A Unified Theory of the Nucleus

by Karl Wildermuth

Overview

The purpose of this monograph is to describe a microscopic nuclear theory which can be used to consider all low-energy nuclear phenomena from a unified viewpoint. In this theory, the Pauli principle is completely taken into account and translation ally invariant wave functions are always employed. Also, this theory is quite flexible; it can be utilized to study reactions initiated not only by nucleons but also by arbitrary composite particles. Throughout this monograph, we have endeavoured to keep the underlying physical ideas as easily comprehensible as possible. Consequently, it becomes frequently necessary to sacrifice mathematical rigour in favour of clarity in presenting these ideas. In this way, it is our hope that this monograph could be useful to many research physicists in the nuclear field, experimentalists and theorists alike. In chapters 1 through 4, the formulation of this theory is presented. Numerical examples concerning bound-state, scattering, and reaction calculations are mainly described in chapters 5 through 7. In chapters 8 through IS we discuss, within the framework of this theory, general properties of nuclear systems. Finally, in chapters 16 and 17, we show in specific cases how one can achieve, without carrying out explicit calculations, a qualitative or even semi-quantitative understanding of these cases by applying the general physical concepts contained inherently in this theory.

Product Details

ISBN-13:	9783528083731
Publisher:	Vieweg+Teubner Verlag
Publication date:	01/01/1977
Series:	Clustering Phenomena in Nuclei , #1
Edition description:	Softcover reprint of the original 1st ed. 1977
Pages:	389
Product dimensions:	5.98(w) x 9.02(h) x 0.03(d)
Language:	German

Table of Contents

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.- 3.6. Applications of Oscillator Cluster Representations to a Qualitative Description of Low-Lying Levels in Light Nuclei.- 3.7. Construction of Generalized Cluster Wave Functions.- 4. Formulation of a Unified Microscopic Nuclear Structure and Reaction Theory.- 4.1. General Remarks.- 4.2. Specific Examples.- 4.3. Extension to General Systems.- 5. Bound-State Calculations.- 5.1. General Remarks.- 5.2. Calculation of Matrix Elements.- 5.3. Ground and Low Excited States of 6Li.- 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.- 7.3. Quantitative Results.- 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.- 9.3. Many-Level Resonance Formula for Pure Elastic-Scattering.- 9.4. Single-Level Resonance Formula IncludingInelastic and Rearrangement Processes.- 9.5. Mutual Influence of Resonance Levels in Inelastic and Rearrangement Processes.- 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.- 10.3. Isobaric-Spin Mixing in the Incoming Channel.- 11. Optical-Model Potentials for Composite Particles.- 11.1. General Remarks.- 11.2. Optical-Model Description of Elastic-Scattering Processes.- 11.3. Specific Examples.- 11.4. Features of Effective Local Potentials between Nuclei.- 12. Direct Reactions.- 12.1. General Remarks.- 12.2. Derivation of the General Formulae.- 12.3. Specific Examples.- 12.4. Influence of the Pauli Principle on Direct-Reactions.- 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.- 13.3. 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.- 14.9. 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 LevelWidth.- 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.- 16.4. Level Spectra of Neighbouring Nuclei.- 16.5. Optical Resonances in Nuclear Reactions.- 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.- 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.