An exact solution of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits

An exact solution of nuclear spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits is presented. The extended one-variable Heine–Stieltjes polynomials associated to the Bethe ansatz equations of the solution are determined, of which the sets of the zeros give the solution of the model, and can be determined relatively easily. A comparison of the solution to that of the standard pairing interaction with constant interaction strength among pairs in any orbit is made. It is shown that the overlaps of eigenstates of the model with those of the standard pairing model are always large, especially for the ground and the first excited state. However, the quantum phase crossover in the non-separable pairing model cannot be accounted for by the standard pairing interaction.