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Fundamentals in Nuclear Physics The Ecole Polytechnique, one of France’s top academic institutions, has a long- standing tradition of producing exceptional scientific textbooks for its students. Theoriginallecturenotes,theCoursdel’EcolePolytechnique,whichwerewritten byCauchyandJordaninthenineteenthcentury,areconsideredtobelandmarks in the development of mathematics. The present series of textbooks is remarkable in that the texts incorporate the most recent scientific advances in courses designed to provide undergraduate students with the foundations of a scientific discipline. An outstanding level of quality is achieved in each of the seven scientific fields taught at the Ecole: pure and applied mathematics, mechanics, physics, chemistry, biology, and econom- ics. The uniform level of excellence is the result of the unique selection of academic staff there which includes, in addition to the best researchers in its own renowned laboratories, a large number of world-famous scientists, appointed as part-time professors or associate professors, who work in the most advanced research centers France has in each field. Another distinctive characteristics of these courses is their overall consistency; each course makes appropriate use of relevant concepts introduced in the other textbooks.ThisisbecauseeachstudentattheEcolePolytechniquehastoacquire basic knowledge in the seven scientific fields taught there, so a substantial link between departments is necessary. The distribution of these courses used to be restrictedtothe900studentsattheEcole.Someyearsagowewereverysuccess- ful in making these courses available to a larger French-reading audience. We now build on this success by making these textbooks also available in English. Jean-Louis Basdevant James Rich Michel Spiro Fundamentals In Nuclear Physics From Nuclear Structure to Cosmology With 184 Figures Prof. Jean-Louis Basdevant Dr. James Rich Ecole Polytechnique Dapnia-SPP De´partement de Physique CEA-Saclay Laboratoire Leprince-Ringuet 91191 Gif-sur-Yvette 91128 Palaiseau France France [email protected] [email protected] Dr. Michel Spiro IN2P3-CNRS 3 Rue Michel-Ange 75794 Paris cedex 16 France [email protected] Coverillustration:Backgroundimage—PhotographofSupernova1987ARings.PhotocreditChris- topherBurrows(ESA/STScI)andNASA,HubbleSpaceTelescope,1994.Smallerimages,fromtop tobottom—PhotographofSupernovaBlast.PhotocreditChunShingJasonPun(NASA/GSFC), RobertP.Kirshner(Harvard-SmithsonianCenterforAstrophysics),andNASA,1997.Interiorof theJETtorus.Copyright1994EFDA-JET.Seefigure7.6forfurtherdescription.Thecombustion chamberattheNovalaserfusionfacility(LawrenceLivermoreNationalLaboratory,USA).Inside thecombustionchamberattheNovalaserfusionfacility(LawrenceLivermoreNationalLabora- tory,USA)TheEuratomJointResearchCentresandAssociatedCentre. LibraryofCongressCataloging-in-PublicationData Basdevant,J.-L.(Jean-Louis) Fundamentalsinnuclearphysics/J.-L.Basdevant,J.Rich,M.Spiro. p.cm. Includesbibliographicalreferencesandindex. ISBN0-387-01672-4(alk.paper) 1. Nuclearphysics. I. Rich,James,1952– II. Spiro,M.(Michel) III. Title. QC173.B277 2004 539.7—dc22 2004056544 ISBN0-387-01672-4 Printedonacid-freepaper. ©2005SpringerScience+BusinessMedia,Inc. All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,com- putersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisfor- bidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if theyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornot theyaresubjecttoproprietaryrights. PrintedintheUnitedStatesofAmerica. (EB) 9 8 7 6 5 4 3 2 1 SPIN10925645 springeronline.com Preface Nuclear physics began one century ago during the “miraculous decade” between 1895 and 1905 when the foundations of practically all modern physics were established. The period started with two unexpected spinoffs of the Crooke’s vacuum tube: Roentgen’s X-rays (1895) and Thomson’s electron (1897), the first elementary particle to be discovered. Lorentz and Zeemann developed the the theory of the electron and the influence of magnetism on radiation. Quantum phenomenology began in December, 1900 with the ap- pearance of Planck’s constant followed by Einstein’s 1905 proposal of what is now called the photon. In 1905, Einstein also published the theories of relativity and of Brownian motion, the ultimate triumph of Boltzman’s sta- tisticaltheory,ayearbeforehistragicdeath.Fornuclearphysics,thecritical discovery was that of radioactivity by Becquerel in 1896. By analyzing the history of science, one