The Nuclear Many-Body Problem (Paperback, Softcover Repri)

1 The Liquid Drop Model.- 1.1 Introduction.- 1.2 The Semi-empirical Mass Formula.- 1.3 Deformation Parameters.- 1.4 Surface Oscillations About a Spherical Shape.- 1.5 Rotations and Vibrations for Deformed Shapes.- 1.5.1 The Bohr Hamiltonian.- 1.5.2 The Axially Symmetric Case.- 1.5.3 The Asymmetric Rotor.- 1.6 Nuclear Fission.- 1.7 Stability of Rotating Liquid Drops.- 2 The Shell Model.- 2.1 Introduction and General Considerations.- 2.2 Experimental Evidence for Shell Effects.- 2.3 The Average Potential of the Nucleus.- 2.4 Spin Orbit Coupling.- 2.5 The Shell Model Approach to the Many-Body Problem.- 2.6 Symmetry Properties.- 2.6.1 Translational Symmetry.- 2.6.2 Rotational Symmetry.- 2.6.3 The Isotopic Spin.- 2.7 Comparison with Experiment.- 2.7.1 Experimental Evidence for Single-Particle (Hole) States.- 2.7.2 Electromagnetic Moments and Transitions.- 2.8 Deformed Shell Model.- 2.8.1 Experimental Evidence.- 2.8.2 General Deformed Potential.- 2.8.3 The Anisotropic Harmonic Oscillator.- 2.8.4 Nilsson Hamiltonian.- 2.8.5 Quantum Numbers of the Ground State in Odd Nuclei.- 2.8.6 Calculation of Deformation Energies.- 2.9 Shell Corrections to the Liquid Drop Model and the Strutinski Method.- 2.9.1 Introduction.- 2.9.2 Basic Ideas of the Strutinski Averaging Method.- 2.9.3 Determination of the Average Level Density.- 2.9.4 Strutinski's Shell Correction Energy.- 2.9.5 Shell Corrections and the Hartree-Fock Method.- 2.9.6 Some Applications.- 3 Rotation and Single-Particle Motion.- 3.1 Introduction.- 3.2 General Survey.- 3.2.1 Experimental Observation of High Spin States.- 3.2.2 The Structure of the Yrast Line.- 3.2.3 Phenomenological Classification of the Yrast Band.- 3.2.3 The Backbending Phenomenon.- 3.3 The Particle-plus-Rotor Model.- 3.3.1 The Case of Axial Symmetry.- 3.3.2 Some Applications of the Particle-plus-Rotor Model.- 3.3.3 The triaxial Particle-plus-Rotor Model.- 3.3.4 Electromagnetic Properties.- 3.4 The Cranking Model.- 3.4.1 Semiclassical Derivation of the Cranking Model.- 3.4.2 The Cranking Formula.- 3.4.3 The Rotating Anisotropic Harmonic Oscillator.- 3.4.4 The Rotating Nilsson Scheme.- 3.4.5 The Deformation Energy Surface at High Angular Momenta.- 3.4.6 Rotation about a Symmetry Axis.- 3.4.7 Yrast Traps.- 4 Nuclear Forces.- 4.1 Introduction.- 4.2 The Bare Nucleon-Nucleon Force.- 4.2.1 General Properties of a Two-Body Force.- 4.2.2 The Structure of the Nucleon-Nucleon Interaction.- 4.3 Microscopic Effective Interactions.- 4.3.1 Bruckner's G-Matrix and Bethe Goldstone Equation.- 4.3.2 Effective Interactions between Valence Nucleons.- 4.3.3 Effective Interactions between Particles and Holes.- 4.4 Phenomenological Effective Interactions.- 4.4.1 General Remarks.- 4.4.2 Simple Central Forces.- 4.4.3 The Skyrme Interaction.- 4.4.4 The Gogny Interaction.- 4.4.5 The Migdal Force.- 4.4.6 The Surface-Delta Interaction (SDI).- 4.4.7 Separable Forces and Multipole Expansions.- 4.4.8 Experimentally Determined Effective Interactions.- 4.5 Concluding Remarks.- 5 The Hartree-Fock Method.- 5.1 Introduction.- 5.2 The General Variational Principle.- 5.3 The Derivation of the Hartree-Fock Equation.- 5.3.1 The Choice of the Set of Trial Wave Functions.- 5.3.2 The Hartree-Fock Energy.- 5.3.3 Variation of the Energy.- 5.3.4 The Hartree-Fock Equations in Coordinate Space.- 5.4 The Hartree-Fock Method in a Simple Solvable Model.- 5.5 The Hartree-Fock Method and Symmetries.- 5.6 Hartree-Fock with Density Dependent Forces.- 5.6.1 Approach with Microscopic Effective Interactions.- 5.6.2 Hartree-Fock Calculations with the Skyrme Force.- 5.7 Concluding Remarks.- 6 Pairing Correlations and Superfluid Nuclei.- 6.1 Introduction and Experimental Survey.- 6.2 The Seniority Scheme.- 6.3 The BCS Model.- 6.3.1 The Wave Function.- 6.3.2 The BCS Equations.- 6.3.3 The Special Case of a Pure Pairing Force.- 6.3.4 Bogoliubov Quasi-particles-Excited States and Blocking.- 6.3.5 Discussion of the Gap Equation.- 6.3.6 Schematic Solution of the Gap Equation.- 7