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 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 British Library 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., 222 Rosewood 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 Mechanics, 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 Campus, Columbia University, Chicago University, Massachusetts Institute of Technology, New York State University Buffalo Campus, Princeton University, 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 their solutions which represent the effort of more than 70 Chinese physicists, plus some 20 more who checked the solutions The series is remarkable for its comprehensive coverage In each area the problems span a wide spectrum of topics, while many problems overlap several areas The problems themselves are remarkable for their versatility 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 in an experimental situation for estimating a quantity from a simple model In short, the exercises blend together the objectives of enhancement of one’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 the students to work out for themselves, of whom much is demanded of the 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 In editing, no attempt has been made to unify the physical terms, units and symbols Rather, they are left to the setters’ and solvers’ own preference 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 final solution, frequently even to the extent of rewriting the entire solution v vi Preface In addition, a subject index to problems has been included to facilitate the 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: Mechanics (Qiang Yan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua, Yang De-tian) Electromagnetism (Zhao Shu-ping, You Jun-han, Zhu Jun-jie) Optics (Bai Gui-ru, Guo Guang-can) Atomic, Nuclear and Particle Physics (Jin Huai-cheng, Yang Baozhong, Fan Yang-mei) Thermodynamics and Statistical Physics (Zheng Jiu-ren) Quantum Mechanics (Zhang Yong-de, Zhu Dong-pei, Fan Hong-yi) 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 Application Program, the Ph.D Qualifying Examination on Experimental High Energy Physics sponsored by Chao-Chong Ting, and the graduate qualifying examinations of seven world-renowned American universities: Columbia University, the University of California at Berkeley, Massachusetts Institute of Technology, the University of Wisconsin, the University of Chicago, Princeton University, and the State University of New York at Buffalo Generally speaking, examination problems in physics in American universities not require too much mathematics They can be characterized 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 though the work was both tedious and strenuous About a hundred teachers 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), Particle Physics (90), Experimental Methods 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 research activities It is hoped that the problems would help the reader not only in enhancing understanding of the basic principles, 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 Atomic Physics (1001–1122) Molecular Physics (1123–1142) 173 Part II Nuclear Physics 205 207 239 269 289 323 382 Basic Nuclear Properties (2001–2023) Nuclear Binding Energy, Fission and Fusion (2024–2047) The Deuteron and Nuclear forces (2048–2058) Nuclear Models (2059–2075) Nuclear Decays (2076–2107) Nuclear Reactions (2108–2120) Part III Particle Physics 401 Interactions and Symmetries (3001–3037) Weak and Electroweak Interactions, Grand Unification Theories (3038–3071) Structure of Hadrons and the Quark Model (3072–3090) 403 Part IV Experimental Methods and Miscellaneous Topics 565 567 646 664 678 690 Kinematics of High-Energy Particles (4001–4061) Interactions between Radiation and Matter (4062–4085) Detection Techniques and Experimental Methods (4086–4105) Error Estimation and Statistics (4106–4118) Particle Beams and Accelerators (4119–4131) Index to Problems 459 524 709 ix PART I ATOMIC AND MOLECULAR PHYSICS ATOMIC PHYSICS (1001 1122) 1001 Assume that there is an announcement of a fantastic process capable of putting the contents of physics library on a very smooth postcard Will it be readable with an electron microscope? Explain (Columbia) Solution: Suppose there are 106 books in the library, 500 pages in each book, and each page is as large as two postcards For the postcard to be readable, the planar magnification should be × 500 × 106 ≈ 109 , corresponding to a linear magnification of 104.5 As the linear magnification of an electron microscope is of the order of 800,000, its planar magnification is as large as 1011 , which is sufficient to make the postcard readable 1002 At 1010 K the black body radiation weighs (1 ton, g, 10−6 g, 10−16 g) per cm3 (Columbia) Solution: The answer is nearest to ton per cm3 The radiant energy density is given by u = 4σT /c, where σ = 5.67 × −8 10 Wm−2 K−4 is the Stefan–Boltzmann constant From Einstein’s massenergy relation, we get the mass of black body radiation per unit volume as u = 4σT /c3 = 4×5.67×10−8×1040 /(3×108 )3 ≈ 108 kg/m3 = 0.1 ton/cm3 1003 Compared to the electron Compton wavelength, the Bohr radius of the hydrogen atom is approximately (a) 100 times larger (b) 1000 times larger (c) about the same (CCT ) Problems and Solutions in Atomic, Nuclear and Particle Physics Solution: The Bohr radius of the hydrogen atom and the Compton wavelength h a of electron are given by a = me2 and λc = mc respectively Hence λc = e2 −1 2π ( c ) = 137 = 22, where e2 / c is the fine-structure constant Hence 2π the answer is (a) 1004 Estimate the electric field needed to pull an electron out of an atom in a time comparable to that for the electron to go around the nucleus (Columbia) Solution: Consider a hydrogen-like atom of nuclear charge Ze The ionization energy (or the energy needed to eject the electron) is 13.6Z2 eV The orbiting electron has an average distance from the nucleus of a = a0 /Z, where a0 = 0.53 × 10−8 cm is the Bohr radius The electron in going around the nucleus in electric field E can in half a cycle acquire an energy eEa Thus to eject the electron we require eEa 13.6 Z2 eV , or E 13.6 Z3 ≈ × 109 Z3 V/cm 0.53 × 10−8 1005 As one goes away from the center of an atom, the electron density (a) decreases like a Gaussian (b) decreases exponentially (c) oscillates with slowly decreasing amplitude (CCT ) 702 Problems and Solutions in Atomic, Nuclear and Particle Physics or 4E − 4EEπ max + m2 + 4p2 = 4m2 + 4p2 , π p giving the maximum pion energy Eπ max = 4E + m2 − 4m2 π p ≈E, 4E as E mp Stationary-target machine: When Eπ is maximum, the two final-state protons are stationary and the pion takes away the momentum of the incident proton Thus Eπ + 2mp = E + mp , or Eπ = E − mp ≈ E as E mp 4125 An electron (mass m, charge e) moves in a plane perpendicular to a uniform magnetic field If energy loss by radiation is neglected the orbit is a circle of some radius R Let E be the total electron energy, allowing for relativistic kinematics so that E mc2 (a) Explain the needed field strength B analytically in terms of the above parameters Compute B numerically, in gauss, for the case where R = 30 meters, E = 2.5 × 109 electron volts For this part of the problem you will have to recall some universal constants (b) Actually, the electron radiates electromagnetic energy because it is being accelerated by the B field However, suppose that the energy loss per revolution ∆E is small compared to E Explain the ratio ∆E/E analytically in terms