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Nuclear and Particle Physics Nuclear and Particle Physics B. R. Martin # 2006 John Wiley & Sons, Ltd. ISBN: 0-470-01999-9 Nuclear and Particle Physics B. R. Martin Department of Physics and Astronomy, University College London Copyright # 2006 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop # 02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Martin, B. R. (Brian Robert) Nuclear and particle physics/B. R. Martin. p. cm. ISBN-13: 978-0-470-01999-3 (HB) ISBN-10: 0-470-01999-9 (HB) ISBN-13: 978-0-470-02532-1 (pbk.) ISBN-10: 0-470-02532-8 (pbk.) 1. Nuclear physics–Textbooks. 2. Particle physics–Textbooks. I. Title. QC776.M34 2006 539.702–dc22 2005036437 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13 978-0 470 01999 9 (HB) ISBN-10 0 470 01999 9 (HB) 978-0 470 02532 8 (PB) 0 470 02532 8 (PB) Typeset in 10.5/12.5pt Times by Thomson Press (India) Limited, New Delhi Printed and bound in Great Britain by Antony Rowe Ltd., Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. To Claire Contents Preface xi Notes xiii Physical Constants and Conversion Factors xv 1 Basic Concepts 1 1.1 History 1 1.1.1 The origins of nuclear physics 1 1.1.2 The emergence of particle physics: the standard model and hadrons 4 1.2 Relativity and antiparticles 7 1.3 Symmetries and conservation laws 9 1.3.1 Parity 10 1.3.2 Charge conjugation 12 1.4 Interactions and Feynman diagrams 13 1.4.1 Interactions 13 1.4.2 Feynman diagrams 15 1.5 Particle exchange: forces and potentials 17 1.5.1 Range of forces 17 1.5.2 The Yukawa potential 19 1.6 Observable quantities: cross sections and decay rates 20 1.6.1 Amplitudes 21 1.6.2 Cross-sections 23 1.6.3 Unstable states 27 1.7 Units: length, mass and energy 29 Problems 30 2 Nuclear Phenomenology 33 2.1 Mass spectroscopy and binding energies 33 2.2 Nuclear shapes and sizes 37 2.2.1 Charge distribution 37 2.2.2 Matter distribution 42 2.3 Nuclear instability 45 2.4 Radioactive decay 47 2.5 Semi-empirical mass formula: the liquid drop model 50 2.6 -decay phenomenology 55 2.6.1 Odd-mass nuclei 55 2.6.2 Even-mass nuclei 58 viii CONTENTS 2.7 Fission 59 2.8 -decays 62 2.9 Nuclear reactions 62 Problems 67 3 Particle Phenomenology 71 3.1 Leptons 71 3.1.1 Lepton multiplets and lepton numbers 71 3.1.2 Neutrinos 74 3.1.3 Neutrino mixing and oscillations 76 3.1.4 Neutrino masses 79 3.1.5 Universal lepton interactions – the number of neutrinos 84 3.2 Quarks 86 3.2.1 Evidence for quarks 86 3.2.2 Quark generations and quark numbers 89 3.3 Hadrons 92 3.3.1 Flavour independence and charge multiplets 92 3.3.2 Quark model spectroscopy 96 3.3.3 Hadron masses and magnetic moments 102 Problems 108 4 Experimental Methods 111 4.1 Overview 111 4.2 Accelerators and beams 113 4.2.1 DC accelerators 113 4.2.2 AC accelerators 115 4.2.3 Neutral and unstable particle beams 122 4.3 Particle interactions with matter 123 4.3.1 Short-range interactions with nuclei 123 4.3.2 Ionization energy losses 125 4.3.3 Radiation energy losses 128 4.3.4 Interactions of photons in matter 129 4.4 Particle detectors 131 4.4.1 Gas detectors 131 4.4.2 Scintillation counters 137 4.4.3 Semiconductor detectors 138 4.4.4 Particle identification 139 4.4.5 Calorimeters 142 4.5 