A Unified Theory of the Nucleus, Softcover reprint of the original 1st ed. 1977

1. Introduction.- 1.1. General Remarks.- 1.2. Difficulties of Some Reaction Theories.- 2. Reformulation of the Schrödinger Equation.- 3. Discussion of the Basis Wave Functions for Nuclear Systems.- 3.1. General Remarks.- 3.2. Qualitative Discussion of Cluster Correlations.- 3.3. Construction of Oscillator Cluster Wave Functions.- 3.4. Discussion of 8Be as an Illustrative Example.- 3.5. Effects of Antisymmetrization.- 3.5a. Fermions without Mutual Interaction in a Square-Well Potential.- 3.5b. The Lowest 4+ ?-Cluster State of 8Be.- 3.5c. Mathematical Equivalence of the Lowest 6Li States Described in the t + 3He and the d + ? Oscillator Cluster Representations.- 3.5d. Summary.- 3.6. Applications of Oscillator Cluster Representations to a Qualitative Description of Low-Lying Levels in Light Nuclei.- 3.6a. 7Liand7Be.- 3.6b. 6He, 6Li, and 6Be.- 3.6c. ?-Cluster States of 16O.- 3.6d. Brief Remarks.- 3.7. Construction of Generalized Cluster Wave Functions.- 3.7a. Introduction of Jacobi Coordinates.- 3.7b. Introduction of Parameter Coordinates.- 3.7c. Introduction of Jastrow Factors.- 3.7d. Summary.- 4. Formulation of a Unified Microscopic Nuclear Structure and Reaction Theory.- 4.1. General Remarks.- 4.2. Specific Examples.- 4.2a. n + ? Scattering.- 4.2b. d + ? Scattering.- 4.2c. Discussion.- 4.3. Extension to General Systems.- 5. Bound-State Calculations.- 5.1. General Remarks.- 5.2. Calculation of Matrix Elements.- 5.2a. Evaluation of Matrix Elements by the Cluster-Coordinate Technique — Example of 8Be.- 5.2b. Evaluation of Matrix Elements by the Generator-Coordinate Technique — Example of 8Be.- 5.3. Ground and Low Excited States of 6Li.- 5.3a. Introduction.- 5.3b. Calculation With a Nucleon-Nucleon Potential Containing a Hard Core — Accurate Treatment of the Jastrow Factor.- 5.3c. Calculation with a Nucleon-Nucleon Potential Containing a Soft Core — Approximate Treatment of the Jastrow Factor.- 5.3d. Calculation with a Nucleon-Nucleon Potential Containing no Repulsive Core.- 5.3e. Summary.- 5.4. Low-Energy T = 0 States of 12C.- 5.5. Low-Lying Levels of 7Be.- 5.6. Concluding Remarks.- 6. Further Comments About the Pauli Principle.- 6.1. General Remarks.- 6.2. Cluster Overlapping and Pauli Principle.- 6.3. Energetical Favouring of a Cluster Inside a Large Nucleus.- 7. Scattering and Reaction Calculations.- 7.1. General Remarks.- 7.2. Derivation of Coupled Equations.- 7.2a. Single-Channel Problem.- 7.2b. Coupled-Channel Problem.- 7.2c. Reaction Calculations Using Hulthén-Kohn-Type Variational Functions.- 7.3. Quantitative Results.- 7.3a. 3He + ? Elastic Scattering.- 7.3b. l = 0 Phase-Shift in ? + ? scattering.- 7.3c. Specific Distortion Effects in d + ? Scattering.- 7.3d. Effect of Reaction Channels on 3He + 3He Scattering Cross Sections.- 7.3e. ? + 16O Scattering — Utilization of the Generator-Coordinate Technique.- 7.3f. p + ? Scattering Around 3/2+ Resonance Level in 5Li.- 7.3g. ? + ? Scattering with Specific Distortion Effect and a Nucleon-Nucleon Potential Containing a Repulsive Core.- 7.3h. p + 3He and n + t Scattering Calculations.- 7.3i. Coupled-Channel Study of t(p, n) 3He Reaction.- 7.4. Concluding Remarks.- 8. Introductory Considerations About the Derivation of General Nuclear Properties.- 8.1. General Remarks.- 8.2. Introduction of Effective Hamiltonians.- 8.3. Elimination of Linear Dependencies.- 8.4. Concluding Remarks.- 9. Breit-Wigner Resonance Formulae.- 9.1. General Remarks.- 9.2. Single-Level Resonance Formula for Pure Elastic-Scattering.- 9.2a. Derivation of the Resonance Formula.- 9.2b. Discussion of the Resonance Formula.- 9.2c. Existence of Sharp Resonances.- 9.2d. Discussion of a Simple Resonance Model.- 9.3. Many-Level Resonance Formula for Pure Elastic-Scattering.- 9.4. Single-Level Resonance Formula Including Inelastic and Rearrangement Processes.- 9.4a. Derivation of the Resonance Formula.- 9.4b. Application of the Resonance Formula to a Specific Example Involving Two Open Channels.- 9.5. Mutual Influence of Resonance Levels in Inelastic and Rearrangement Processes.- 9.5a. Derivation of a Two-Level Breit-Wigner Formula.- 9.5b. A Specific Example.