Theoretical Nuclear Physics

The lecture deals with the theoretical description of the atomic nucleus as strongly interacting quantum many-body system. Based on the knowledge from the quantum-mechanics course, general methods of many-body quantum mechanics are discussed, which are of great importance also in other fields of modern physics. These methods are then applied to explore the strucutre of nuclei and their observables on a microscopic level. From the (preliminary) contents: Introduction: the nucleus as interacting quantum many-body system - modern nuclear strucutre theory - new experiments and bridge to astrophysics - nuclear observables Elements of Quantum Mechanics: angular momentum, spin, and isospin - many-particle Hilbert space - angular momentum coupling Nucleon-Nucleon Interaction: empirical properties - symmetries and operator structure - effective theories of the NN interaction - partial-wave matrix elements Two-Nucleon Problem: Hamiltonian of the two-nucleon system - two-nucleon bound state (deuteron) - two-nucleon scattering - more than two nucleons Many-Nucleon Problem: second quantization and Fock space - non-interacting many-nucleon system (Fermi gas) - interacting many-nucleon system Hartree-Fock Approximation: variational method - Hartree-Fock in coordinate representation - Hartree-Fock in basis representation - Skyrme-Hartree-Fock - link to the naive shell model Exact Diagonalization: ab initio methods - model space and truncations - convegence and uncertainties - no-core shell model - pre-diagonalization: similarity renormalization group Medium-Mass Methods: many-body perturbation theory - coupled-cluster appraoch - in-medium similarity renormalization group - valence-space shell model Electromagnetic Observables: electromagnetic moments and transitions - low-lying excitatons - collective excitations - equations-of-motion methods