Course 8: Theoretical approaches to describe exotic nuclei
Motivation and background.
The course aims at teaching modern theoretical approaches that are used in studies of weakly bound and unbound quantum many-body systems. The theoretical concepts which will be explained on examples of the atomic nucleus can be applied in any mesoscopic system.
1. General concepts of the theory of resonance states and processes
1.1 Resonances in scattering theory
1.2 Quasi-stationary (Gamow) states
1.3 Normalization and orthogonality of the Gamow functions
1.4 The resonance amplitude associated with the Gamow states
1.4 Resonance states in the R-matrix theory
1.5 The rigged Hilbert space in Physics
1.6 The quantum mechanical arrow of time
2. Projection methods
2.1 Orthogonal projecting method
2.2 Analytic continuation of the scattering-theory equations
2.3 One-particle resonances
2.4 Resonances in three-particle system
3. Theory of resonances based on analytical continuation in the coupling constant
3.1 Two-particle resonances in real and complex potentials
3.2 Threshold singularities of energy eigenvalues
3.3 Many-particle resonance and near-threshold states
4. Continuum Shell Model
4.1 Dynamics of quantum system embedded in a continuum
4.2 Effective Hamilton operator and S-matrix
4.3 Avoided level crossings in the complex plane
4.4 Dynamical features of open quantum systems at high level density
4.5 Resonance trapping vs uniform level broadening
4.6 Statistical vs dynamical aspects of resonances at high level density
5. Shell Model in the complex energy plane
5.1 Gamow states and Berggren ensemble
5.2 Complex scaling method
5.3 One-body space of the GSM
5.4 Gamow Shell Model
5.5 Unification of nuclear structure and reactions
6. Near-threshold phenomena (I)
6.1 Wigner threshold effect for reaction cross-section
6.2 Effects of configuration interaction in intensities and phase shifts
6.3 Thomas-Ehrman effect
6.4 Continuum coupling effects in binding systematics
6. Near-threshold phenomena (II)
6.1 Alignment of near-threshold states with the decay channel
6.2 Radial overlap functions and spectroscopic factors
6.3 Mirror symmetry breaking
6.4 Isospin mixing
6.5 The asymptotic normalization constant in mirror systems
7. Near-threshold phenomena (III)
7.1 Cluster states
7.2 Halo structures
7.3 Pairing anti-halo effect
7.3 Resonance anamneses
8. Particle decays
8.1 One-proton radioactivity
8.2 Two-proton radioactivity
Syllabus of 30+30+60 hours (lectures+exercises+work on projects).