of the parameters Then evaluate this ratio numerically for the particular value of R given above (CUSPEA) Solution: (a) Let v be the velocity of the electron Its momentum is p = mγv, where γ = (1 − v2 )− Newton’s second law of motion gives c dp dv = mγ = ev × B , dt dt Experimental Methods and Miscellaneous Topics 703 as |v| and hence γ are constant since v ⊥ B, or dv evB = dt mγ As v2 dv = , dt R where R is the radius of curvature of the electron orbit, mγv B= , eR or √ pc E − m2 c4 E B= = ≈ eRc eRc eRc = 2.5 × 109 × 1.6 × 10−19 = 2.8 × 10−1 T 1.6 × 10−19 × 30 × × 108 = 2.8 × 103 Gs (b) The power radiated by the electron is P = = e2 γ v2 − ˙ 6πε0 c3 ˙ v×v c ˙ e2 v γ 6πε0 c3 e2 v γ , 6πε0 c3 R2 ˙ as v ⊥ v The energy loss per revolution is then 4π e2 2πRP ∆E = = (γβ)3 γmc2 v 4πε0 mc2 R = 4π r0 4π r0 (γβ)3 E = (γ − 1) E , R R where r0 = 2.8 × 10−15 m is the classical radius of electron and β = 2.5×109 With γ = 0.51×106 = 4.9 × 103 , = 4π 2.8 × 10−15 ∆E ≈ × × (4.9 × 103 )3 E 30 = 4.6 × 10−5 The results can also be obtained using the relevant formulas as follows v c 704 Problems and Solutions in Atomic, Nuclear and Particle Physics (a) p(GeV/c) = 0.3B(T)R(m) giving B= p 2.5 = ≈ 0.28 T 0.3R 0.3 × 30 (b) ∆E(keV) ≈ 88E(GeV)4 /R(m) giving ∆E = 88E × 10−6 /R E = 88 × 2.53 × 10−6 /30 = 4.6 × 10−5 4126 Draw a simple, functional cyclotron magnet in cross section, showing pole pieces of m diameter, yoke and windings Estimate the number of ampere-turns required for the coils if the spacing between the pole pieces is 10 cm and the required field is T (= 20 kgauss) µ0 = 4π × 10−7 J/A2 · m (Columbia) Solution: Figure 4.14 shows the cross section of a cyclotron magnet The magnetic flux φ crossing the gap betwen the pole pieces is φ= NI , R R= d , µ0 S where d being the gap spacing and S the area of each pole piece, is the reluctance φ By definition the magnetic induction is B = S Thus N I = φR = Bd × 10 × 102 = = 1.59 ì 105 A-turns à0 × 10−7 Experimental Methods and Miscellaneous Topics 705 Fig 4.14 4127 In general, when one produces a beam of ions or electrons, the space charge within the beam causes a potential difference between the axis and the surface of the beam A 10-mA beam of 50-keV protons (v = × 106 m/sec) travels along the axis of an evacuated beam pipe The beam has a circular cross section of 1-cm diameter Calculate the potential difference between the axis and the surface of the beam, assuming that the current density is uniform over the beam diameter (Wisconsin) Solution: The beam carries a current R I= j · dS = j2πrdr = πR2 j = πR2 ρv , where j and ρ are the current and charge densities respectively Thus ρ= I πR2 v 706 Problems and Solutions in Atomic, Nuclear and Particle Physics At a distance r from the axis, Gauss’ flux theorem 2πrlE = πr2 lρ/ε0 gives the electric field intensity as rρ r I E= = 2ε0 2πε0 vR2 As E = − dV , the potential difference is dr R ∆V = E(r)dr = = I 2πε0 vR2 rdr = I 4πε0 v × 109 × 10 × 10−3 = 30 V × 106 4128 Cosmic ray flux at ground level is 1/year, 1/min, 1/ms, 1/µs, cm−2 sterad−1 (Columbia) Solution: The answer is 1/(min · cm2 · sterad) At ground level, the total cosmic ray flux is 1.1 × 102 /(m2 · s · sterad), which consists of a hard component of 0.8 × 102 /(m2 · s · sterad) and a soft component of 0.3 × 102 /(m2 · s · sterad) 4129 Particle flux in a giant accelerator is 104 , 108 , 1013 , 1018 per pulse (Columbia) Solution: A typical particle flux in a proton accelerator is 1013 /pulse 4130 Which particle emits the most synchrotron radiation light when bent in a magnetic field? Experimental Methods and Miscellaneous Topics 707 (a) Proton (b) Muon (c) Electron (CCT ) Solution: The synchrotron radiation is emitted when the trajectory of a charged particle is bent by a magnetic field Problem 4125 gives