Advances in Nuclear Physics: Volume 5

Advances in Nuclear Physics: Volume 5

by Michel Baranger, Erich Vogt


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Product Details

ISBN-13: 9781461582335
Publisher: Springer US
Publication date: 10/12/2012
Series: Advances in Nuclear Physics , #5
Edition description: 1972
Pages: 484
Product dimensions: 5.98(w) x 9.02(h) x 0.04(d)

Table of Contents

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.

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