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ATOMIC AND NUCLEAR THE MODERN UNIVERSITY PliYSICS SERIES

This series is intended for readers whose main interest is in physics, or who need the methods of physics in the study of science and technology. Some of the books will provide a sound treatment of topics essential in any physics training, while other, more advanced, volumes will be suitable as preliminary reading for research in the field covered. New titles will be added from time to time.

Clark: A First Course in Quantum Littlefield and Thorley: Atomic and Nuclear Physics Lothian: and Its Uses Lovell, Avery and Vernon: Physical Properties of Materials Perina: Coherence of Tritton: Physical Wolbarst: Symmetry and Quantum Systems ATOMIC AND NUCLEAR PHYSICS An Introduction

3rd edition

T. A. LITTLEFIELD and

N. THORLEY Senior Lecturer School of Physics University of Newcastle upon Tyne

~ SPRINGER SCIENCE+BUSINESS MEDIA, LLC © 1979, Springer Science+Business Media New York Originally published by Van Nostrand Reinhold Co. Ltd. in 1979

First edition 1963 Second edition 1968

All rights reserved. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage or retrieval systems - without the written permission of the publishers

Library of Congress Cataloging in Publication Data

Littlefield, Thomas Albert, 1912- Atomic and nuclear physics.

(The Modern university physics series) Bibliography: p. Includes index. 1. . 2. Nuclear physics. 3. QUafitum theory. I. Thorley, Norman, 1913 - joint author. II. Title. QCI73.L76 1979 539.7 78-31250 ISBN 0-442-30189-8 ISBN 0-442-30190-1 pbk. ISBN 0-442-30178-2 ELBS

ISBN 978-0-442-30190-3 ISBN 978-1-4684-1470-7 (eBook) DOI 10.1007/978-1-4684-1470-7 \ \ \ K+

Computer display of the decay of the two charmed DO(cu)-+K-n+ and DO(cu)-+K+~- produced from an energetic - collision. The display shows the cross• section of the beam pipe (centre) and the surrounding spark chambers and scintillation counters of the detector arrangement. The tracks of the particles are plotted by the triggered spark chambers. (Photograph taken from Fundamental Particles with Charm, Roy F. Schwitters, Scientilic American, October 1977, p. 57.) T ABLE OF PHYSICAL CONSTANTS

Speed of light (vacuum) c=2·997 926 x 108 m s-1 Elementary charge () e= 1·602189 x 10-19 C Unified atomic mass constant U = 1'660 565 x 10 - 27 kg Electron rest mass m.=9·109 534 x 10- 31 kg = 5·485803 x 10-4 u Proton rest mass mp= 1·672 648 x 10-27 kg = 1·007 276 u rest mass mn = 1·674954 x 10-27 kg = 1·008 665 u Mass of mH = 1·673559 x 10-27 kg = 1·007 825 u Electron charge-to-mass ratio e/m.= 1·7588045 x 1011 C kg- 1 Proton-to-electron mass ratio mp/m.= 1836'151 Neutron-to-electron mass ratio mn/me= 1838·682 Avogadro constant N A =6'022 045 x 1023 mol- 1 Planck constant h=6'626176 x 10-34 J s 11 = 1·054 589 x 10 - 34 J s Faraday constant F=9'648456 x 104 C mol- 1 First Bohr radius ao = 5'291 771 x 10- 11 m Gas constant R=8·31441 J K- 1 mol- 1 Boltzmann constant k = 1· 380 662 x 10 - 23 J K - 1 Bohr magnet on IlB=9'274 078 X 10-24 J T- 1 Nuclear magneton IlN=5'050 824 x 10-27 J T- 1 conversion factors 1 eV = 1·602189 x 10- 19 J 1 u=931·502 MeV Rydberg constant Roo = 1·097 373 x 107 m- 1 Magnetic constant (permeability of a vacuum) 1l0=41t X 10- 7 H m- 1 Electric constant (permittivity of a vacuum) Bo=8'854188 x 10-12 F m- 1 Standard atmosphere 1 atm = 103 125 Pa

