From Nucleons to Nucleus (eBook)

PART I: PARTICLES AND HOLES 1. Manipulation of geometric coefficients 1.1 The Clebsch-Gordan coefficients and 3j-symbols 1.2 The 6-j and 9-j symbols 2. Tensor operators and the Wigner-Eckart theorem 2.1 Sherical tensor operators 2.2 The Wigner-Eckart theorem 3. The nuclear mean field and many-nucleon configurations 3.1 The nuclear mean field 3.2 Many-nucleon configurations 4. The occupation-number representation 4.1 Particle creation and annihilation 4.2 Occupation-number representation of one- and two-body operators 4.3 Evaluation of the many-particle matrix elements: Wick's theorem 4.4 Particle-hole representation 4.5 Derivation of the Hartree-Fock equation by using the Wick's theorem 5. The mean-field shell model 5.1 Valence space 5.2 One-particle and one-hole nuclei 5.3 Two-particle and two-hole nuclei 5.4 Particle-hole nuclei 5.5 Isospin representation of few-nucleon systems 5.5.1 General isospin formalism 5.5.2 The isospin representation of two-particle and two-hole nuclei 5.5.3 The isospin representation of particle-hole nuclei 6. Electromagnetic multipole moments and transitions 6.1 General properties of electromagnetic observables 6.2 Electromagnetic transitions in one-particle and one-hole nuclei 6.3 Electromagnetic transitions in two-particle and two-hole nuclei 6.4 Electromagnetic transitions in particle-hole nuclei 6.4.1 Charge-conserving particle-hole excitations 6.4.2 Charge-changing particle-hole excitations 6.5 Isoscalar and isovector transitions 7. Beta-decay transitions 7.1 General properties of the nuclear beta decay 7.2 Matrix elements and decay half-lives 7.3 Beta-decay transitions in one-particle and one-hole nuclei 7.4 Beta-decay transitions in particle-hole nuclei 7.5 Beta-decay transitions in two-particle and two-hole nuclei 7.6 Forbidden unique beta decays 7.7 Beta-decay transitions between particle-hole states 8. The nuclear two-body interaction and two-particle configuration mixing 8.1 General properties of the nuclear two-body interaction 8.2 Separable interactions: the surface-delta interaction 8.3 Configuration mixing in two-particle nuclei 8.4 Configuration mixing in two-hole nuclei 8.5 Electromagnetic and beta-decay transitions in two-particle and two-hole nuclei 9. Particle-hole excitations and the TDA 9.1 The Tamm-Dancoff approximation 9.2 The TDA for general separable forces 9.3 Excitation spectra of doubly-magic nuclei 9.4 Electromagnetic transitions in doubly-magic nuclei 9.4.1 Transitions to the particle-hole ground state 9.4.2 Transitions between two TDA states 9.5 Electric transitions in the schematic separable model 10. Charge-changing particle-hole excitations: the pn-TDA 10.1 The proton-neutron Tamm-Dancoff approximation 10.2 Electromagnetic transitions in the pn-TDA 10.3 Beta-decay transitions in the pn-TDA 10.3.1 Transitions to the particle-hole vacuum 10.3.2 Transitions to the particle-hole excitations of the TDA 11. The random-phase approximation 11.1 The equations-of-motion method 11.2 Sophisticated particle-hole theories: the RPA 11.3 Properties of the RPA solutions 11.4 RPA solutions of the schematic separable model 11.5 RPA description of doubly-magic nuclei 11.6 Electromagnetic transitions in the RPA framework 11.6.1 Transitions to the RPA ground state 11.6.2 The energy-weighted sum rule 11.6.3 Electric transitions to the RPA ground state in the schematic model 1