the energy loss per revolution as 4π e2 β γ , ∆E = 4πε0 R where R, the radius of curvature of the trajectory, is given by mγβc eB Thus for particles of the same charge and γ, ∆E ∝ m−1 Hence the answer is (c) R= 4131 The magnetic bending radius of a 400 GeV particle in 15 kgauss is: (a) 8.8 km (b) 97 m (c) 880 m (CCT ) Solution: The formula p(GeV/c) = 0.3B(T )R(m) gives p 400 = = 880 m 0.3B 0.3 × 1.5 Or, from first principles one can obtain R= mγβc mγc2 400 × 109 × 1.6 × 10−19 ≈ = = 880 m , eB eBc 1.6 × 10−19 × 1.5 × × 108 as B = 15 kGs = 1.5 T Hence the answer is (c) R= INDEX TO PROBLEMS Abnormal magnetic moment of µ 3009 Absorption spectrum of HCl 1135 Accelerators 4119, 4120, 4121, 4122, 4123, 4124 α-decay 2033, 2035, 2107 α-spectrum measurement 2086 Allowed and forbidden transitions of Mg 1086 Angular momentum quantization 1035 Associated production of strange particles 3009 Atom formed by e with µ+ 1061 µ− with nucleus 1059, 1060, 1062, 1063, 1064, 1066 µ− with π + 1065 Ω− with Pb nucleus 1058 spin-1 ‘electrons’ with He nucleus 1026 Atomic clock 1057 Atomic model of Bohr 1042, 1049 Thomas-Fermi 1013 Thomson 1045 Atomic transitions 1038, 1043, 1044, 1068, 1069, 1070, 1071, 1086 Auger effect 1008 Bag model of hadron 3080, 3081 β-decay 1039, 1047, 2006, 2085 of Fermi and Gamow-Teller types 2088 β-decay, Fermi’s theory of 3009 β + -decay 2087, 2088 vs K-capture 2084 Binding energy of electron in atom 1106 Black-body radiation 1002, 1077 Bohr orbit 1033 Bohr radius 1003 Bohr-Sommerfeld quantization 1036 Bragg reflection from NaCl crystal 1101 Carbon dating 2106, 4112 ˇ Cerenkov radiation 4084, 4085, 4125 709 710 Index to Problems Charged particle in magnetic field 4002, 4007, 4131 Charmed particle detection by µ 4104 Charmonium from p¯/e− e+ annihilations 4105 p Clebsch-Gordan coefficients 3026 Colliding-beam kinematics 4001 Colliding-beam machine vs single-beam machine 4123, 4124 Color quantum number 3072, 3078, 3079 Compton effect 1034 Compton wavelength 4010, 4035, 4036, 4037 Continuous electron-spin resonance spectroscope 1111 Cosmic black-body radiation 4039 Cosmic-ray µ in geomagnetic field 4004, 4005 Coulomb barrier penetration 2007 Count rate statistics 4107, 4108, 4111, 4113, 4114, 4115, 4118 Cyclotron magnet 4126 Cyclotron vs synchrotron 4120 D particle 3087, 3088 Decay, angular distribution of products of 3054, 3055 conservation laws in 3016, 3017, 3018, 3021, 3049 relative rates of 3027, 3055 Decay of hyperon 3017 K 3021, 3056, 4059 Λ 3053, 3054, 3055 Li 2080 µ 3022, 4026 n 3014 π 3013, 3050 π, µ 3049, 3050 p 3066, 4060 Σ 3024 Decays 3012, 3013, 3029 leptonic 3038, 3039, 3040 nonleptonic weak (hyperon) 3035 Density of nuclear matter 2008 Detailed balancing 3036 Detection of particles by scintillator 4073 Index to Problems Deuterium ‘molecule’ (dqd) 1142 Deuteron photodistintegration 2049 represented by square well 2050 states 2053, 2056 theory 2058 Diatomic molecule 1124, 1129 modeled as dumbbell 1128, 1133 represented by harmonic oscillator 1124 Dissociation energy of hydrogen molecule 1125 Doublet structure of sodium line 1035, 1092 Drell-Yan quark annihilation 3079 Effect of external potential on atomic energy levels 1012 Electric dipole moment of n 3009 Electric dipole transition 1040, 1079, 1080, 1081, 1093, 1096, 2092 Electric field needed to ionize atom 1004 Electric multipole transition 1038, 2093 Electric polarizability of atom 1076 Electron configuration of atom 1039, 1071, 1075, 1081, 1082, 1083 1085, 1087, 1088, 1090, 1093, 1095, 1098, 1116 Electron in nucleus, argument against 2001 Electrostatic energy of speherical charge 2009 Energy levels in atom with spin-3/2 ‘electrons’ 1067 He atom 1071, 1072, 1074, 1100 H-like atom 1044 Mg atom 1086 molecule 1127, 1139, 1140, 1141 system of heavy quark-antiquark