These figures are adapted from Quantities, Units and Symbols, published by the Symbols Committee of the Royal Society, London, 1975. PREFACE TO THE THIRD EDITION

After the death of Dr. Littlefield it was decided that I should undertake the revision ofthe whole of Atomic and Nuclear Physics: an Introduction for the third edition, and it was soon apparent that major changes were necessary. I am confident that these changes would have had Dr. Littlefield's approval. The prime consideration for the present edition has been to modernize at a minimum cost. As much as possible of the second edition has therefore been retained, but where changes have been made they have been fairly drastic. Thus the chapters on fine structure, wave mechanics, the vector model of the atom, Pauli's principle and the Zeeman effect have been completely restructured. The chapters on nuclear models, cosmic rays, fusion systems and fundamental particles have been brought up to date while a new chapter on charm and the latest ideas on has been included. It is hoped that the presentation of the last named will give readers a feeling that physics research can be full of adventure and surprises. The student targets for the book are the first and second years of an undergraduate course in atomic and nuclear physics at our universities and polytechnics. It will also be useful to those first and second year engineers requiring an atomic and nuclear physics background. The book must not be judged as a final honours text since too many topics are omitted and the mathematical depth is insufficient for this purpose. It is more suitable for all general or ordinary degree students and for first year single honours students. It could also be profitably used by H.N.C. students taking . The changes made and the new material used are well within the compass of such students. No references to original papers have been given because it is the writer's experience that only those students who are deeply concerned with the subject in their third years take the trouble to use the library for reference purposes. Furthermore, the addition of references within or at the end of each chapter would have added to the cost of this edition. However, many new problems have been included, some of which (marked N) have been taken from the physics papers of the University of Newcastle upon Tyne, and the writer would like to record his thanks to the Senate of this university for permission to use these questions. I must also thank my colleagues Dr. I. D. C. Gurney, Dr. E. L. Lewis, Dr. B. Peart and Professor K. T. Dolder for helpful discussions and I am indebted to Professor A. W. Wolfendale for help with the section on research. Needless to say the writer takes full responsibility for any lack of clarity which

vii persists and would be glad to receive comments, corrections and criticisms of the text which might be included in a future printing. Grateful acknowledgement is made to the Culham Laboratory of the U.K.A.E.A. at Abingdon for the use of Fig. 24.11. Grateful acknowledgement and thanks are due to Mrs. Dot"othy Cooper for the excellent art work she produced from the writer's sketches; to the publishers Van Nostrand Reinhold Co. Ltd.; and most especially to Miss L. J. Ward, the College Editor, for her patience during the preparation of this edition. Finally, to my wife, Mrs. Joan Thorley, for much encouragement over the last few months and for transforming my scrawl into a typescript.

N.T. Dec 1978

Vlll CONTENTS

Table of Physical Constants XVI

Chapter 1 KINETIC THEORY 1 1.1 The Atom in History 1 1.2 Brownian Motion 2 1.3 Basic Assumptions of Kinetic Theory 3 1.4 Pressure of a Gas 4 1.5 Molecular Velocities 6 1.6 Temperature of a Gas: Avogadro's Hypothesis 6 1. 7 Mean Free Path 7 1.8 Thermal Conductivity and 8 1.9 Specific Heat Capacities 9 1.10 Atomicity 10 1.11 Molar Heat Capacities 12 1.12 Van der Waals' Equation 12 1.13 Molecular Sizes 15 1.14 Summary 16

Chapter 2 THE ELECTRON 19 2.1 Electrical Conduction in Solutions 19 2.2 Conduction in Gases 20 2.3 Properties of Cathode Rays 22 2.4 Thomson's Method for Measuring Charge per Unit Mass (elm) 22 2.5 Dunnington's Method for elm 23 2.6 Charge on the Electron 25

