Nuclear many-body theory provides the foundation for understanding and exploiting the new generation of experimental probes of nuclear structure that are now becoming available. The twentieth volume of Advances in Nuclear Physics is thus devoted to two major theoretical chapters addressing two fundamental issues: understanding single-particle properties in nuclei and the consistent formulation of a relativistic theory appropriate for hadronic physics. The long-standing problem of understanding single-particle behavior in a strongly interacting nuclear system takes on new urgency and sig­ nificance in the face of detailed measurements of the nuclear spectral function in (e, e'p) experiments. In the first chapter, Mahaux and Sartor confront head-on the ambiguities in defining single-particle properties and the limitations in calculating them microscopically. This thoughtful chapter provides a thorough, pedagogical review of the relevant aspects of many­ body theory and of previous treatments in the nuclear physics literature. It also presents the author's own vision of how to properly formulate and understand single-particle behavior based on the self-energy, or mass operator. Their approach provides a powerful, unified description of the nuclear mean field that covers negative as well as positive energies and consistently fills in that information that cannot yet be calculated reliably microscopically by a theoretically motivated phenomenology. Particular emphasis is placed upon experiment, both in the exhaustive comparisons with experimental data and in the detailed discussion of the relations of each of the theoretical quantities defined in the chapter to physical observables.

Inhalt

1 Single-Particle Motion in Nucle.- 1. Introduction.- 2. The Phenomenological Shell-Model Potential.- 2.1. Single-Particle Wave Equation.- 2.2. Single-Particle Energies.- 3. Quasiparticle Excitations.- 3.1. Configuration Mixing.- 3.2. Single-Particle Excitations.- 3.3. Quasihole and Quasiparticle Excitations.- 3.4. Effect of the Continuum.- 3.5. Discussion.- 4. The Optical Model.- 4.1. Single-Particle Wave Equation.- 4.2. Phenomenological Optical-Model Potentials.- 4.3. Generalized Optical-Model Potentials.- 4.4. Discussion.- 5. Nuclear Matter.- 5.1. Momentum Distribution.- 5.2. Optical Model in Nuclear Matter.- 5.3. Single-Particle Green's Function.- 5.4. Spectral Functions.- 5.5. Lehmann Representation.- 5.6. Mass Operator.- 5.7. Quasiparticle Approximation.- 5.8. Effective Masses.- 5.9. Mean Removal Energy and Average Binding Energy.- 5.10. Perturbation Expansion.- 5.11. Dispersion Relations.- 5.12. Brueckner-Hartree-Fock Approximation.- 5.13. Second Order in the Reaction Matrix.- 5.14. Third Order in the Reaction Matrix.- 5.15. Hole-Line Expansion.- 5.16. Numerical Results.- 5.17. Discussion.- 6. Microscopic Theory of Single-Particle Properties.- 6.1. Introduction.- 6.2. Natural Orbitals.- 6.3. Maximum Overlap Orbitals.- 6.4. Overlap Functions.- 6.5. Green's Functions.- 6.6. Spectral Functions.- 6.7. Sum Rules.- 6.8. Noninteracting System.- 6.9. Mass Operator.- 6.10. Particle and Hole Green's Functions.- 6.11. Overlap Functions for Bound States.- 6.12. Overlap Functions for Scattering States.- 6.13. Analytical Properties.- 6.14. Perturbation Expansion.- 6.15. Bilinear Expansion.- 6.16. The Mean Field.- 6.17. Quasiparticle States.- 6.18. Sum Rules.- 6.19. Analysis of Experimental Data.- 6.20. Discussion.- 7. Construction of the Mean Field at Positive and Negative Energies.- 7.1. Microscopic Calculations.- 7.2. Practical Form of the Dispersion Relation.- 7.3. Parametrization of the Imaginary Part of the Mean Field.- 7.4. Dispersive Contribution to the Real Part.- 7.5. Hartree-Fock-Type Contribution.- 7.6. Comparison with Empirical Potentials and Experimental Cross Sections.- 7.7. Effective Mass.- 7.8. Single-Particle Energies.- 7.9. Practical Approximation for the Spectral Function.- 7.10. Valence Shells.- 7.11. Spectral Function of Bound Quasiparticle States.- 7.12. Quasibound States.- 7.13. Principal Quantum Numbers.- 7.14. Quasiparticle Widths.- 7.15. Average Effective Mass.- 7.16. Root-Mean-Square Radii.- 7.17. Occupation Probabilities.- 7.18. Summed Spectroscopic Strengths.- 7.19. A Sum Rule Limit?.- 7.20. Comparison with Related Previous Analyses.- 7.21. Influence of the High Energy Parametrization of the Imaginary Part.- 7.22. The Proton-208Pb System.- 7.23. Measurement of Spectroscopic Factors.- 7.24. Can Occupation Probabilities Be Measured?.- 7.25. Other Nuclei.- 7.26. Discussion.- 8. Overview.- References.