Physics of Atomic Nuclei

665 Pages·2017·7.039 MB·English

by  Vladimir Zelevinsky, Alexander Volya

PhysicsofAtomicNuclei
Iliadis,C.
NuclearandParticlePhysics – An NuclearPhysicsofStars
Introduction2e
2Edition
2009
2015
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Griffiths,D.
Lilley,J.
IntroductiontoElementary
NuclearPhysics – Principles&
Particles
Applications
2Edition
2001
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Stock,R.(ed.)
Kratz,J.,Lieser,K.H.
EncyclopediaofNuclearPhysics
NuclearandRadiochemistry anditsApplications
FundamentalsandApplications
2013
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Physics of Atomic Nuclei
VladimirZelevinsky
AlexanderVolya
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v
Contents
Dedication xiii
Preface xv
1 BuildingBlocksandInteractions 1
1.1 WhatAretheNucleiMadeOf? 1
1.2 ProtonandNeutron 3
1.3 StrongInteractions 4
1.4 ElectromagneticInteractionsandChargeDistribution 5
1.5 MagneticProperties 10
1.6 WeakInteractions 11
1.7 NeutronDecay 13
1.8 NuclearWorld 15
References 19
2 Isospin 21
2.1 QuantumNumbersintheTwo-BodyProblem 21
2.2 IntroducingIsospin 23
2.3 IsospinInvariance 25
2.4 Space–SpinSymmetryandIsospinInvariance 26
2.5 GlimpseofaMoreGeneralPicture 30
2.6 RelationsbetweenCrossSections 31
2.7 SelectionRules 35
2.8 IsobaricMassFormulae 38
References 41
3 Two-BodyDynamicsandtheDeuteron 43
3.1 Low-EnergyNuclearForces 43
3.2 Example:ArgonnePotential 45
3.3 MesonExchange 48
3.4 Deuteron:CentralForcesands-Wave 51
3.5 TensorForcesandd-Wave 55
3.6 MagneticDipoleMoment 58
3.7 ElectricQuadrupoleMoment 59
References 65
vi Contents
4 Two-BodyScattering 67
4.1 ScatteringProblem 67
4.2 PhaseShifts 69
4.3 ScatteringLength 71
4.4 SignoftheScatteringLength 78
4.5 ResonanceScatteringatLowEnergies 80
4.6 EffectiveRadius 82
4.7 ScatteringofIdenticalParticles 83
4.8 CoulombScattering 86
4.9 Coulomb-NuclearInterference 87
References 89
5 LiquidDropModel 91
5.1 BindingEnergies 91
5.2 ShapeVariables 95
5.3 MicroscopicVariables 97
5.4 MultipoleMoments 98
5.5 KineticEnergyandInertialParameters 100
5.6 ShapeVibrations 102
5.7 StabilityoftheChargedSphericalLiquidDrop 104
References 111
6 VibrationsofaSphericalNucleus 113
6.1 SoundWaves 113
6.2 IsovectorModes 117
6.3 GiantResonanceandLinearResponse 119
6.4 ClassificationofNormalModes 121
6.5 QuantizationofNuclearVibrationalModes 125
6.6 MultiphononExcitations 128
6.7 AngularMomentumClassification 132
References 134
7 FermiGasModel 135
7.1 MeanFieldandQuasiparticles 135
7.2 PerfectFermiGas 137
7.3 GroundState 138
7.4 CorrelationBetweenParticles 142
7.5 AsymmetricSystemsandChemicalEquilibrium 143
7.6 PressureandSpeedofSound 146
7.7 GravitationalEquilibrium 148
7.8 NuclearMatterEquationofState 150
References 151
8 SphericalMeanField 153
8.1 Introduction 153
8.2 MagicNumbers 153
8.3 SeparationEnergy 155
Contents vii
8.4 PeriodicityofNuclearSpectra 156
8.5 HarmonicOscillatorPotential 157
8.6 OrbitalMomentumRepresentation 160
8.7 SquareWellPotential 162
8.8 Spin–OrbitCoupling 163
8.9 RealisticLevelScheme 165
8.10 SemiclassicalOriginsofShellStructure 166
References 168
9 IndependentParticleShellModel 169
9.1 ShellModelConfigurations 169
9.2 Particle–HoleSymmetry 171
9.3 MagneticMoment 172
9.4 QuadrupoleMoment 174
9.5 RecoilCorrections 177
9.6 IntroductiontoGroupTheoryofMultiparticleConfigurations 178
References 183
10 LightNuclei 185
10.1 AShortWalkalongtheBeginningoftheNuclearChart 185
10.2 HaloinQuantumSystems 190
10.3 NuclearHalos 192
10.4 One-BodyHalo 193
10.5 Two-BodyHalos 195
10.6 EfimovStates 199
References 202
11 Many-BodyOperatorFormalism 203
11.1 SecondaryQuantization 203
11.2 PhysicalObservables:One-BodyOperators 208
11.3 Two-BodyOperators 209
11.4 InterparticleInteraction 210
11.5 InteractioninaSphericalBasis 213
11.6 RecouplingofAngularMomentum 215
References 222
12 NuclearDeformation 223
12.1 IdeaofNuclearDeformation 223
12.2 CollectiveModel 224
12.3 AdiabaticApproximation 226
12.4 OnsetofDeformation 228
12.5 QuadrupoleDeformationintheBody-FixedFrame 230
12.6 QuadrupoleShapeVariables 232
12.7 VarietyofQuadrupoleShapes 233
12.8 EmpiricalDeformation 235