Chapter 3 NATURAL RADIOACTIVITY 30 3.1 Introduction 30 3.2 elm for p-Rays 30 3.3 Bucherer's Method for elm of p-Rays 32 3.4 The Charge-Mass Ratio (ElM) for IX-Rays 33 3.5 Charge on IX-Particles 35 3.6 Identification of IX-Particles 36 3.7 Early Models of the Atom 37 3.8 The of IX-Particles 38 3.9 Estimates of Nuclear Diameter and Charge 41 3.10 The Neutron 42

IX Chapter 4 RADIOACTIVE SERIES AND 46 4.1 Introduction 46 4.2 Equation of 46 4.3 Mean Lifetime of Radioactive Substance 47 4.4 Half-Lives of Radioactive Substances 49 4.5 Radioactive Series 49 4.6 Radioactive Equilibrium 50 4.7 Isotopes 52 4.8 The Bainbridge Mass Spectrograph 55

Chapter 5 THE ELECTROMAGNETIC 59 5.1 Theories of Light 59 5.2 Interference 59 5.3 Diffraction 61 5.4 Spectra 62 5.5 The Electromagnetic Theory 63 5.6 Hertz's Experiment 65 5.7 The Electromagnetic Spectrum 66

Chapter 6 QUANTUM THEORY 69 6.1 The Continuous Spectrum 69 6.2 Planck's Quantum Theory 70 6.3 The Photoelectric Effect 71 6.4 Einstein's Equation 72 6.5 The Discovery of X-Rays 74 6.6 Diffraction of X-Rays 75 6.7 X-Ray Wavelengths 77 ~.8 Continuous Spectrum of X-Rays 79 6.9 Compton Effect 80 6.10 Summary 82

CHAPTER 7 SPECTRA 85 7.1 The Hydrogen Spectrum 85 7.2 The Bohr Theory of the Hydrogen Atom 86 7.3 Effect 90 7.4 The Spectrum of Sodium 93 7.5 Quantum Defects - Interpretation 95 7.6 Selection Rules and the Correspondence Principle 97 7.7 Excitation Potentials 99 7.8 Controlled Excitation of Spectra 101 7.9 X-Ray Spectra 101 7.10 Moseley's Work 102 7.11 The Interpretation of X-Ray Spectra 104

Chapter 8 FINE STRUCTURE AND ELECTRON 109 8.1 Fine Structure of Alkali-Metal Spectra 109 8.2 Electron Spin 111 x 8.3 Characteristic X-Rays and Absorption Spectra 114 8.4 Multiplicity of X-Ray Levels 116

Chapter 9 WAVES AND PARTICLES 120 9.1 The Dilemma 120 9.2 De Broglie's Theory 120 9.3 Velocity 121 9.4 The Davisson and Germer Experiment 122 9.5 The Experiment of Thomson and Reid 124 9.6 The Electron Microscope 125 9.7 Heisenberg's Uncertainty Principle 125 9.8 Born's Statistical Interpretation of Waves and Particles 127

Chapter 10 WAVE MECHANICS 131 10.1 Some Preliminaries 131 10.2 The Need for Change 132 10.3 The Schrodinger Wave Equation 134 10.4 An Alternative Approach 137 10.5 Solution of the Schrodinger Wave Equation 137 10.6 Simple One-Electron Atom Model 139 10.7 The Hydrogen Atom 143 10.8 Angular Momenta 146 10.9 Summary 147

Chapter 11 THE VECTOR MODEL OF THE ATOM 150 11.1 Quantum Numbers and Angular Momenta: Summary of Symbols and Notation 150 11.2 Magnetic Moments - Orbital and Spin 151 11.3 The Stern-Gerlach Experiment 153 11.4 Spatial of Electron Spin 156 11.5 Spin-Orbit Coupling and the Total Angular Momentum j 157

Chapter 12 TWO-ELECTRON ATOMS - PAULI PRINCIPLE 162 12.1 Wave Functions of Two-Electron Atoms 162 12.2 Vector Coupling for Two 165 12.3 The Helium Spectrum 167 12.4 jj Coupling 170 12.5 The Electronic Structure of the Elements and the 172 12.6 The Periodic Table - Some Empirical Rules 176 12.7 Hyperfine Structure and Nuclear Spin Angular Momentum 180

