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This page intentionally left blankAn Introduction to Nuclear PhysicsThis clear and concise introduction to nuclear physics provides an excel-lent basis for a `core' undergraduate course in this area.The book opens by setting nuclear physics in the context of elemen-tary particle physics and then shows how simple models can provide anunderstanding of the properties of nuclei, both in their ground states andexcited states, and also of the nature of nuclear reactions. The bookincludes chapters on nuclear ssion, its application in nuclear powerreactors, and the role of nuclear physics in energy production and nucleo-synthesis in stars.This new edition contains several additional topics: muon-catalysedfusion, the nuclear and neutrino physics of supernovae, neutrino massand neutrino oscillations, and the biological effects of radiation.A knowledge of basic quantum mechanics and special relativity isassumed. Appendices deal with other more specialised topics. Each chap-ter ends with a set of problems for which outline solutions are provided.NOEL COTTINGHAM and DEREK GREENWOOD are theoreticians working inthe H. H. Wills Physics Laboratory at the University of Bristol. NoelCottingham is also a visiting professor at the Universite Pierre et MarieCurie, Paris.They have also collaborated in an undergraduate text, Electricity andMagnetism, and a graduate text, An Introduction to the Standard Model ofParticle Physics. Both books are published by the Cambridge UniversityPress.An Introduction toNuclear PhysicsSecond editionW. N. COTTINGHAMUniversity of BristolD. A. GREENWOODUniversity of Bristoliuniisuio n\ rui iiiss s\xoicari oi rui uxiviisir\ oi caxniiociThe Pitt Building, Trumpington Street, Cambridge, United Kingdomcaxniioci uxiviisir\ iiissThe Edinburgh Building, Cambridge CB2 2RU, UK40 West 20th Street, New York, NY 10011-4211, USA477 Williamstown Road, Port Melbourne, VIC 3207, AustraliaRuiz de Alarcn 13, 28014 Madrid, SpainDock House, The Waterfront, Cape Town 8001, South Africahttp://www.cambridge.orgFirst published in printed format ISBN 0-521-65149-2 hardbackISBN 0-521-65733-4 paperbackISBN 0-511-04046-6 eBookCambridge University Press 1986, 2004First published 1986Reprinted 1987 (with corrections and additions), 1988, 1990, 1992, 1998Second edition 20012001(netLibrary)ContentsPreface to the second edition ixPreface to the rst edition xConstants of nature, conversion factors and notation xiiGlossary of some important symbols xiii1 Prologue 11.1 Fermions and bosons 21.2 The particle physicist's picture of nature 21.3 Conservation laws and symmetries: parity 31.4 Units 4Problems 52 Leptons and the electromagnetic and weak interactions 72.1 The electromagnetic interaction 72.2 The weak interaction 92.3 Mean life and half life 122.4 Leptons 132.5 The instability of the heavy leptons: muon decay 152.6 Parity violation in muon decay 16Problems 173 Nucleons and the strong interaction 193.1 Properties of the proton and the neutron 193.2 The quark model of nucleons 213.3 The nucleonnucleon interaction: the phenomenologicaldescription 223.4 Mesons and the nucleonnucleon interaction 263.5 The weak interaction: -decay 283.6 More quarks 293.7 The Standard Model of particle physics 31Problems 31vvi Contents4 Nuclear sizes and nuclear masses 334.1 Electron scattering by the nuclear charge distribution 334.2 Muon interactions 364.3 The distribution of nuclear matter in nuclei 374.4 The masses and binding energies of nuclei in their groundstates 394.5 The semi-empirical mass formula 414.6 The -stability valley 444.7 The masses of the -stable nuclei 484.8 The energetics of -decay and ssion 504.9 Nuclear binding and the nucleonnucleon potential 52Problems 525 Ground-state properties of nuclei: the shell model 565.1 Nuclear potential wells 565.2 Estimates of nucleon energies 585.3 Energy shells and angular momentum 605.4 Magic numbers 655.5 The magnetic dipole moment of the nucleus 665.6 Calculation of the magnetic dipole moment 675.7 The electric quadrupole moment of the nucleus 68Problems 726 Alpha decay and spontaneous ssion 746.1 Energy release in -decay 746.2 The theory of -decay 756.3 Spontaneous ssion 83Problems 877 Excited states of nuclei 897.1 The experimental determination of excited states 897.2 Some general features of excited