12.9 Single-ParticleQuantumNumbers 239
12.10 AnisotropicHarmonicOscillator 240
12.11 AsymptoticQuantumNumbers 245
viii Contents
12.12 NilssonPotential 246
12.13 MoreExamples 247
References 250
13 PairingCorrelations 251
13.1 PhysicalEvidence 251
13.2 SeniorityScheme 256
13.3 MultipoleMomentsintheSeniorityScheme 260
13.4 DegenerateModel 261
13.5 CanonicalTransformation 265
13.6 BCSTheory:TrialWaveFunction 269
13.7 EnergyMinimization 271
13.8 SolutionfortheEnergyGap 273
13.9 ExcitationSpectrum 276
13.10 CondensationEnergy 278
13.11 TransitionAmplitudes 279
References 281
14 Gamma-Radiation 283
14.1 Introduction 283
14.2 ElectromagneticFieldandGaugeInvariance 283
14.3 Photons 285
14.4 InteractionofRadiationwithMatter 288
14.5 RadiationProbability 291
14.6 ElectricDipoleRadiation 292
14.7 ElectricQuadrupoleRadiation 295
14.8 MagneticDipoleRadiation 296
14.9 Photoabsorption 298
14.10 MultipoleExpansion 299
References 303
15 NuclearGamma-TransitionsandRelatedElectromagnetic
Processes 305
15.1 Single-ParticleTransitions 305
15.2 CollectiveTransitions 308
15.3 NuclearIsomerism 310
15.4 Isospin 312
15.5 StructuralSelectionRules 315
15.6 MonopoleTransitions 318
15.7 InternalElectronConversion 320
15.8 CoulombExcitation 322
15.9 NuclearPhotoeffect 326
15.10 ElectronScattering 330
References 335
16 NuclearRotation 337
16.1 Introduction:RotationalBands 337
Contents ix
16.2 FiniteRotations 345
16.3 RotationMatricesasFunctionsontheGroup 346
16.4 EulerAngles 347
16.5 AngularMomentuminEulerAngles 351
16.6 EigenfunctionsofAngularMomentum 354
16.7 RigidRotor 355
16.8 SymmetryProperties 357
16.9 SimplestSolutions 358
16.10 Ground-StateBand 359
16.11 IntensityRules 360
16.12 ElectricQuadrupoleMoment 363
16.13 MagneticMoment 366
16.14 SymmetryPropertiesRevisited 367
16.15 CoriolisMixingandDecouplingParameter 368
16.16 ClassicalRotationandRouthian 370
16.17 CrankedRotation 372
16.18 MomentofInertia 375
16.19 AdiabaticExpansion 377
16.20 RotationofaPerfectFermiGas 379
16.21 PerfectBoseGasandIdealLiquid 381
16.22 PairingEffects 384
16.23 BandCrossing 385
References 388
17 Self-ConsistentField 391
17.1 ExchangeInteraction 391
17.2 Hartree–FockEquations 395
17.3 OperatorFormulation 397
17.4 Single-ParticleDensityMatrix 398
17.5 Hartree–Fock–BogoliubovApproximation 400
17.6 GeneralCanonicalTransformation 402
17.7 Solutions 404
17.8 GeneralizedDensityMatrix 407
17.9 PairingandParticleNumberConservation 409
17.10 EffectiveInteraction 411
17.11 SkyrmeFunctionals 413
17.12 GeneralizationtoNonzeroTemperature 418
References 419
18 CollectiveModes 421
18.1 SchematicModel 421
18.2 RandomPhaseApproximation 426
18.3 CanonicalFormoftheRPA 427
18.4 ModelwithFactorizedForces 430
18.5 CollectiveModesasBosons 432
18.6 MappingofDynamics 433
18.7 NormalizationandtheMassParameter 435
x Contents
18.8 SymmetryBreaking 438
18.9 GeneratorCoordinateMethod 444
References 446
19 Bosons,SymmetriesandGroupModels 447
19.1 Introduction 447
19.2 Low-LyingQuadrupoleExcitationsasInteractingBosons 448
19.3 AlgebraofBosonOperators 450
19.4 SubgroupsandCasimirOperators 452
19.5 s–dModel 455
19.6 IrreducibleRepresentationsandQuantumNumbers 458
19.7 VibrationalLimit 461
19.8 (6)Limit 466
19.9 (3)Limit 468
19.10 ShapesandPhaseTransitionsintheIBM 470
References 473
20 StatisticalProperties 475
20.1 Introduction 475
20.2 LevelDensity:GeneralProperties 478
20.3 Darwin–FowlerMethod 480
20.4 RelationtoStatisticalThermodynamics 482
20.5 ThermodynamicsofaNuclearFermiGas 483
20.6 StatisticsofAngularMomentum 486
20.7 ShellModelMonteCarloApproach 488
20.8 ThermodynamicsofCompoundReactions 490
20.9 StatisticalDescriptionofResonances 492
References 497
21 NuclearFission 499
21.1 Introduction 499
21.2 Alpha-Decay 502
21.3 NeutronFission 505
21.4 Photofission 509
21.5 FissionasaLarge-AmplitudeCollectiveMotion 510
21.6 NonadiabaticEffectsandDissipation 512
21.7 FissionIsomers 514
21.8 ParityViolationinFission 518
References 522
22 Heavy-ionReactions:SelectedTopics 525
22.1 Introduction 525
22.2 ExperimentalIndications 526
22.3 MacroscopicDescription 530
22.4 EquilibrationasaDiffusionProcess 534
22.5 TowardaMicroscopicDescription 540
22.6 SketchofaMoreGeneralApproach 541