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Group Symmetries in Nuclear Structure

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概要 This book is the result of a graduate-level "special topics" course I gave at the University of Rochester in 1970. The purpose of the course was to discuss as far as possible all known symmetries in n...uclei, with special emphasis on dynamical symmetries. Since there was no comprehensive account of this subject in the literature, I was encouraged to write a review based on my lecture notes. The end result is the present volume. Like the course, the book is intended mainly for graduate students and research workers in nuclear physics. The only prior knowledge required to follow the book is graduate-level quantum mechanics and nuclear physics and hence I believe that it can be useful to both experimental and theoretical nuclear physicists. In addition, the book should prepare a student to read the latest literature on the subject and also train him to do group theoretic work in nuclear physics. The organization of the material in the book is described in Chapter 1.続きを見る
目次 1: Introduction
2: Classification of Symmetries
2.1. Space-Time (Geometrical) Symmetries
2.2. Exact Dynamical Symmetry (Unknown Origin)
2.3. Almost Exact Dynamical Symmetry (Unknown Origin)
2.4. Approximate Dynamical Symmetry
2.5. Dynamical Symmetries in Vector Spaces ('Model' Symmetries)
2.6. Shape Symmetries
3: Symmetries and Groups
3.1. Groups and Representations of Groups
3.2. ?-Particle Model in Light Nuclei
3.3. Summary
4: Lie Groups and Their Algebras
4.1. Definition of a Lie Group
4.2. Infinitesimal Operators of a Lie Group
4.3. Representations of Lie Groups and Labeling of States
4.4. Representations of Lie Groups: Irreducible Tensors
4.5. Outer Product and Littlewood Rules
4.6. Matrix Groups and Their Representations
4.7. Two Theorems Concerning Goodness of Symmetry
5: Manifestation of Symmetries
5.1. Relationship between Energies
5.2. Symmetry Effect in Nuclear Reactions
5.3. Selection Rules
5.4. The Goodness of Symmetries
6: Spectral Distribution Methods
6.1. Introduction
6.2. The Method
6.3. Evaluation of Moments
6.4. Normality of the Distribution
6.5. Application of Distribution Method to Nuclear Spectroscopy
7: The Unitary Group and Its Subgroups
7.1. Introduction
7.2. Subgroups of U(N)
7.3. Unitary Decomposition of Operators
7.4. Method of Separation
7.5. Number Nonconserving Operators
7.6. Decomposition by Contraction
7.7. Extension to Many Orbits: Configuration Averages
7.8. Unitary Group and Hartree-Fock Approximation
7.9. Application of Configuration Distributions
8: Angular Momentum and Isospin
8.1. Introduction
8.2. Multipole Sum-Rule Methods
8.3. Isospin Distributions
8.4. Strength Distributions
8.5. Mixing of Isospin Symmetry in Nuclei
8.6. Isobaric Mass Formula
8.7. Angular Momentum Averaging
9: Space-Symmetry Group-Wigner Supermultiplet Scheme
9.1. The Group SU(4) and the Supermultiplet Scheme
9.2. Casimir Operators of SU(4) and the Space Exchange Operator M
9.3. Evidence for Space Symmetry
9.4. ?-Particle Spectroscopy
9.5. ? Decay and Magnetic Moments of f7/2 Shell Nuclei
9.6. Muon Capture in Nuclei
9.7. SU(4) Classification of Nuclear Interaction
9.8. Study of SU(4) Symmetry Using Spectral Distribution Method
9.9. The 'Goodness' of SU(4) Symmetry
9.10. SU(4)-ST Averaging
10: SU(3) Symmetry
10.1. Introduction
10.2. Brief Summary of Rotational Features in Light Nuclei
10.3. Search for the Intermediate Group G
10.4. Classification of States within an SU(3) Representation
10.5. States in the Projected Representation
10.6. Shell Model Calculation in the SU(3) Basis
10.7. SU(3) Classification of Interactions in the ds Shell
10.8. Mixing of SU(3) Symmetry in the ds Shell
10.9. Pseudo-LS and Pseudo-SU(3) Coupling Schemes
10.10. Configuration Mixing across Major Shells
10.11. 'Macroscopic' SU(3) Symmetry
11: Seniority and Symplectic Symmetry
11.1. Introduction
11.2. Seniority in a Single j Shell
11.3. Representations of Sp(2j + 1)
11.4. Casimir Operators and Their Eigenvalues
11.5. Goodness of Symmetry
11.6. Seniority in the j = 9/2 Shell
11.7. Symplectic Symmetry for the 1f7/2 Shell
11.8. Quasispin
11.9. Quasispin and Its Relation to Seniority
11.10. Multishell Seniority
11.11. Multishell Seniority Averaging
11.12. Multishell Seniority and the Two-Body Interaction
11.13. A New Truncation Scheme for Shell-Model Calculations
12: Summary and Final Remarks
References.
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登録日 2020.06.27
更新日 2020.06.28