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 nuclei, 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…mehr
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 nuclei, 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.
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. IsobaricMass 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.
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. IsobaricMass 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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