Theoretical models

In this section, we investigate several exactly solvable models to see
the interplay between the particle-hole and particle-particle channels
of interaction.
In all cases, the Hamiltonian has the form

where is either the intrinsic (i.e., deformed) single-particle Hamiltonian or the laboratory-system quadrupole-quadrupole Hamiltonian, and is always the monopole-pairing (seniority) Hamiltonian:

In Eq. (14)

denotes the monopole-pair creation operator, and denotes the time-reversed state.

Properties of the Hamiltonian (13) depend on the ratio

(16) |

where represents the strength of . For both (weak pairing) and (strong pairing), one can treat the Hamiltonian (13) perturbatively. However, the situation encountered most often in the nuclear physics context is the intermediate case (0.4) in which pairing correlations are strongly influenced by the nuclear mean field.

- Limiting cases
- Degenerate shell: Seniority model
- Equidistant-level model (infinitely many levels)
- Deformed shell (finite non-degenerate spectrum)
- Pairing-plus-quadrupole model