This book is aimed at enabling the reader to obtain a working knowledge of the nuclear shell model and to understand nuclear structure within the framework of the shell model. Attention is concentrated on a coherent, self-contained exposition of the main ideas behind the model with ample illustrations to give an idea beyond formal exposition of the concepts. Since this text grew out of a course taught for advanced undergraduate and first-year graduate students in theoretical nuclear physics, the accents are on a detailed exposition of the material with step-by-step derivations rather than on a superficial description of a large number of topics. In this sense, the book differs from a number of books on theoretical nuclear physics by narrowing the subject to only the nuclear shell model. Most of the expressions used in many of the existing books treating the nuclear shell model are derived here in more detail, in a practitioner's way. Due to frequent student requests I have expanded of detail in order to take away the typical phrase " . . . after some the level simple and straightforward algebra one finds . . . ". The material could probably be treated in a one-year course (implying going through the problem sets and setting up a number of numerical studies by using the provided computer codes). The book is essentially self-contained but requires an introductory course on quantum mechanics and nuclear physics on a more general level.

Inhalt

1. Angular Momentum in Quantum Mechanics.- 1.1 Central Force Problem and Orbital Angular Momentum.- 1.2 General Definitions of Angular Momentum.- 1.2.1 Matrix Representations.- 1.2.2 Example for Spin 1/2 Particles.- 1.3 Total Angular Momentum for a Spin 1/2 Particle.- 1.4 Coupling of Two Angular Momenta: Clebsch-Gordan Coefficients.- 1.5 Properties of Clebsch-Gordan Coefficients.- 1.6 Racah Recoupling Coefficients: Coupling of Three Angular Momenta.- 1.7 Symmetry Properties of 6j-Symbols.- 1.8 Wigner 9j-Symbols: Coupling and Recoupling of Four Angular Momenta.- 1.9 Classical Limit of Wigner 3j-Symbols.- Short Overview of Angular Momentum Coupling Formulas.- 2. Rotations in Quantum Mechanics.- 2.1 Rotation of a Scalar Field-Rotation Group O(3).- 2.2 General Groups of Transformations.- 2.3 Representations of the Rotation Operator.- 2.3.1 The Wigner D-Matrices.- 2.3.2 The Group SU(2)-Relation with SO(3).- 2.3.3 Application: Geometric Interpretation of Intrinsic Spin 1/2.- 2.4 Product Representations and Irreducibility.- 2.5 Cartesian Tensors, Spherical Tensors, Irreducible Tensors.- 2.6 Tensor Product.- 2.7 Spherical Tensor Operators: The Wigner-Eckart Theorem.- 2.8 Calculation of Matrix Elements.- 2.8.1 Reduction Rule I.- 2.8.2 Reduction Rule II.- Short Overview of Rotation Properties, Tensor Operators, Matrix Elements.- 3. The Nuclear Shell Model.- 3.1 One-particle Excitations.- 3.1.1 Introduction.- 3.1.2 The Radial Equation and the Single-particle Spectrum: the Harmonic Oscillator in the Shell Model.- 3.1.3 Illustrative Examples of Energy Spectra.- 3.1.4 Hartree-Fock Methods: A Simple Approach.- 3.2 Two-particle Systems: Identical Nucleons.- 3.2.1 Two-particle Wavefunctions.- 3.2.2 Two-particle Residual Interaction.- 3.2.3 Calculation of Two-Body Matrix Elements.- 3.2.4 Configuration Mixing: Model Space and Model Interaction.- 3.3 Three-particle Systems and Beyond.- 3.3.1 Three-particle Wave Functions.- 3.3.2 Extension to n-particle Wave Functions.- 3.3.3 Some Applications: Three-particle Systems.- 3.4 Non-identical Particle Systems: Isospin.