The Nuclear Shell Model [E-Book] / by Kris L. G. Heyde.
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 illustratio...
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Full text |
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Personal Name(s): | Heyde, Kris L. G., author |
Imprint: |
Berlin, Heidelberg :
Springer,
1990
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Physical Description: |
XII, 377 p. 6 illus. online resource. |
Note: |
englisch |
ISBN: |
9783642972034 |
DOI: |
10.1007/978-3-642-97203-4 |
Series Title: |
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Springer Series in Nuclear and Particle Physics
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Subject (LOC): |
- 1. Angular Momentum in Quantum Mechanics
- 1.1 Central Force Problem and Orbital Angular Momentum
- 1.2 General Definitions of Angular Momentum
- 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
- 2.4 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
- 3. The Nuclear Shell Model
- 3.1 One-particle Excitations
- 3.2 Two-particle Systems: Identical Nucleons
- 3.3 Three-particle Systems and Beyond
- 3.4 Non-identical Particle Systems: 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
- 4.6 Magnetic 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
- 7.6 Broken-Pair Model
- 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
- 8.3 Excited-State Properties of 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.