Heyde The Nuclear Shell Model

1990
ISBN: 978-3-642-97203-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 377 Seiten, eBook

Reihe: Springer Series in Nuclear and Particle Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Heyde, Kris L.G.

Inhaltsverzeichnis

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 theHartree-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 BCSFormalism.- Problems.- References.