Graduate Texts in Physics Anwar Kamal Nuclear Physics Graduate Texts in Physics Forfurthervolumes: www.springer.com/series/8431 Graduate Texts in Physics Graduate Texts in Physics publishes core learning/teaching material for graduate- and ad- vanced-levelundergraduatecoursesontopicsofcurrentandemergingfieldswithinphysics, both pure and applied. These textbooks serve students at the MS- or PhD-level and their instructorsascomprehensivesourcesofprinciples,definitions,derivations,experimentsand applications(asrelevant)fortheirmasteryandteaching,respectively.Internationalinscope and relevance, the textbooks correspond to course syllabi sufficiently to serve as required reading.Theirdidacticstyle,comprehensivenessandcoverageoffundamentalmaterialalso makethemsuitableasintroductionsorreferencesforscientistsentering,orrequiringtimely knowledgeof,aresearchfield. SeriesEditors ProfessorRichardNeeds CavendishLaboratory JJThomsonAvenue CambridgeCB30HE,UK [email protected] ProfessorWilliamT.Rhodes DepartmentofComputerandElectricalEngineeringandComputerScience ImagingScienceandTechnologyCenter FloridaAtlanticUniversity 777GladesRoadSE,Room456 BocaRaton,FL33431,USA [email protected] ProfessorSusanScott DepartmentofQuantumScience AustralianNationalUniversity ScienceRoad Acton0200,Australia [email protected] ProfessorH.EugeneStanley CenterforPolymerStudiesDepartmentofPhysics BostonUniversity 590CommonwealthAvenue,Room204B Boston,MA02215,USA [email protected] ProfessorMartinStutzmann WalterSchottkyInstitut TUMünchen 85748Garching,Germany [email protected] Anwar Kamal Nuclear Physics AnwarKamal(deceased) Murphy,TX,USA ISSN1868-4513 ISSN1868-4521(electronic) GraduateTextsinPhysics ISBN978-3-642-38654-1 ISBN978-3-642-38655-8(eBook) DOI10.1007/978-3-642-38655-8 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014941884 ©Springer-VerlagBerlinHeidelberg2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Dedicatedtomyparents Preface This is an introductory textbook of nuclear physics for upper undergraduate stu- dents.ThebookisbasedonlecturesgivenatBritish,AmericanandIndianUniver- sitiesoverseveralyears. The idea of writing a text book on this subject was born some forty years ago. Itisattemptedtosurveythemajordevelopmentsinnuclearphysicsduringthepast 100 years. In Rutherford’s time and early 1950’s, only a few Elementary particles wereknownandtheexistenceoftheneutrinowastakenforgranted.Thedevelop- mentofthesubjectissofascinatingthatwewereinclinedtopresentthehistorical factsinchronologicalorder. The prerequisites for the use of this book are the elements of quantum me- chanicscomprisingSchrodinger’sequationandapplications,Born’sapproximation, thegoldenrule,differentialequationsandVectorCalculus.Basicconceptsareex- plainedwithlinediagramswhereverrequired.Anattemptismadetostrikeabalance between theory and experiment. Theoretical predictions are compared with latest observationstoshowagreementordiscrepancieswiththetheory. The subject matter is developed in each chapter with the necessary mathemat- ical details. Feynman diagrams are used extensively to explain the fundamental interactions. The subjects of various chapters are so much intimately connected that the logical sequential presentation of various topics became a vexing prob- lem. For example, from the point of view of introducing quarks, the logical sequence would be strong, electromagnetic, weak and electroweak interactions, but from the point of view of introducing Feynman’s diagrams, the desirable sequence would be electromagnetic, weak, electroweak and strong interactions, which is why one finds some variance in sequences for particle physics in vari- oustextbooks.Theonlyremedyistomakecrossreferencestothechapterswhich