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1．Introduction1

1.1 Nuclear Structure Physics1

1.2 The Basic Equation2

1.3 Microscopic versus Collective Models3

1.4 The Role of Symmetries5

2．Symmetries7

2.1 General Remarks7

2.2 Translation8

2.2.1 The Operator for Translation8

2.2.2 Translational Invariance9

2.2.3 Many-Particle Systems10

2.3 Rotation11

2.3.1 The Angular Momentum Operators11

2.3.2 Representations of the Rotation Group16

2.3.3 The Rotation Matrices20

2.3.4 SU(2)and Spin21

2.3.5 Coupling of Angular Momenta25

2.3.6 Intrinsic Angular Momentum27

2.3.7 Tensor Operators30

2.3.8 The Wigner-Eckart Theorem35

2.3.9 6j and 9j Symbols37

2.4 Isospin39

2.5 Parity42

2.5.1 Definition42

2.5.2 Vector Fields42

2.6 Time Reversal43

3．Second Quantization47

3.1 General Formalism47

3.1.1 Motivation47

3.1.2 Second Quantization for Bosons50

3.1.3 Second Quantization for Fermions52

3.2 Representation of Operators53

3.2.1 One-Particle Operators53

3.2.2 Two-Particle Operators56

3.3 Evaluation of Matrix Elements for Fermions58

3.4 The Particle-Hole Picture60

4．Group Theory in Nuclear Physics65

4.1 Lie Groups and Lie Algebras65

4.2 Group Chains72

4.3 Lie Algebras in Second Quantization73

5．Electromagnetic Moments and Transitions75

5.1 Introduction75

5.2 The Quantized Electromagnetic Field75

5.3 Radiation Fields of Good Angular Momentum77

5.3.1 Solutions of the Scalar Helmholtz Equation77

5.3.2 Solutions of the Vector Helmholtz Equation78

5.3.3 Properties of the Multipole Fields81

5.3.4 Multipole Expansion of Plane Waves82

5.4 Coupling of Radiation and Matter85

5.4.1 Basic Matrix Elements85

5.4.2 Multipole Expansion of the Matrix Elements and Selection Rules88

5.4.3 Siegert's Theorem90

5.4.4 Matrix Elements for Emission in the Long-Wavelength Limit91

5.4.5 Relative Importance of Transitions and Weisskopf Estimates95

5.4.6 Electric Multipole Moments97

5.4.7 Effective Charges97

6．Collective Models99

6.1 Nuclear Matter99

6.1.1 Mass Formulas99

6.1.2 The Fermi-Gas Model101

6.1.3 Density-Functional Models103

6.2 Nuclear Surface Deformations106

6.2.1 General Parametrization106

6.2.2 Types of Multipole Deformations108

6.2.3 Quadrupole Deformations110

6.2.4 Symmetries in Collective Space115

6.3 Surface Vibrations117

6.3.1 Vibrations of a Classical Liquid Drop117

6.3.2 The Harmonic Quadrupole Oscillator124

6.3.3 The Collective Angular-Momentum Operator128

6.3.4 The Collective Quadrupole Operator130

6.3.5 The Quadrupole Vibrational Spectrum132

6.4 Rotating Nuclei138

6.4.1 The Rigid Rotor138

6.4.2 The Symmetric Rotor143

6.4.3 The Asymmetric Rotor145

6.5 The Rotation-Vibration Model147

6.5.1 Classical Energy147

6.5.2 Quantal Hamiltonian151

6.5.3 Spectrum and Eigenfunctions155

6.5.4 Moments and Transition Probabilities159

6.6 γ-Unstable Nuclei168

6.7 More General Collective Models for Surface Vibrations170

6.7.1 The Generalized Collective Model170

6.7.2 Proton-Neutron Vibrations177

6.7.3 Higher Multipoles177

6.8 The Interacting Boson Model178

6.8.1 Introduction178

6.8.2 The Hamiltonian180

6.8.3 Group Chains182

6.8.4 The Casimir Operators184

6.8.5 The Dynamical Symmetries187

6.8.6 Transition Operators192

6.8.7 Extended Versions of the IBA193

6.8.8 Comparison to the Geometric Model196

6.9 Giant Resonances197

6.9.1 Introduction197

6.9.2 The Goldhaber-Teller Model200

6.9.3 The Steinwedel-Jensen Model202

6.9.4 Applications205

7．Microscopic Models207

7.1 The Nucleon-Nucleon Interaction207

7.1.1 General Properties207

7.1.2 Functional Form210

7.1.3 Interactions from Nucleon-Nucleon Scattering211

7.1.4 Effective Interactions214

7.2 The Hartree-Fock Approximation217

7.2.1 Introduction217

7.2.2 The Variational Principle218

7.2.3 The Slater-Determinant Approximation219

7.2.4 The Hartree-Fock Equations220

7.2.5 Applications225

7.2.6 The Density Matrix Formulation227

7.2.7 Constrained Hartree-Fock229

7.2.8 Alternative Formulations and Three-Body Forces230

7.2.9 Hartree-Fock with Skyrme Forces231

7.3 Phenomenological Single-Particle Models237

7.3.1 The Spherical-Shell Model237

7.3.2 The Deformed-Shell Model248

7.4 The Relativistic Mean-Field Model261

7.4.1 Introduction261

7.4.2 Formulation of the Model261

7.4.3 Applications266

7.5 Pairing269

7.5.1 Motivation269

7.5.2 The Seniority Model272

7.5.3 The Quasispin Model278

7.5.4 The BCS Model280

7.5.5 The Bogolyubov Transformation285

7.5.6 Generalized Density Matrices290

8．Interplay of Collective and Single-Particle Motion293

8.1 The Core-plus-Particle Models293

8.1.1 Basic Considerations293

8.1.2 The Weak-Coupling Limit294

8.1.3 The Strong-Coupling Approximation296

8.1.4 The Interacting Boson-Fermion Model302

8.2 Collective Vibrations in Microscopic Models303

8.2.1 The Tamm-Dancoff Approximation303

8.2.2 The Random-Phase Approximation(RPA)309

8.2.3 Time-Dependent Hartree-Fock and Linear Response312

9．Large-Amplitude Collective Motion317

9.1 Introduction317

9.2 The Macroscopic-Microscopic Method318

9.2.1 The Liquid-Drop Model318

9.2.2 The Shell-Correction Method320

9.2.3 Two-Center Shell Models324

9.2.4 Fission in Self-Consistent Models335

9.3 Mass Parameters and the Cranking Model337

9.3.1 Overview337

9.3.2 The Irrotational-Flow Model337

9.3.3 The Cranking Formula338

9.3.4 Applications of the Cranking Formula340

9.4 Time-Dependent Hartree-Fock344

9.5 The Generator-Coordinate Method346

9.6 High-Spin States353

9.6.1 Overview353

9.6.2 The Cranked Nilsson Model355

Appendix:Some Formulas from Angular-Momentum Theory359

References363

Subject Index369