved in working out and checking of the solutions, notably Ren Yong, Qian Jian-ming, Chen Tao, Cui Ning-zhuo, Mo Hai-ding, Gong Zhu-fang and Yang Bao-zhong. CONTENTS Preface v Introduction vii Part I. Atomic and Molecular Physics 1 1. Atomic Physics (1001–1122) 3 2. Molecular Physics (1123–1142) 173 Part II. Nuclear Physics 205 1. Basic Nuclear Properties (2001–2023) 207 2. Nuclear Binding Energy, Fission and Fusion (2024–2047) 239 3. The Deuteron and Nuclear forces (2048–2058) 269 4. Nuclear Models (2059–2075) 289 5. Nuclear Decays (2076–2107) 323 6. Nuclear Reactions (2108–2120) 382 Part III. Particle Physics 401 1. Interactions and Symmetries (3001–3037) 403 2. Weak and ElectroweakInteractions, Grand Unification Theories (3038–3071) 459 3. Structure of Hadrons and the Quark Model (3072–3090) 524 Part IV. Experimental Methods and Miscellaneous Topics 565 1. Kinematics of High-Energy Particles (4001–4061) 567 2. Interactions between Radiation and Matter (4062–4085) 646 3. Detection Techniques and Experimental Methods (4086–4105) 664 4. Error Estimation and Statistics (4106–4118) 678 5. Particle Beams and Accelerators (4119–4131) 690 Index to Problems 709 ix