pair 3090 Energy level corrections 1048 due to finite size of nucleus 1050, 1051 due to presence of electric field 1121, 1122 due to presence of magnetic field 1057, 1080, 1116, 1117, 1118 1119, 1120 Error estimation 4109 η particle production and decay 3032 Exchange force 1132 711 712 Index to Problems Excitation by bombardment of atom with electron 1011 molecule with neutron 1131 Excitation energies of mirror nuclei 2011 Experiments important in history of atomic physics 1113 Fermi plateau 4069 Fermi transition between isospin multiplets 2091 Fine structure of atomic levels 1009, 1028, 1052, 1054, 1055, 1099 Fission 2029, 2030, 2035, 2037, 2041, 2043, 2117 Franck-Hertz experiment 1034 Frequency shift of photon falling through gravity 2099 Fusion 2006, 2044, 2045, 2046 γ-ray absorption 2094, 2095 γ-ray emission 2096, 2097 Geiger-Nuttall law of α-decays 2076, 2078 Gell-Mann–Nishijima relation 3074 Gluons 3082 Gluons, evidence for 3072 G-parity operator 3005 Half life of particle 4002 radioactive nucleus 2040, 2066, 2077, 2079 Hall effect 1112 Heavy neutrino 3048 Helicity 3043, 3050 Helicity of µ from π decay 4061 Higgs boson 3064 Hund’s rule 1008, 1078, 1082, 1095 Hyperfine structure of atomic levels 1029, 1030, 1041, 1052, 1053 1054, 1099 Inertness of noble gas 1077 Intermediate boson 3059, 3061 Ionization energy 1007, 1009, 1046, 1076 Isobaric analog states 2014, 2069 Isobaric nuclei 2081, 2082 Isospin assignment 2014 Isospin muliplet 2012, 2013 Index to Problems JJ coupling 1094 Josephson effect 1112 J/ψ particle 3009 K lifetime 4059 production 3058 regeneration 3009 Kinematics of collision 4013, 4019, 4020, 4021, 4022, 4024, 4025, 4027, 4028 4029, 4030, 4031, 4033, 4034, 4038, 4040, 4054, 4055 decay 4006, 4023, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048 4049, 4050, 4051, 4052, 4053, 4056, 4057, 4058 relativistic particle 4003, 4004, 4006, 4008, 4009, 4030 KS /KL ratio 3056, 3057 Lamb-Rutherford experiment 1034 Lamb shift 1008, 1032, 1037 Λ particle production in πp scattering 3021 Land´ g-factor 1083, 1091, 1109 e Land´ interval rule 1008 e Lepton number conservation 3011 Lepton types 3011 Lifetime measurements 4103 Lifetimes against different types of interaction 3018 LS coupling 1079, 1080, 1081, 1083, 1088, 1089, 1091, 1094, 1097 Lyman alpha-line 1009 Magnetic moment of atom 1077 deuteron 2057 electron 1009 nucleus 2015, 2070 Magnetic monopole 2071 Meson of charge 2, argument against 3021 Metal as free electrons in potential well 1014 Molecule, homonuclear 1130 hydrogen 1132 H+ 1123 Măssbauer spectroscopy 1111 o 713 714 Index to Problems Multiple-choice questions on accelerators 4129, 4130 atomic physics 1005, 1018, 1020, 1021, 1023, 1027, 1030, 4069, 4088 1126, 1127 cosmic rays 4128 elementary interactions 3002, 3004, 3007, 3045, 4011, 4070, 4071 4083, 4116 experimental errors 4106, 4117 experimental methodology 1001, 3046, 4089, 4090, 4091, 4092, 4093 4094, 4095, 4096, 4097, 4098, 4099, 4102 nuclear physics 2008, 2040, 2108, 3020 particle kinematics 4100, 4101 particle physics 3008, 3010, 3051, 4062, 4063, 4064, 4065, 4066 4067, 4068, 4074, 4075, 4086, 4087 Neutrino capture by isotopes 2089 from the sun 2046 interaction cross section 3045, 3046 interaction with matter 3047 mass 3044 oscillation 3068 properties 3042, 3043 types 3042, 3067 Neutron-antineutron oscillation 3069, 3070 Neutron decay modes 3014 Neutron density in uranium 2039 Neutron interaction in scintillator 4078 Neutron irradiation of gold 2101 Li 2103 nuclei 2104 Neutron passage through graphite rod 4082 Neutron scattering cross sections 2118, 2119, 4079, 4081 Neutron star 2047 Noble gas atomic structure 1077, 1083 Nuclear binding energy 2025, 2026, 2027, 2028 Index to Problems excitation energy 2108, 2111 ground state 2035 reaction 2109, 2110, 