can be convinced that there is some rationale in the fact that all of these discoveries came nearly simul- taneously, after the scientifically triumphant 19th century. The exception is radioactivity,anunexpectedbabywhosediscoverycouldhavehappenedsev- eral decades earlier. Talentedscientists,theCuries,Rutherford,andmanyothers,tooktheob- servationofradioactivityandconstructedtheideasthatarethesubjectofthis book.Ofcourse,thediscoveryofradioactivityandnuclearphysicsisofmuch broader importance. It lead directly to quantum mechanics via Rutherford’s planetaryatomicmodelandBohr’sinterpretationofthehydrogenspectrum. This in turn led to atomic physics, solid state physics, and material science. Nuclearphysicshadtheimportantby-productofelementaryparticlephysics and the discovery of quarks, leptons, and their interactions. These two fields are actually impossible to dissociate, both in their conceptual and in their experimental aspects. Thesame“magicdecade”occurredinothersectorsofhumanactivity.The secondindustrialrevolutionisoneaspect,withthedevelopmentofradioand telecommunications. Theautomobileindustry developed atthesameperiod, with Daimler, Benz, Panhard and Peugeot. The Wright brothers achieved a dream of mankind and opened the path of a revolution in transportation. MedicineandbiologymadeincredibleprogresswithLouisPasteurandmany others. In art, we mention the first demonstration of the “cinématographe” VI Preface by Auguste and Louis Lumière on december 28 1895, at the Grand Café, on Boulevard des Capucines in Paris and the impressionnist exhibition in Paris in 1896. Nowadays, is is unthinkable that a scientific curriculum bypass nuclear physics. It remains an active field of fundamental research, as heavy ion accelerators of Berkeley, Caen, Darmstadt and Dubna continue to produce new nuclei whose characteristics challenge models of nuclear structure. It has major technological applications, most notably in medicine and in energy production where a knowledge of some nuclear physics is essential for participation in decisions that concern society’s future. Nuclear physics has transformed astronomy from the study of planetary trajectoriesintotheastrophysicalstudyofstellarinteriors.Nodoubtthemost important result of nuclear physics has been an understanding how the ob- served mixture of elements, mostly hydrogen and helium in stars and carbon and oxygen in planets, was produced by nuclear reactions in the primordial universe and in stars. This book emerged from a series of topical courses we delivered since the late 1980’s in the Ecole Polytechnique. Among the subjects studied were the physics of the Sun, which uses practically all fields of physics, cosmology for which the same comment applies, and the study of energy and the environ- ment. This latter subject was suggested to us by many of our students who felt a need for deeper understanding, given the world in which they were going to live. In other words, the aim was to write down the fundamentals of nuclear physics in order to explain a number of applications for which we felt a great demand from our students. Such topics do not require the knowledge of modern nuclear theory that is beautifully described in many books, such as The Nuclear Many Body Problem by P. Ring and P Schuck. Intentionally, we have not gone into such developments. In fact, even if nuclear physics had stopped, say, in 1950 or 1960, practically all of its applications would exist nowadays. These applications result from phenomena which were known at that time, and need only qualitative explanations. Much nuclear phenomenology can be under- stoodfromsimpleargumentsbasedonthingslikethePauliprincipleandthe Coulomb barrier. That is basically what we will be concerned with in this book. On the other hand, the enormous amount of experimental data now easily accesible on the web has greatly facilitated the illustration of nuclear systematics and we have made ample use of these resources. This book is an introduction to a large variety of scientific and technological fields. It is a first step to pursue further in the study of such or such an aspect. We have taught it at the senior undergraduate level at the Ecole Polytechnique. We believe that it may be useful for graduate students, or more generally scientists, in a variety of fields. In the first three chapters, we present the “scene” , i.e. we give the basic notions which are necessary to develop the rest. Chapter 1 deals with the Preface VII basic concepts in nuclear physics. In chapter 2, we describe the simple nuclear models, and