- 3.4.1 Isospin: Introduction and Concepts.- 3.4.2 Isospin Formalism.- 3.4.3 Two-Body Matrix Elements with Isospin.- 4. Electromagnetic Properties in the Shell Model.- 4.1 General.- 4.2 Electric and Magnetic Multipole Operators.- 4.3 Single-particle Estimates and Examples.- 4.4 Electromagnetic Transitions in Two-particle Systems.- 4.5 Quadrupole Moments.- 4.5.1 Single-particle Quadrupole Moment.- 4.5.2 Two-particle Quadrupole Moment.- 4.6 Magnetic Dipole Moment.- 4.6.1 Single-particle Moment: Schmidt Values.- 4.6.2 Two-particle Dipole Moment.- 4.7 Additivity Rules for Static Moments.- 5. Second Quantization.- 5.1 Creation and Annihilation Operators.- 5.2 Operators in Second Quantization.- 5.3 Angular Momentum Coupling in Second Quantization.- 5.4 Hole Operators in Second Quantization.- 5.5 Normal Ordering, Contraction, Wick's Theorem.- 5.6 Application to the Hartree-Fock Formalism.- 6. Elementary Modes of Excitation: Particle-Hole Excitations at Closed Shells.- 6.1 General.- 6.2 The TDA Approximation.- 6.3 The RPA Approximation.- 6.4 Application of the Study of 1p-1h Excitations: 16O.- 7. Pairing Correlations: Particle-Particle Excitations in Open-Shell Nuclei.- 7.1 Introduction.- 7.2 Pairing in a Degenerate Single j-Shell.- 7.3 Pairing in Non-Degenerate Levels: Two-Particle Systems.- 7.4 n Particles in Non-Degenerate Shells: BCS-Theory.- 7.5 Applications of BCS.- 7.5.1 Odd-Even Mass Differences, E1qp.- 7.5.2 Energy Spectra.- 7.5.3 Electromagnetic Transitions.- 7.5.4 Spectroscopic Factors.- 7.6 Broken-Pair Model.- 7.6.1 Low-Seniority Approximation to the Shell Model.- 7.6.2 Broken-Pair or Generalized-Seniority Scheme for Semi-Magic Nuclei.- 7.6.3 Generalization to Both Valence Protons and Neutrons.- 7.7 Interacting Boson-Model Approximation to the Nuclear Shell Model.- 8. Self-Consistent Shell-Model Calculations.- 8.1 Introduction.- 8.2 Construction of a Nucleon-Nucleon Force: Skyrme Forces.- 8.2.1 Hartree-Fock Bogoliubov (HFB) Formalism for Nucleon-Nucleon Interactions Including Three-Body Forces.- 8.2.2 Application of HFB to Spherical Nuclei.- 8.2.3 The Extended Skyrme Force.- 8.2.4 Parameterization of Extended Skyrme Forces: Nuclear Ground-State Properties.- 8.3 Excited-State Properties of SkE Forces.- 8.3.1 Particle-Particle Excitations: Determination of x3.- 8.3.2 The Skyrme Interaction as a Particle-Hole Interaction.- 8.3.3 Rearrangement Effects for Density-Dependent Interactions and Applications for SkE Forces.- 9. Some Computer Programs.- 9.1 Clebsch-Gordan Coefficients.- 9.2 Wigner 6j-Symbol.- 9.3 Wigner 9j-Symbol.- 9.4 Calculation of Table of Slater Integrals.- 9.5 Calculation of ?-Matrix Element.- 9.6 Matrix Diagonalization.- 9.7 Radial Integrals Using Harmonic Oscillator Wave Functions.- 9.8 BCS Equations with Constant Pairing Strength.- A. The Angular Momentum Operator in Spherical Coordinates.- B. Explicit Calculation of the Transformation Coefficients for Three-Angular Momentum Systems.- C. Tensor Reduction Formulae for Tensor Products.- D. The Surface-Delta Interaction (SDI).- G. The Magnetic Multipole Operator.- H. A Two-Group (Degenerate) RPA Model.- I. The Condon-Shortley and Biedenharn-Rose Phase Conventions: Application to Electromagnetic Operators and BCS Theory.- 1.1 Electromagnetic Operators: Long-Wavelength Form and Matrix Elements.- 1.2 Properties of the Electromagnetic Multipole Operators Under Parity Operation,Time Reflection and Hermitian Conjugation.- 1.3 Phase Conventions in the BCS Formalism.- Problems.- References.