2112, 2115, 2116, 2120 Nuclear precession in magnetic field 2005 Nuclear radius determination 2002, 2035 from mirror nuclei 2009, 2010 Nuclear reactor of breeder type 2042 fission type 2043 Nuclear shell model 2065, 2067, 2068, 2072 magic numbers 2060, 2071 single-particle levels 2061, 2062, 2064, 2069 Nucleon form factor 2021 Nucleon-nucleon interactions 2048, 2090 Nucleus, double-magic 2066 effect of deformation of 2004, 2073 magnetic moment of 2006 models of 2059 Nucleus represented by potential box 2063 N/Z ratio for stable nuclei 2031, 2032 Pairing force 2075 Para- and ortho-states 1134 of He atom 1073, 1077 of hydrogen molecule 1133 Parity of atomic level 1097 Parity of π0 3021 Parity operator 3052 Parity violation in ep scattering 3065 Particle interactions 3013, 3017, 3019, 3037 angular distribution in 4032 conservation laws in 3001, 3006, 3015, 3016, 3025 cross sections for 3037 relative cross sections for 3025, 3026 relative strengths of 3001 threshold for 3019, 3036, 4012, 4014, 4015, 4016, 4017, 4018, 4031 4032 715 716 Index to Problems Particle interactions between e+ , e− 3077 e, ν 3059, 3060 e+ , p and e− , p 3021 K , e 3062 N , N 2090, 3017, 3019 ν, q 3063 π, d 3030, 3019 p, p 3013 ¯ Particle tracks in emulsion/bubble chamber 3033, 3069 Particle types 3003 Particle with magnetic moment in magnetic field 1025 Photoexcitation of atom 1010, 1019 Photon interactions in matter 4076, 4077 π quantum numbers and properties 3023 Potential difference across particle beam 4127 Pressure exerted by electron on cavity walls 1024 Proton-radioactivity 2034 Ψ particle 3084, 3085, 3086 Pulsed nuclear magnetic resonance spectroscope 1111 Quantum chromodynamics 3082, 3083 Quantum numbers of hadron 3074, 3075 Quark model of hadron 3072, 3073, 3074, 3075 Radioactive capture p + n → d + γ 2051, 2052 Radioactivity series 2100, 2102 Raman spectrum 1136, 1137 Recombination of split neutron beams 1027 Relative population in energy level 1090 Resonance particles 3034 Resonance states in e+ e− annhilation 3089 s wave scattering 1016 Scattering by atom of p 2018 Scattering by hard sphere 2016 Scattering by nucleus of α 2113 e 2021 p 2023 Index to Problems Scattering cross section calculations involving Born approximation 2017 known total cross section 2022 phase shift 2019, 2020 Rutherford formula 1017 Semi-emperical nuclear mass formula 2024, 2036 Separation energy of neutron from nucleus 2071 Σ particle 3028 Singlet and triplet states of hydrogen molecule 1041 Spectral line broadening 1006, 1055 by Doppler effect 1021, 1022 Spectral line intensity 1077, 1084 Spectroscopic notation for atomic levels 1069, 1070, 1071, 1075 1078, 1085, 1089, 1090, 1093, 1116 Spin echo experiment 1110 Spin of free proton 1009 Spin-orbit interaction 1031, 1056 Spontaneous transition, lifetime for 1039 Stern-Gerlach experiment 1015, 1034, 1077, 1114, 1115 SU(3) multiplets 3076, 3078 Synchrotron 4122 System of bosons 2074 nucleons 2073 two nucleons 2048, 2054, 2055 Time-reversal operator 3052 Transition between molecular levels 1135, 1138, 1140, 1141 Transmission spectrum of HCl 1138 Two-neutrino experiments 3009 Van de Graaff generator experiment 2114 X-ray absorption spectrum 1103, 1108 emission spectrum determination 1107 K-lines 1102, 1104, 1105 Zeeman effect 1120 Zeeman effect, anomalous 1008 717 ... → p − eA Use this and c 42 Problems and Solutions in Atomic, Nuclear and Particle Physics the equation of motion for the linear momentum p to derive a quantized condition on the magnetic flux... 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), Particle Physics. .. π c2 g1 · ΓIω ω g2 14 Problems and Solutions in Atomic, Nuclear and Particle Physics Introducing the form factor g(ω) and considering ω and Iω as average values in the band of g(ω), we can write