states 937.3 The decay of excited states: -decay and internal conversion 977.4 Partial decay rates and partial widths 997.5 Excited states arising from -decay 100Problems 1018 Nuclear reactions 1038.1 The BreitWigner formula 1038.2 Neutron reactions at low energies 1078.3 Coulomb effects in nuclear reactions 1098.4 Doppler broadening of resonance peaks 111Problems 1139 Power from nuclear ssion 1159.1 Induced ssion 1159.2 Neutron cross-sections for 235U and 238U 1169.3 The ssion process 1189.4 The chain reaction 1199.5 Nuclear ssion reactors 1219.6 Reactor control and delayed neutrons 1229.7 Production and use of plutonium 1249.8 Radioactive waste 1259.9 The future of nuclear power 126Problems 12710 Nuclear fusion 13010.1 The Sun 13010.2 Cross-sections for hydrogen burning 13210.3 Nuclear reaction rates in a plasma 13510.4 Other solar reactions 13910.5 Solar neutrinos 14010.6 Fusion reactors 14310.7 Muon-catalysed fusion 146Problems 14811 Nucleosynthesis in stars 15111.1 Stellar evolution 15111.2 From helium to silicon 15511.3 Silicon burning 15611.4 Supernovae 15711.5 Nucleosynthesis of heavy elements 160Problems 16112 Beta decay and gamma decay 16312.1 What must a theory of -decay explain? 16312.2 The Fermi theory of -decay 16612.3 Electron and positron energy spectra 16812.4 Electron capture 17112.5 The Fermi and GamowTeller interactions 17312.6 The constants Vud and gA 17712.7 Electron polarisation 17812.8 Theory of -decay 17912.9 Internal conversion 184Problems 18513 Neutrinos 18613.1 Neutrino cross-sections 18613.2 The mass of the electron neutrino 18813.3 Neutrino mixing and neutrino oscillations 189Contents vii13.4 Solar neutrinos 19313.5 Atmospheric neutrinos 195Problems 19614 The passage of energetic particles through matter 19914.1 Charged particles 19914.2 Multiple scattering of charged particles 20614.3 Energetic photons 20714.4 The relative penetrating power of energetic particles 211Problems 21215 Radiation and life 21415.1 Ionising radiation and biological damage 21415.2 Becquerels (and curies) 21515.3 Grays and sieverts (and rads and rems) 21615.4 Natural levels of radiation 21715.5 Man-made sources of radiation 21815.6 Risk assessment 219Problems 220Appendix A: Cross-sections 222A.1 Neutron and photon cross-sections 222A.2 Differential cross-sections 224A.3 Reaction rates 225A.4 Charged particle cross-sections: Rutherford scattering 226Appendix B: Density of states 227Problems 230Appendix C: Angular momentum 230C.1 Orbital angular momentum 230C.2 Intrinsic angular momentum 232C.3 Addition of angular momenta 233C.4 The deuteron 234Problems 235Appendix D: Unstable states and resonances 235D.1 Time development of a quantum system 236D.2 The formation of excited states in scattering: resonancesand the BreitWigner formula 241Problems 244Further reading 245Answers to problems 246Index 267viii ContentsPreface to the second editionThe main structure of the rst edition has been retained, but we havetaken the opportunity in this second edition to update the text and clarifyan occasional obscurity. The text has in places been expanded, and alsoadditional topics have been added. The growing interest of physics stu-dents in astrophysics has encouraged us to extend our discussions of thenuclear and neutrino physics of supernovae, and of solar neutrinos. Thereis a new chapter devoted to neutrino masses and neutrino oscillations. Inother directions, a description of muon-catalysed fusion has beenincluded, and a chapter on radiation physics introduces an importantapplied eld.We should like to thank Dr John Andrews and Professor DenisHenshaw for their useful comments on parts of the text, Mrs VictoriaParry for her secretarial assistance, and Cambridge University Press fortheir continuing support.W. N. CottinghamD. A. GreenwoodBristol, March 2000ixPreface to the rst editionIn writing this text we were concerned to assert the continuing importanceof nuclear physics in an undergraduate physics course. We set the subjectin the context of current notions of particle physics. Our treatment ofthese ideas, in Chapters 1 to 3, is descriptive, but it provides a unifyingfoundation for the rest of the book. Chapter 12, on [-decay, returns tothe basic theory. It also seems to us important that a core course shouldinclude some account of the applications of nuclear physics in contro