Advances in Nuclear Physics: Volume 5

ISBN-13: 9781461582335 / Angielski / Miękka / 2012 / 484 str.

Michel Baranger; Erich Vogt

Opis

In both the present volume of Advances in Nuclear Physics and in the next volume, which will follow in a few months' time, we have stretched our normal pattern of reviews by including articles of more major proportions than any we have published before. As a result we have only three review articles in Volume 5. From the beginning of this series it has been our aim, as editors, to achieve variation in the scope, style, and length of individual articles sufficient to match the needs of the individual topic, rather than to restrain authors within rigid limits. It has not been our experience that this flexibility has led to unnecessary exuberance on the part of the authors. We feel that the major articles now entering the series are entirely justified. The article by Professor Delves on "Variational Techniques in the Nuclear Three-Body Problem" is an authoritative, definitive article on a subject which forms a cornerstone of nuclear physics. If we start with two body interactions, then the three-nucleon system is, perhaps, the only many nucleon system whose exact description may lie within the scope of human ingenuity. In recent years some new techniques of scattering theory, origi nating mostly in particle physics, have led to a great deal of new interest in the nuclear three-body problem. In this series we have had two articles (by Mitra and by Duck) on the new approaches."

Spis treści

1 Variational Techniques in the Nuclear Three-Body Problem.- 1. Introduction.- 2. Variation Principles for Bound States.- 2.1. The Rayleigh-Ritz Principle.- 2.2. Bound States of Three Bosons.- 2.3. Estimates of the Accuracy of a Variational Calculation.- 3. Numerical Techniques.- 3.1. Choice of Trial Function.- 3.2. The Calculation of the Normalization and Hamiltonian Integrals.- 3.3. Solution of the Finite Matrix Equation.- 3.4. Control and Analysis of Round-off and Integration Errors.- 4. Bound State Calculations with Realistic Local Potentials.- 4.1. Reduction of the Equations of Motion.- 4.2. Construction of the Trial Function.- 4.3. Calculations in the Harmonic Oscillator Basis.- 4.4. Calculations Using Hard-Core Potentials.- 5. Variational Methods for Scattering States.- 5.1. Two-Body Single Channel Scattering.- 5.2. Many-Body Two-Particle Scattering States.- 5.3. Variation Principles for Many-Body Scattering States.- 5.4. Neutron-Deuteron Elastic Scattering.- 5.5. Alternate Variational Principles for the Schrödinger Equation.- 6. Variational Methods for the Faddeev Equations.- 6.1. Variational Principle for Inhomogeneous Equations.- 6.2. The Two-Body t Matrix (DA 72).- 6.3. Variational Principle for the Faddeev Equations.- 6.4. Alternative Principles for the Breakup Reaction.- 7. Summing Up.- Acknowledgments.- Appendix A.- Convergence of Variational Methods.- References.- 2 Nuclear Matter Calculations.- 1. Introduction.- 1.1. Outline.- 1.2. Introduction to the Theory.- 2. Calculation of the G Matrix.- 2.1. General Principles.- 2.2. Bethe-Goldstone Equation.- 2.3. Kallio-Day Method.- 2.4. Reduction to Partial Waves.- 2.5. Day’s Derivation of the Radial Wave Equation.- 2.6. Binding Energy.- 2.7. The Brueckner Self-Consistency Problem.- 3. Comparison of Methods for Constructing the G Matrix.- 3.1. Kallio-Day Method.- 3.2. Köhler’s Method.- 3.3. Related Methods.- 3.4. Tabakin-Haftel Method.- 3.5. Coester-Day-Vincent-Cohen Method.- 3.6. Brueckner-Gammel Method.- 3.7. Dahl-Ostgaard-Brandow Method.- 3.8. Moszkowski-Scott Method.- 3.9. Summary.- 4. Results of Calculations for Realistic Forces.- 4.1. Potentials Considered.- 4.2. Results for Group One Potentials.- 4.3. Importance of Various Partial Waves.- 4.4. Results for OBEP and Supersoft-Core Forces.- 4.5. Interpretation of OBEP Forces.- 4.6. Mechanism of Saturation in Nuclear Matter.- 4.7. Convergence of the Reference Spectrum Series.- 4.8. Average Center of Mass Momentum.- 4.9. Symmetry Energy.- 5. Additional Considerations.- 5.1. Minimal Relativity.- 5.2. Three-Body Forces.- 5.3. Phase Equivalent Potentials.- 5.4. Nuclear Matter Without Potentials.- 5.5. Saturation Conditions on the Two-Body Potential.- 6. Higher-Order Cluster Contributions.- 6.1. Three-Body Clusters.- 6.2. Intermediate-State Potential Energy and Three-Body Clusters.- 6.3. Four-Body Clusters in Nuclear Matter.- 7. Toward Finite Nuclei.- 7.1. Rationale.- 7.2. Local Density Approximation.- 7.3. Thomas-Fermi Theory.- 7.4. Effective Potentials.- 7.5. Neutron Star Matter.- 8. Conclusion.- References.- 3 Clustering in Light Nuclei.- 1. Introduction.- 1.1. Few Nucleon Correlations.- 1.2. Clustering.- 1.3. Four-Body Correlation.- 1.4. Normal Shell Model States.- 1.5. Excited Rotational Levels and Molecule-like Structure.- 2. Shell Model and Deformed Hartree-Fock Model.- 2.1. Shell Model.- 2.2. Deformed Hartree-Fock Model.- 3. Weak Coupling Model and Quartet States.- 4. Cluster Model.- 4.1. Cluster Wave Functions.- 4.2. Brink’s Method.- 4.3. Generator Coordinate Method and Treatment of Relative Motion Between Clusters.- 4.4. The LCCO Method.- 4.5. Adiabatic Conditions.- 4.6. Hamiltonian.- 5. Individual Nuclei.- 5.1. 6Li.- 5.2. 8Be.- 5.3. 12C.- 5.4. 20Ne.- 5.5. 16O.- 6. Electromagnetic Properties and Form Factors for Electron Scattering.- 6.1. 6Li.- 6.2. 12C.- 6.3. 20Ne.- 7. Comparison Between Models in the Normal Shell Model States.- 8. Effect of the Spin-Orbit Interaction and Hybridization.- 9. Exotic States and Alpha Particle Widths.- 9.1. The Alpha-Particle Width.- 9.2. Alpha Transfer Reactions.- 10. Discussion and Possible Further Developments.- Appendix: Matrix Elements Between Two Brink Wave Functions.- References.