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

TL;DR

This paper presents an exact analytical solution for a complex nuclear pairing model involving two non-degenerate j-orbits, extending previous models and providing insights into eigenstate overlaps and quantum phase behavior.

Contribution

It introduces an exact solution method for a non-separable pairing model with orbit dependence, expanding the analytical tools for nuclear structure studies.

Findings

Eigenstates have high overlaps with standard pairing model states.

The solution involves extended Heine-Stieltjes polynomials.

Quantum phase crossover cannot be explained by standard pairing interactions.

Abstract

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.