discuss nuclear stability. Chapter 3 is devoted to nuclear reactions. Chapter 4 goes a step further. It deals with nuclear decays and the fundamental electro-weak interactions. We shall see that it is possible to give a comparatively simple, but sound, description of the major progress particle physics and fundamental interactions made since the late 1960’s. In chapter 5, we turn to the first important practical application, i.e. radioactivity. We shall see examples of how radioactivity is used be it in medicine, in food industry or in art. Chapters6and7concernnuclearenergy.Chapter6dealswithfissionand thepresentaspectsofthatsourceofenergyproduction.Chapter7dealswith fusion which has undergone quite remarkable progress, both technologically and politically in recent years with the international ITER project. Fusion brings us naturally, in chapter 8 to the subject of nuclear as- trophysics and stellar structure and evolution. Finally, we present an introduction to present ideas about cosmology in chapter 9. A more advanced description can be found in Fundamentals of Cosmology, written by one of us (J. R.). We want to pay a tribute to the memory of Dominique Vautherin, who constantly provided us with ideas before his tragic death in December 2000. We are grateful to Martin Lemoine, Robert Mochkovitch, Hubert Flocard, Vincent Gillet, Jean Audouze and Alfred Vidal-Madjar for their invaluable helpandadvicethroughouttheyears.WealsothankMichelCassé,Bertrand Cordier, Michel Cribier, David Elbaz, Richard Hahn, Till Kirsten, Sylvaine Turck-Chièze, and Daniel Vignaud for illuminating discussions on various aspects of nuclear physics. Palaiseau, France Jean-Louis Basdevant, James Rich, Michel Spiro April, 2005 Contents Introduction.................................................. 1 1. Basic concepts in nuclear physics ......................... 9 1.1 Nucleons and leptons ................................... 9 1.2 General properties of nuclei.............................. 11 1.2.1 Nuclear radii.................................... 12 1.2.2 Binding energies ................................. 14 1.2.3 Mass units and measurements...................... 17 1.3 Quantum states of nuclei ............................... 25 1.4 Nuclear forces and interactions ........................... 29 1.4.1 The deuteron .................................... 31 1.4.2 The Yukawa potential and its generalizations ........ 35 1.4.3 Origin of the Yukawa potential..................... 38 1.4.4 From forces to interactions ........................ 39 1.5 Nuclear reactions and decays............................. 41 1.6 Conservation laws ...................................... 43 1.6.1 Energy-momentum conservation.................... 44 1.6.2 Angular momentum and parity (non)conservation .... 46 1.6.3 Additive quantum numbers........................ 46 1.6.4 Quantum theory of conservation laws ............... 48 1.7 Charge independence and isospin ......................... 51 1.7.1 Isospin space .................................... 51 1.7.2 One-particle states ............................... 52 1.7.3 The generalized Pauli principle..................... 55 1.7.4 Two-nucleon system .............................. 55 1.7.5 Origin of isospin symmetry; n-p mass difference ...... 56 1.8 Deformed nuclei........................................ 58 1.9 Bibliography........................................... 62 Exercises .................................................. 62 2. Nuclear models and stability.............................. 67 2.1 Mean potential model................................... 69 2.2 The Liquid-Drop Model ................................. 74 2.2.1 The Bethe–Weizsäcker mass formula ............... 74 X Contents 2.3 The Fermi gas model ................................... 77 2.3.1 Volume and surface energies ....................... 79 2.3.2 The asymmetry energy............................ 81 2.4 The shell model and magic numbers ...................... 81 2.4.1 The shell model and the spin-orbit interaction ....... 85 2.4.2 Some consequences of nuclear shell structure......... 88 2.5 β-instability ........................................... 90 2.6 α-instability ........................................... 94 2.7 Nucleon emission ....................................... 98 2.8 The production of super-heavy elements................... 100 2.9 Bibliography........................................... 101 Exercises .................................................. 101 3. Nuclear reactions......................................... 