Chapter 13 THE ZEEMAN EFFECT 183 13.1 Introduction 183 13.2 The Normal Zeeman Effect 183 13.3 Explanation of Zeeman Effect in Terms of Vector Model 184 13.4 Zeeman Effect of Cadmium 643·8 nm Line 187 13.5 The Anomalous Zeeman Effect and the Lande Splitting Factor 188

xi 13.6 Zeeman Splitting in a Strong Magnetic Field: the Paschen-Back Effect 192 13.7 Conclusion 193

Chapter 14 THE STRUCTURE OF THE NUCLEUS 196 14.1 Introduction 196 14.2 Nuclear Constituents: Isotopes and Isobars 197 14.3 The Size of the Nucleus 200 14.4 Exact Atomic Masses - Mass Excess 11M 201 14.5 Binding of - Mass Defect 203 14.6 Stable and Unstable Nuclides 207 14.7 Derivation of Practical Form of E=moc2 208

Chapter 15 PROPERTIES AND USES OF NATURAL RADIOACTIVITY 212 15.1 The Nature of Radioactivity 212 15.2 a-Particles and the Geiger-Nuttall Rule 213 15.3 The Theory of a-Decay 216 15.4 [3-Rays and the 218 15.5 The Absorption and Range of [3-Rays 221 15.6 The Properties of (-Rays 223 15.7 Radioactivity as a Measurable Quantity 226

Chapter 16 NUCLEAR BOMBARDING EXPERIMENTS 231 16.1 Single a-Particle Scattering 231 16.2 Nuclear Alchemy 231 16.3 Cockcroft-Walton Proton Experiments 235 16.4 The Neutron 236 16.5 Nuclear Reactions 236 16.6 Formation of Tritium 237

Chapter 17 THE MEASUREMENT AND DETECTION OF CHARGED PARTIClES 240 17.1 The Wilson 240 17.2 The Bubble Chamber 241 17.3 Ionization Chambers 244 17.4 The Proportional Counter 245 17.5 The Geiger-Muller Counter 248 17.6 Scintillation Counters and Semiconductor Counters 251 17.7 The Spark Chamber 252 17.8 The Cerenkov Counter 254 17.9 Neutron Counting 255 17.10 The Photographic Plate 255 17.11 Summary 255

xii Chapter 18 ACCELERATING MACHINES AS USED IN NUCLEAR PHYSICS 258 18.1 Introduction 258 18.2 The Cockcroft-Walton Proton Accelerator 258 18.3 The Van de GraafT Electrostatic Generator 260 18.4 The Linear Accelerator 261 18.5 The Lawrence 263 18.6 The Synchrocyclotron 265 18.7 Electron Accelerating Machines. The Betatron 265 18.8 Electron Synchrotron 266 18.9 Proton Synchrotron 267 18.10 The Alternating-Gradient Synchrotron 268 18.11 Intersecting Beam Accelerators 269 18.12 The Growth and Future of Large Accelerating Machines 269

Chapter 19 NUCLEAR MODELS AND MAGIC NUMBERS 277 19.1 Introduction 277 19.2 Neutron Cross-Sections and Nuclear Radii 277 19.3 The Liquid-Drop Model 281 19.4 Nuclear Shells and Magic Numbers 284 19.5 The Theory of the 286 19.6 The Collective Model 290 19.7 Superheavy Elements: Experimental and Theoretical 291 19.8 Latest Developments 293 19.9 The Melting of the Moon 294

Chapter 20 ARTIFICIAL RADIOACTIVITY 298 20.1 The Discovery of the Positron 298 20.2 K- 301 20.3 The Origin of Electrons and within the Nucleus 302 20.4 Nuclear Isomerism 303 20.5 The Production of Radioisotopes 306 20.6 Some Uses of Radioisotopes 307

