Nuclear superfluidity: pairing in finite systems

393 Pages·2005·4.501 MB·English

by  David M. Brink, Ricardo A. Broglia

Nuclear Superfluidity
PairinginFiniteSystems
NuclearSuperfluidityisthefirstmoderntextdevotedexclusivelytopair-correlationsinnuclei.
It begins by exploring pair-correlations in a variety of systems including superconductivity in
metalsatlowtemperaturesandsuperfluidityinliquid3Heandinneutronstars. Thebookgoes
ontointroducebasictheoreticalmethods,symmetrybreakingandsymmetryrestorationinfinite
many-bodysystems. Thelastfourchaptersaredevotedtointroducingnewresultsontheroleof
polarizationeffectsinthestructureofbothnormalandexoticnuclei. Centraltothisdiscussion
isthefactthatwhilebarenucleon–nucleoninteractionsareessentialfortheproductionofpair-
correlationsinnuclei,thecouplingofpairsofnucleonstolow-energynuclearcollectiveexcitations
alsoplaysanimportantrole.
This book will be essential reading for researchers and students in both experimental and
theoretical nuclear physics, and related research fields such as metal clusters, fullerenes and
quantumdots.
DAVID M. BRINKobtainedhisfirstdegreeattheUniversityofTasmaniain1951andhisD.Phil.
atOxfordUniversityin1955.Between1958and1993heheldacademicpositionsintheUniversity
ofOxford,includingaFellowshipatBalliolCollegeandtheMoseleyReadershipinTheoretical
Physics,andtaughtmanybranchesofphysicsatgraduateandundergraduatelevel. From1993
to1998hewasProfessoroftheHistoryofPhysicsattheUniversityofTrentoinItaly. Professor
BrinkisaFellowoftheRoyalSocietyandin1982wasarecipientoftheRutherfordMedalof
the Institute of Physics. He has published several books including Semi-classical Methods in
Nucleus–NucleusScattering(CambridgeUniversityPress,1985).
RICARDO A. BROGLIA earned his Ph.D. at the University of Cuyo, Argentina, in 1965.
Following positions at the University of Buenos Aires, the Niels Bohr Institute and the Uni-
versity of Minnesota, he joined the staff of the Niels Bohr Institute in 1970, where he is now
adjunctProfessor. HehasheldvisitingpositionsattheStateUniversityofNewYorkatStony
Brook,BrookhavenNationalLaboratory,LosAlamosScientificLaboratoryandOakRidgeNa-
tionalLaboratory. In1985hewascalledtooccupythechairofNuclearStructureattheUniversity
ofMilan. ProfessorBroglia’sresearchinterestsincludenuclearstructureandnuclearreactions,
thephysicsofmetalclustersandfullerenes,andthefoldingandaggregationofproteins. Hehas
publishedseveralbooksonthesesubjectsincludingFiniteQuantumSystemsjointlywithGeorge
Bertsch(CambridgeUniversityPress,1994).
CAMBRIDGEMONOGRAPHSON
PARTICLEPHYSICS
NUCLEARPHYSICSANDCOSMOLOGY
24
GeneralEditors:T.Ericson,P.V.Landshoff
1. K.Winter(ed.):NeutrinoPhysics
2. J.F.Donoghue,E.GolowichandB.R.Holstein:DynamicsoftheStandardModel
3. E.LeaderandE.Predazzi:AnIntroductiontoGaugeTheoriesandModernParticlePhysics,Volume
1:ElectroweakInteractions,the‘NewParticles’andthePartonModel
4. E.LeaderandE.Predazzi:AnIntroductiontoGaugeTheoriesandModernParticlePhysics,Volume
2:CP-Violation,QCDandHardProcesses
5. C.Grupen:ParticleDetectors
6. H.GrosseandA.Martin:ParticlePhysicsandtheSchro¨dingerEquation
7. B.Andersson:TheLundModel
8. R.K.Ellis,W.J.StirlingandB.R.Webber:QCDandColliderPhysics
9. I.I.BigiandA.I.Sanda:CPViolation
10. A.V.ManoharandM.B.Wise:HeavyQuarkPhysics
11. R.K.Bock,H.Grote,R.Fru¨hwirthandM.Regler:DataAnalysisTechniquesforHigh-Energy
Physics,Secondedition
12. D.Green:ThePhysicsofParticleDetectors
13. V.N.GribovandJ.Nyiri:QuantumElectrodynamics
14. K.Winter(ed.):NeutrinoPhysics,Secondedition
15. E.Leader:SpininParticlePhysics
16. J.D.Walecka:ElectronScatteringforNuclearandNucleonStructure
17. S.Narison:QCDasaTheoryofHadrons
18. J.F.LetessierandJ.Rafelski:HadronsandQuark–GluonPlasma
19. A.Donnachie,H.G.Dosch,P.V.LandshoffandO.Nachtmann:PomeronPhysicsandQCD
20. A.Hofmann:ThePhysicsofSynchrotronRadiation
21. J.B.KogutandM.A.Stephanov:ThePhasesofQuantumChromodynamics
22. D.Green:HighPt PhysicsatHadronColliders
23. T.Hatsuda,K.YagiandY.Miake:Quark–GluonPlasma
24. D.M.BrinkandR.A.Broglia:NuclearSuperfluidity
Nuclear Superfluidity
Pairing in Finite Systems
DAVIDM.BRINK and RICARDOA.BROGLIA
cambridge university press
