Nuclear Physics

625 Pages·2014·7.03 MB·English

by  Anwar Kamal (auth.)

Graduate Texts in Physics
Anwar Kamal
Nuclear Physics
Graduate Texts in Physics
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Graduate Texts in Physics
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ProfessorMartinStutzmann
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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
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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