were previously studied and to those in which the relevant material is antici- pated. The size of the book did not allow to also include applied nuclear physics and cosmicrays.Attheendofeachchapter,asetofquestionsisgiven.Alargenumber ofworkedexamplesisadditionallypresented.Acomparablenumberofunworked vii viii Preface problemswithanswershelpsthestudenttotesttheunderstanding.Theexamplesand problemsarenotnecessarilyofplug-intypebutaregiventoexplaintheunderlying physics.Usefulappendicesareprovidedattheendofthebook. Murphy,TX,USA AnwarKamal Note: These two volumes are the last books by my father Dr. Ahmad Kamal, the work he had conceivedas his dream project and indeed his scientific masterpiece. Unfortunately, he passed away before he could see his manuscript in print. While wehavetriedourbesttobringthepublishingprocesstoassatisfactoryconclusion as possible, we regret any errors you may discover, in particular, that some of the referencescouldnotbeascompletelyspecificallycitedaswouldotherwisebethe case.Wetrustthattheseerrorshoweverdonotcompromisethequalityorstandard ofthecontentofthetext. SuraiyaKamal DaughterofDr.AhmadKamal Acknowledgements I am grateful to God for helping us to complete the dream project of Dr. Ahmad Kamalafterhisdemise,whichseemedverydifficultandevenimpossibleattimes. IwouldliketothankSpringer-Verlag,inparticularDr.ClausAsheron,Mr.Do- natas Akmanavicˇius, Ms. Adelheid Duhm and Ms. Elke Sauer for their constant encouragement,patience,cooperation,andforbringingthebooktoitscurrentform. Thisprojectwouldnotbecompletewithouttheconstantsupportandencourage- mentofMrs.MaryamKamal,wifeofDr.AhmadKamal.Herdeterminationkeptus allmovingtogetthesebooksdone.Mysincerethanksisduetothefamily,friends andwell-wishersoftheauthorwhohelpedandprayedforthecompletionofthese books. SuraiyaKamal DaughterofDr.AhmadKamal ix Contents 1 PassageofChargedParticlesThroughMatter . . . . . . . . . . . . 1 1.1 VariousTypesofProcesses . . . . . . . . . . . . . . . . . . . . 1 1.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2.1 Laboratory(Lab)System(LS)andCentreofMass System(CM) . . . . . . . . . . . . . . . . . . . . . . . 1 1.2.2 TotalLinearMomentumintheCMSystemIsZero . . . 2 1.2.3 RelationBetweenVelocitiesintheLSandCMS . . . . 3 1.2.4 RelationBetweentheAnglesinLSandCMS . . . . . . 4 1.2.5 RecoilAngle . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.6 LimitsontheScatteringAngleθ . . . . . . . . . . . . . 6 1.2.7 LimitsontheRecoilAngleϕ . . . . . . . . . . . . . . . 7 1.2.8 ScatteringinThreeDimensions . . . . . . . . . . . . . 8 1.2.9 ScatteringCross-Section . . . . . . . . . . . . . . . . . 9 1.2.10 RelationBetweenDifferentialScatteringCross-Sections 10 1.2.11 KinematicsofElasticCollisions . . . . . . . . . . . . . 11 1.2.12 ToDeriveanExpressionfortheRecoilVelocityv 2 asaFunctionofϕ . . . . . . . . . . . . . . . . . . . . . 12 1.2.13 AvailableEnergyintheLabSystemandCMSystem . . 12 1.3 RutherfordScattering . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.1 DerivationofScatteringFormula . . . . . . . . . . . . . 20 1.3.2 Darwin’sFormula. . . . . . . . . . . . . . . . . . . . . 27 1.3.3 Mott’sFormula . . . . . . . . . . . . . . . . . . . . . . 28 (cid:2) 1.3.4 Cross-SectionforScatteringintheAngularIntervalθ (cid:2)(cid:2) andθ . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3.5 ProbabilityofScattering . . . . . . . . . . . . . . . . . 28 1.3.6 RutherfordScatteringintheLSandCMSystem . . . . 29 1.3.7 ValidityofClassicalDescriptionofScattering . . . . . . 31 1.3.8 CoulombScatteringwithaShieldedPotentialUnder Born’sApproximation . . . . . . . . . . . . . . . . . . 32 1.3.9 DiscussionofRutherford’sFormula . . . . . . . . . . . 33 xi