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Published in the United States of America by Cambridge University Press, New York
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© Cambridge University Press 2005
This publication is in copyright. Subject to statutory exception and to the provision of
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without the written permission of Cambridge University Press.
First published in print format 2005
isbn-13 978-0-511-11365-9 eBook (NetLibrary)
isbn-10 0-511-11365-x eBook (NetLibrary)
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Contents
Preface pagexi
1 Introduction 1
1.1 Pairinginnuclei,superconductors,liquid3Heandneutronsstars 1
1.2 Macroscopicwavefunctionandphaserigidity 3
1.3 Brokensymmetryandcollectivemodes 6
1.4 Superfluid4He(HeII) 8
1.5 Criticalvelocityforsuperconductors 13
1.6 Pairinginnuclei 14
1.7 Superconductivity 19
1.8 Superfluidityofliquid3He 25
1.9 Comparisonofpairinginnucleiwithsuperconductivity 26
1.10 Neutronstars 30
2 Thepairingforceandseniority 33
2.1 Evidenceforpairingcorrelations 33
2.2 Thepairinginteraction 36
2.3 Theδ-functionnucleon–nucleonpotential 39
2.4 Thedegeneratemodelandquasi-spin 42
2.5 Pairingbindingenergyformula 44
2.6 Quasi-spinwavefunctions 45
2.7 Pairingrotations 47
2.8 ExactsolutionofthepairingHamiltonian 48
3 TheBCStheory 52
3.1 TheBCSwavefunction 52
3.2 Theenergy 55
3.3 Excitedstatesandquasiparticles 57
3.4 Themean-fieldHamiltonian 60
vii
viii Contents
3.5 Thecorrelationenergy 61
3.6 Pairingcorrelationsinthewavefunction 64
3.7 ThedegeneratemodelintheBCSapproximation 65
3.8 Gaugeinvariance 66
3.9 Matrix elements of one-body operators 67
3.10 Pairingandisospin 69
4 Spontaneoussymmetrybreaking 72
4.1 General background 72
4.2 Pairing in atomic nuclei (0D systems; ξ(cid:2)R)75
4.3 Infinite 3D neutral superconductors (ξ(cid:3)L)88
5 Pairingvibrations 92
5.1 The two-level model 92
5.2 Applications 102
5.3 Multipolepairingvibrations 108
6 Phasetransitions 117
6.1 Theexperimentalsituation 119
6.2 Staticpairingcorrelations: theBCStheoryofpairingphasetransitions
instronglyrotatingnuclei 122
6.3 Pairingfluctuations 138
6.4 Momentsofinertia 141
6.5 Condensation-inducedtunnelling 144
6.6 ResponsefunctiontechniquetocalculateRPAfluctuations 145
7 Plasticbehaviourofnucleiandotherfinitesystems 154
7.1 Exoticdecay 155
7.2 Avarietyofapplications 163
7.3 Low-lyingsurfacevibrations 165
7.4 Fissioninmetalclusters 168
8 Sourcesofpairinginnuclei 170
8.1 Thebarenucleon–nucleonpotentialandthepairinginteraction 171
8.2 Mean-fieldtheory 177
8.3 Randomphaseapproximation 184
8.4 Correlationenergycontributiontonuclearmasses 199
9 Beyondmeanfield 204
9.1 Doorwaystates 204
9.2 Effectivemass(ω-mass) 211
9.3 Theω-massandtheinducedinteraction 215
10 Inducedinteraction 219
10.1 Simpleestimates 219
10.2 Microscopiccalculations 223
Contents ix
10.3 Slabmodel 231
10.4 Inducedpairinginteraction,effectivemassandvertexcorrection
processes 239
10.5 Superfluidityintheinnercrustofneutronstars 244
11 Pairinginexoticnuclei 257
11.1 Thehalonucleus11Li 258
11.2 Thehalonucleus12Be 275
AppendixA Abriefre´sume´ ofsecondquantization 280
A.1 Fermions 280
A.2 Particlesandholes 286
A.3 Bosons 288
A.4 Quasi-bosons 290
AppendixB Singleparticleinanon-localpotential 292
B.1 Singleparticleinanon-local,ω-dependentpotential 294
AppendixC Usefulrelationsinthetreatmentofcollectivemodes 297
C.1 Limitonthemultipolarityofcollectivesurfacevibrations 297
C.2 Therelationbetween Fˆ andαˆ 297
AppendixD Particle-vibrationcoupling 299
D.1 Estimateof(cid:4)lj||Y ||lj(cid:5) 301
L
D.2 Asimpleestimateof(cid:4)R ∂U(cid:5) 303
0∂r
AppendixE Modelofthesingle-particlestrengthfunction 305
AppendixF SimplemodelofPauliprinciplecorrections 308
AppendixG Pairingmean-fieldsolution 310
G.1 SolutionofthepairingHamiltonian 310
G.2 Two-quasiparticleexcitations 315
G.3 Minimization 317
G.4 BCSwavefunction 318
AppendixH Pairinginasinglej-shell 320
H.1 BCSsolution 320
H.2 Crankingmomentofinertia 322
H.3 Two-particletransfer 323
H.4 Polarizationeffects 324
AppendixI Fluctuationsandsymmetryrestoration 327
I.1 Conjugatevariables 327
I.2 Rotationaboutanaxis 328
I.3 Rotationsingaugespace 329
I.4 Symmetryrestoringfluctuationsandpairingrotations 330