107 3.1 Cross-sections.......................................... 108 3.1.1 Generalities...................................... 108 3.1.2 Differential cross-sections.......................... 111 3.1.3 Inelastic and total cross-sections.................... 112 3.1.4 The uses of cross-sections.......................... 113 3.1.5 General characteristics of cross-sections ............. 115 3.2 Classical scattering on a fixed potential ................... 121 3.2.1 Classical cross-sections ............................ 122 3.2.2 Examples ....................................... 123 3.3 Quantum mechanical scattering on a fixed potential ........ 126 3.3.1 Asymptotic states and their normalization........... 127 3.3.2 Cross-sections in quantum perturbation theory....... 129 3.3.3 Elastic scattering................................. 132 3.3.4 Quasi-elastic scattering............................ 135 3.3.5 Scattering of quantum wave packets ................ 136 3.4 Particle–particle scattering .............................. 143 3.4.1 Scattering of two free particles ..................... 143 3.4.2 Scattering of a free particle on a bound particle ...... 146 3.4.3 Scattering on a charge distribution ................. 149 3.4.4 Electron–nucleus scattering ........................ 151 3.4.5 Electron–nucleon scattering........................ 153 3.5 Resonances ............................................ 157 3.6 Nucleon–nucleus and nucleon–nucleon scattering............ 161 3.6.1 Elastic scattering................................. 161 3.6.2 Absorption ...................................... 167 3.7 Coherent scattering and the refractive index ............... 169 3.8 Bibliography........................................... 171 Exercises .................................................. 171 Contents XI 4. Nuclear decays and fundamental interactions ............. 175 4.1 Decay rates, generalities................................. 175 4.1.1 Natural width, branching ratios .................... 175 4.1.2 Measurement of decay rates ....................... 176 4.1.3 Calculation of decay rates ........................ 178 4.1.4 Phase space and two-body decays .................. 183 4.1.5 Detailed balance and thermal equilibrium ........... 184 4.2 Radiative decays ....................................... 187 4.2.1 Electric-dipole transitions ......................... 188 4.2.2 Higher multi-pole transitions....................... 190 4.2.3 Internal conversion ............................... 193 4.3 Weak interactions ...................................... 195 4.3.1 Neutron decay ................................... 196 4.3.2 β-decay of nuclei ................................. 202 4.3.3 Electron-capture ................................. 207 4.3.4 Neutrino mass and helicity ........................ 209 4.3.5 Neutrino detection................................ 214 4.3.6 Muon decay ..................................... 218 4.4 Families of quarks and leptons ........................... 221 4.4.1 Neutrino mixing and weak interactions.............. 221 4.4.2 Quarks.......................................... 228 4.4.3 Quark mixing and weak interactions ................ 232 4.4.4 Electro-weak unification........................... 235 4.5 Bibliography........................................... 241 Exercises .................................................. 241 5. Radioactivity and all that ................................ 245 5.1 Generalities............................................ 245 5.2 Sources of radioactivity ................................. 246 5.2.1 Fossil radioactivity ............................... 247 5.2.2 Cosmogenic radioactivity.......................... 252 5.2.3 Artificial radioactivity ............................ 254 5.3 Passage of particles through matter....................... 256 5.3.1 Heavy charged particles ........................... 257 5.3.2 Particle identification ............................. 263 5.3.3 Electrons and positrons ........................... 265 5.3.4 Photons......................................... 266 5.3.5 Neutrons ........................................ 269 5.4 Radiation dosimetry .................................... 270 5.5 Applications of radiation ................................ 273 5.5.1 Medical applications .............................. 273 5.5.2 Nuclear dating ................................... 274 5.5.3 Other uses of radioactivity ........................ 280 5.6 Bibliography........................................... 281 Exercises .................................................. 282