INTRODUCTION TO NUCLEAR AND PARTICLE PHYSICS

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1 INTRODUCTION TO NUCLEAR AND PARTICLE PHYSICS ASHOK DAS THOMAS FERBEL University of Rochester JOHN WILEY & SONS, INC. NEW YORK CHICHESTER BRISBANE TORONTO SINGAPORE

2 CONTENTS Preface and Introduction Apologies vii Units and Tables of Nuclear and Particle Properties Other References ix Acknowledgments ix viii vii Chapter I. Rutherford Scattering 1 Introductory Remarks 1 Rutherford Scattering 2 Scattering Cross Section 12 Measuring Cross Sections 15 Laboratory Frame and the Center-of-Mass Frame 17 Relativistic Variables 21 Quantum Treatment of Rutherford Scattering 25 Problems 26 Suggested Readings 27 XI

3 хи Chapter II. Nuclear Phenomenology Introductory Remarks 28 Properties of Nuclei 28 Labeling of Nuclei 28 Masses of Nuclei 29 Sizes of Nuclei 32 Nuclear Spins and Dipole Moments 33 Stability Curve 35 Instability of Nuclei 36 Nature of the Nuclear Force 38 Problems 43 Suggested Readings 44 Chapter III. Nuclear Models Introductory Remarks 45 Liquid Drop Model 46 The Fermi-Gas Model 48 Shell Model 51 Infinite Square Well 56 Harmonic Oscillator 57 Spin-Orbit Potential 59 Predictions of the Shell Model 62 Collective Model 64 Superdeformed Nuclei 66 Problems 67 Suggested Readings 68 Chapter IV. Nuclear Radiation Introductory Remarks 69 Alpha Decay 69 Example 72 Barrier Penetration 73 Beta Decay 77 Gamma Decay 85 Problems 87 Suggested Readings 88 Chapter V. Applications of Nuclear Physics Introductory Remarks 89 Fission 89

4 CONTENTS xiii Chain Reaction 96 Nuclear Fusion 98 Radioactive Decay 102 Example Radioactive Equilibrium 106 Natural Radioactivity and Radioactive Dating 107 Example Problems 110 Suggested Readings 112 Chapter VI. Energy Deposition in Media 113 Introductory Remarks 113 Energy Loss 114 Charged Particles 114 Units of Energy Loss and Range 117 Example Example Straggling, Multiple Scattering, and Statistical Processes 119 Example Energy Loss through Bremsstrahlung 121 Example Interactions of Photons with Matter 124 Photoelectric Effect 125 Compton Scattering 126 Pair Production 127 Example Example Example Interactions of Neutrons 131 Interaction of Hadrons at High Energies 131 Problems 132 Suggested Readings 133 Chapter VII. Particle Detection 134 Introductory Remarks 134 Ionization Detectors 134 Ionization Counters 136 Proportional Counters 138 Geiger-Müller Counters 141 Scintillation Detectors 142

5 XIV CONTENTS Time of Flight 145 Cherenkov Detectors 148 Semiconductor Detectors 149 Calorimeters 150 Layered Detection 153 Problems 154 Suggested Readings 155 Chapter VIII. Accelerators 156 Introductory Remarks 156 Electrostatic Accelerators 157 Cockcroft-Walton Machines 157 Van de Graaff Accelerator 158 Resonance Accelerators 159 Cyclotron 159 Example 161 Linac or Linear Accelerator 162 Synchronous Accelerators 163 Phase Stability 166 Strong Focusing 168 Colliding Beams 170 Problems 173 Suggested Readings 175 Chapter IX. Properties and Interactions of Elementary Particles 176 Introductory Remarks 176 Forces 177 Elementary Particles 180 Quantum Numbers 183 Baryon Number 183 Lepton Number 184 Strangeness 185 Isospin 188 Gell-Mann-Nishijima Relation 190 Production and Decays of Resonances 192 Determining Spins 194 Violation of Quantum Numbers 198 Weak Interactions 198 Hadronic Weak-Decays 198

6 CONTENTS Semileptonic Processes 199 Electromagnetic Processes 200 Problems 200 Suggested Readings 202 Chapter X. Symmetries 203 Introductory Remarks 203 Symmetries in the Lagrangian Formalism 204 Symmetries in the Hamiltonian Formalism 208 Infinitesimal Translations 209 Infinitesimal Rotations 212 Symmetries in Quantum Mechanics 214 Continuous Symmetries 217 Example Isotopic Spin 221 Local Symmetries 224 Problems 226 Suggested Readings 226 Chapter XI. Discrete Transformations 227 Introductory Remarks 227 Parity 227 Example 1 Parity of я- - Meson 232 Example 2-Parity of Д( 1232) 233 Violation of Parity 233 Time Reversal 235 Charge Conjugation 238 CPT Theorem 241 Problems 241 Suggested Readings 242 Chapter XII. Neutral Kaons and CP Violation 243 Introductory Remarks 243 Neutral Kaons 244 CP Eigenstates of Neutral Kaons 246 Strangeness Oscillation 248 Kj Regeneration 249 Violation of CP Invariance 250 Time Development and Analysis of the K -K System 254 Semileptonic K Decays 260 Problems 262 Suggested Readings 263

7 XVI CONTENTS Chapter XIII. The Standard Model 264 Introductory Remarks 264 Quarks and Leptons 265 Quark Content of Mesons 266 Quark Content of Baryons 268 Need for Color 269 Example Quark Model for Mesons 271 Weak Isospin and Color Symmetry 273 Gauge Bosons 274 Dynamics of the Gauge Particles 276 Symmetry Breaking 279 Quantum Chromodynamics and Confinement 284 Quark-Gluon Plasma 288 Comments on Phenomenology and Comparison with Data 289 Problems 294 Suggested Readings 295 Chapter XIV. Beyond the Standard Model 296 Introductory Remarks 296 Grand Unification 297 Supersymmetry 301 Supergravity, Superstrings 304 Suggested Readings 307 Appendix A Special Relativity 309 Appendix В Spherical Harmonics 313 Appendix С Spherical Bessel Functions 315 Appendix D Basics of Group Theory 317 Appendix E Table of Physical Constants 322 Index 323

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