内容

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.