Chapter 21 NEUTRON PHYSICS 310 21.1 Introduction 310 21.2 Properties of the Neutron 310 21.3 Neutron Bombardment Reactions 313 21.4 Archaeological Dating by the 14C Method 314 21.5 Tree-Ring Calibration of 14C Dates 315

Chapter 22 AND ITS IMPLICATIONS 320 22.1 Introduction 320 22.2 The Theory of Nuclear Fission 321 22.3 The Energy of Nuclear Fission 325 22.4 The Distribution of Fission Products 327 22.5 Characteristics of Fission 328

xiii 22.6 The {3-Decay Chains of Fission 330 22.7 Controlled Fission-Nuclear Reactors 331 22.8 Reactors 334 22.9 Nuclear Power Prospects 335

Chapter 23 THE TRANSURANIC ELEMENTS 340 23.1 Neptunium (Z =93) to ? 340 23.2 Formation of Transuranic Elements 341 23.3 Neptunium, Np (Z=93) 341 23.4 , Pu (Z = 94) 342 23.5 Americium, Am (Z = 95), and , Cm (Z = 96) 343 23.6 Berkelium, Bk (Z = 97), and Californium, Cf (Z = 98) 343 23.7 Einstein, Es (Z =99), and , Fm (Z = 100) 344 23.8 Mendelevium, Md (Z = 101), and (Z = 102) 344 23.9 , Lw (Z = 103) 344 23.10 Elements with Z = 104, 105, 106 and 107 345 23.11 The Actinide Series 345

Chapter 24 THERMONUCLEAR REACTIONS AND 348 24.1 Introduction 348 24.2 The Source of Stellar Energy 348 24.3 The 349 24.4 Nuclear Fusion Reactions in the Plasma 350 24.5 Conditions for a Maintained Fusion Reaction 351 24.6 The Possibility of a Fusion Reactor 355 24.7 Tokomak Fusion Systems 357 24.8 Energy in the Future 360

Chapter 25 COSMIC RAYS 364 25.1 Discovery 364 25.2 Nature of Cosmic Rays 364 25.3 The Origin of Cosmic Rays 366 25.4 Geomagnetic Effects 368 25.5 Cosmic Rays at Sea-Level 369 25.6 Extensive Air Showers 371 25.7 The Detection of Cosmic Ray Particles 371 25.8 The Future of Cosmic Ray Research 373

Chapter 26 STABLE AND SEMI-STABLE PARTICLES 377 26.1 Introduction 377 26.2 The Positron: Particles and 379 26.3 , and 385 26.4 392 26.5 Classification of the Elementary Particles 392 26.6 Mesic Atoms: The Atom 394

XIV Chapter 27 SHORT-LIVED RESONANCE STATES 401 27.1 Forces and Fields 401 27.2 What is an ? 402 27.3 Short-Lived or Resonance Particles 403 27.4 Conservation Laws: and Conservation 409 27.5 Multiplet Structure - and Hypercharges 410 27.6 Classification of Elementary Particles 415 27.7 Particle Symmetries 416 27.8 Quarks 420 27.9 Conclusions 423

Chapter 28 CHARM AND ALL THAT 426 28.1 The Forces of Nature 426 28.2 The Three-Quirk Trick 430 28.3 The New - Charm 433 28.4 The November Revolution - the IN Particle 435 28.5 Quark Multiplet Representation 436 28.6 and Colour 438 28.7 The Confinement of Quarks 440 28.8 The Hunting of the Quark 441 28.9 Latest News: New Quarks 442 28.10 Conclusions 443

Appendix A RELATIVITY THEORY 447

Appendix B THE DANGERS OF ATOMIC 452 B.1 Introduction 452 B.2 Biological Effects of Nuclear and Electromagnetic Radiations 452 B.3 Maximum Permissible Radiation Levels for Safety 455 B.4 Precautions against Radiation Hazards 456

Appendix C COMPLETE LIST OF NUCLIDES OF THE ELEMENTS 458

Index 481

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