Nuclear Shell Theory

ContentsPreface Introduction Part I. Single Particle Shell Model 1. Wave Functions in a Central Field 2. Total Angular Momentum of Spin-½ Particles 3. Transformation Properties of Spherical Harmonics 4. Radial Functions and Their Properties 5. Central Potentials in Frequent Use 6. Degeneracies in a Central Field 7. Spin-Orbit Interaction and Order of Single Nucleon Levels 8. Centrifugal and Coulomb Barriers 9. Magnetic Moments and Beta Decay Part II. Tensor Algebra. Two-Particle Systems 10. Irreducible Tensors 11. Tensor Fields 12. Infinitesimal Rotations and Irreducible Tensors 13. Vector Addition Coefficients 14. Tensor Products. The Wigner-Eckart Theorem 15. Racah Coefficients 16. Multipole Expansion of the Electromagnetic Field 17. Electromagnetic Transitions in Nuclei 18. Two Interacting Particles in a Central Field 19. Antisymmetric Wave Functions and Isospin 20. The Two-Particle Interaction 21. Tensor-Expansion of the Interaction 22. Closed Shells. Particles and Holes 23. Two Particles in the Harmonic Oscillator Potential Part III. Three- or More-Particle Systems 24. The m-Scheme 25. The Transformation from the m-Scheme to the J-Scheme 26. Coefficients of Fractional Parentage 27. Pairs of Particles Coupled to J = 0 28. C. f. p. and Matrix Elements in the Seniority Scheme 29. Average Interaction Energies in the Seniority Scheme 30. Applications to Nuclear and Coulomb Energies 31. Antisymmetric States in LS-Coupling 32. The Group Theoretical Classification of States 33. Many-Nucleon Wave Functions with Definite Isospin 34. The Seniority Scheme in the Nuclear j" Configuration 35. Coefficients of Fractional Parentage in the Seniority Scheme 36. Average Energies of States with Given T, v, and t 37. Nonequivalent Particles; Configuration Interaction Appendix Central Field Single Particle Hamiltonian and Wave Functions Spherical Harmonics Coulomb Potential Associated Laguerre Polynomials k" (x) Harmonic Oscillator Single Nucleon States in the Nuclear Shell Model Transformation Properties Wave Functions of Particles with Spin ½ Landé Formula Clebsch-Gordan Coefficients Three-j Symbols 9j-Symbols Racah Coefficients (6j-Symbols) Change of Coupling Transformations Some Special Clebsch-Gordan Coefficients and 3j-Symbols Some Special Racah and 9j Coefficients Irreducible Tensors Vector Spherical Harmonics Electromagnetic Transitions and Moments Matrix Elements of Interactions Coefficients of Fractional Parentage for Identical Particles Seniority Operator and Seniority Scheme Matrix Elements in the Seniority Scheme Average Interaction Energies Wave Functions with Isotopic Spin The Seniority Scheme Particles in Nonequivalent Orbits Configuration Interaction Coefficients of Fractional Percentage Energies in Terms of Slater Integrals for Wigner Force in LS-Coupling Energies in Terms of Slater Integrals for Wigner and Majorana Forces in jj-Coupling Slater Integrals Fᴷ and Gᴷ in Terms of Harmonic Oscillator Integrals 1INDEX