Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate j-orbits.

Exact solution of spherical mean-field plus a special orbit-dependent non-separable pairing Hamiltonian with multi non-degenerate j -orbits, which is related to two previously known hyperbolic Gaudin models, is explored. It is shown that the Hamiltonian with suitable constraints on the pairing interaction parameters turns to be exactly solvable. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe-Gaudin-Richardson ansatz equations of the solution for any number of pairs k are determined. It is shown that the pair excitation energies can be calculated more easily than those of the separable pairing model studied previously. As examples of the solution, pairing excitation energies with the number of pairs up to the half-filling in the ds -shell with 3 j -orbits and in the pf -shell with 4 j -orbits are presented and compared with those of the mean-field plus the general separable, the special separable, and the standard pairing models. It is shown that the pairing excitation energies of the model are close to those of the mean-field plus special separable pairing or general separable pairing model. [ABSTRACT FROM AUTHOR]