- 9.6. Behaviour of the Partial Level Width Near a Threshold and Energy-Dependent Width Approximation.- 10. Resonance Reactions and Isobaric-Spin Mixing.- 10.1. General Remarks.- 10.2. Isobaric-Spin Mixing in the Compound Region.- 10.2a. Derivation of a Two-Level Resonance Formula.- 10.2b. The 16.62 and 16.92 MeV States in 8Be as a Specific Example.- 10.3. Isobaric-Spin Mixing in the Incoming Channel.- 10.3a. Qualitative Description.- 10.3b. Quantitative Formulation in the Case of a Single Open Channel.- 10.3c. Brief Discussion in the Case of Many Open Channels.- 11. Optical-Model Potentials for Composite Particles.- 11.1. General Remarks.- 11.2. Optical-Model Description of Elastic-Scattering Processes.- 11.2a. Preliminary Remarks About the Optical-Model Potential.- 11.2b. Optical-Model Potential for Pure Elastic Scattering.- 11.2c. Optical-Model Potential in the Presence of Reaction Channels.- 11.2d. Mean Free Path of a Cluster in a Target Nucleus.- 11.3. Specific Examples.- 11.3a. 3He + ? Scattering.- 11.3b. p + 16O Scattering.- 11.3c. ? +16O Scattering.- 11.4. Features of Effective Local Potentials between Nuclei.- 11.4a. Wave-Function Equivalent Local Potentials.- 11.4b. Phase-Equivalent Local Potentials.- 12. Direct Reactions.- 12.1. General Remarks.- 12.2. Derivation of the General Formulae.- 12.3. Specific Examples.- 12.3a. 3He(d, p) ? Reaction.- 12.3b. 6Li(p, 3He) ? Reaction.- 12.4. Influence of the Pauli Principle on Direct-Reactions.- 12.4a. Study of Direct-Reaction Mechanisms in the Plane-Wave Born Approximation.- 12.4b. Study of Direct-Reaction Mechanisms with the Coupled-Channel Formulation.- 12.5. Concluding Remarks.- 13. Some Considerations About Heavy-Ion Transfer Reactions.- 13.1. General Remarks.- 13.2. Specific Examples to Study the Influence of Antisymmetrization.- 13.2a. ? + 6Li Elastic Scattering at Low Energies.- 13.2b. 6Li (p, 3He) ? Reaction in States of Large Orbital Angular Momentum.- 13.3. Further Discussion of the Odd-Even Feature in the Effective Potential between Nuclei.- 13.4. Concluding Remarks.- 14. Collective States.- 14.1. General Remarks.- 14.2. Rotational States of Even-Even Nuclei with K = 0.- 14.3. Generalization of Rotational Wave Functions.- 14.4. Energetical Preference of Rotational Configurations.- 14.5. Electromagnetic Transitions between Rotational Levels.- 14.6. Relationship with other Descriptions of Nuclear Rotational States.- 14.7. Construction of Intrinsic Wave Functions for Quantitative Studies of Collective States in Medium-Heavy and Heavy Nuclei.- 14.8. Specific Examples.- 14.8a. ? + 16O Cluster States in 20Ne.- 14.8b. Rotational States in 22Ne.- 14.8c. Backbending.- 14.9. Concluding Remarks.- 15. Brief Discussion of Time-Dependent Problems.- 15.1. General Remarks.- 15.2. Connection between the Lifetime of a Compound State and Its Level Width.- 15.2a. Relationship between Phase Shift and Time Delay.- 15.2b. Quantitative Relationship between the Level Width and the Lifetime of a Compound Nuclear State.- 15.2c. Calculation of the Level Width — 6Li as an Example for a Decaying System.- 15.3. Time-Dependent Projection Equation with Time-Dependent Interaction.- 16. Qualitative Considerations of Some Nuclear Problems.- 16.1. General Remarks.- 16.2. Coulomb-Energy Effects in Mirror Levels.- 16.3. Reduced Widths and ?-Transition Probabilities.- 16.3a. Reduced Widths of Nuclear Levels.- 16.3b. ? -Transition Probabilities.- 16.4. Level Spectra of Neighbouring Nuclei.- 16.5. Optical Resonances in Nuclear Reactions.- 16.5a. Optical Resonances in the Incoming Channel.- 16.5b. Optical Resonances in Reaction Channels.- 17. Nuclear Fission.- 17.1. General Remarks.- 17.2. Substructure Effects in Fission Processes.- 17.3. Mass Distribution of Fission Fragments.- 17.4. Deformation Energy of Fissioning Nucleus.- 17.4a. Dynamical Consideration of the Fission Process.- 17.4b. Calculation of the Deformation Energy — Strutinsky Prescription.- 17.4c. Calculation of the Deformation Energy-Cluster Prescription.- 17.4d. Discussion.- 18. Conclusion.- Appendix A — Cluster Hamiltonians and Jacobi Coordinates.- Appendix B — Designation of Oscillator States.- Appendix C — Demonstration of the Projection Technique.- Appendix D — Connection with Conventional Direct-Reaction Theory.- References.