From Nucleons to Nucleus

From Nucleons to Nucleus deals with single-particle and collective features of spherical nuclei. Each nuclear model is introduced and derived in detail. The formalism is then applied to light and medium-heavy nuclei in worked-out examples, and finally the acquired skills are strengthened by a wide selection of exercises, many relating the models to experimental data. Nuclear properties are discussed using particles, holes and quasiparticles. A large number of matrix elements of standard operators have been tabulated for reference.

From Nucleons to Nucleus is based on lectures on nuclear physics given by the author. Its main scope is thus to serve as a textbook for advanced students. But also researchers will appreciate it as wellbalanced reference to theoretical nuclear physics.

Inhalt

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