Layered detectors 145 Problems 148 5 Quark Dynamics: the Strong Interaction 151 5.1 Colour 151 5.2 Quantum chromodynamics (QCD) 153 5.3 Heavy quark bound states 156 5.4 The strong coupling constant and asymptotic freedom 160 5.5 Jets and gluons 164 5.6 Colour counting 166 CONTENTS ix 5.7 Deep inelastic scattering and nucleon structure 168 Problems 177 6 Electroweak Interactions 181 6.1 Charged and neutral currents 181 6.2 Symmetries of the weak interaction 182 6.3 Spin structure of the weak interactions 186 6.3.1 Neutrinos 187 6.3.2 Particles with mass: chirality 189 6.4 WÆ and Z0 bosons 192 6.5 Weak interactions of hadrons 194 6.5.1 Semileptonic decays 194 6.5.2 Neutrino scattering 198 6.6 Neutral meson decays 201 6.6.1 CP violation 202 6.6.2 Flavour oscillations 206 6.7 Neutral currents and the unified theory 208 Problems 213 7 Models and Theories of Nuclear Physics 217 7.1 The nucleon – nucleon potential 217 7.2 Fermi gas model 220 7.3 Shell model 223 7.3.1 Shell structure of atoms 223 7.3.2 Nuclear magic numbers 225 7.3.3 Spins, parities and magnetic dipole moments 228 7.3.4 Excited states 230 7.4 Non-spherical nuclei 232 7.4.1 Electric quadrupole moments 232 7.4.2 Collective model 236 7.5 Summary of nuclear structure models 236 7.6 -decay 238 7.7 -decay 242 7.7.1 Fermi theory 242 7.7.2 Electron momentum distribution 244 7.7.3 Kurie plots and the neutrino mass 246 7.8 -emission and internal conversion 248 7.8.1 Selection rules 248 7.8.2 Transition rates 250 Problems 252 8 Applications of Nuclear Physics 255 8.1 Fission 255 8.1.1 Induced fission – fissile materials 255 8.1.2 Fission chain reactions 258 8.1.3 Nuclear power reactors 260 8.2 Fusion 266 8.2.1 Coulomb barrier 266 x CONTENTS 8.2.2 Stellar fusion 267 8.2.3 Fusion reaction rates 270 8.2.4 Fusion reactors 273 8.3 Biomedical applications 278 8.3.1 Biological effects of radiation: radiation therapy 278 8.3.2 Medical imaging using radiation 282 8.3.3 Magnetic resonance imaging 290 Problems 294 9 Outstanding Questions and Future Prospects 297 9.1 Particle physics 297 9.1.1 The Higgs boson 297 9.1.2 Grand unification 300 9.1.3 Supersymmetry 304 9.1.4 Particle astrophysics 307 9.2 Nuclear physics 315 9.2.1 The structure of hadrons and nuclei 316 9.2.2 Quark–gluon plasma, astrophysics and cosmology 320 9.2.3 Symmetries and the standard model 323 9.2.4 Nuclear medicine 324 9.2.5 Power production and nuclear waste 326 Appendix A: Some Results in Quantum Mechanics 331 A.1 Barrier penetration 331 A.2 Density of states 333 A.3 Perturbation theory and the Second Golden Rule 335 Appendix B: Relativistic Kinematics 339 B.1 Lorentz transformations and four-vectors 339 B.2 Frames of reference 341 B.3 Invariants 344 Problems 345 Appendix C: Rutherford Scattering 349 C.1 Classical physics 349 C.2 Quantum mechanics 352 Problems 354 Appendix D: Solutions to Problems 355 References 393 Bibliography 397 Index 401 Preface It is common practice to teach nuclear physics and particle physics together in an introductory course and it is for such a course that this book has been written. The material is presented so that different selections can be made for a short course of about 25–30 lectures depending on the lecturer’s preferences and the students’ backgrounds.