Exact solution of the mean-field plus separable pairing model reexamined

Abstract

Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with non-degenerate single-particle energies and non-degenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one-and two-orbit cases are known, verification of the solutions for these two special cases is made. In order to demonstrate structure and features of the solution, the model with three orbits in the ds-shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for large number of orbits and pairs seems still difficult.

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

“…The separable pairing problem was studied in [25], in which the single-particle energies are all degenerate. The separable pairing interaction with two non-degenerate levels was analyzed in [26], of which solution with multi non-degenerate levels of a special case was given in [27][28][29], while the general case has been analyzed in [30]. In this work, it will be shown that the orbit-dependent non-separable pairing interaction among valence nucleons over two non-degenerate orbits can also be solved analytically.…”

Nuclear supersymmetry and dual algebraic structures

“…Richardson [49] explained the method to exactly solve the pure pairing model including non-degenerate single-particle orbits for both fermion and boson systems. Extensions to the Richardson-Gaudin theory have been made using the Bethe ansatz methodology, [50][51][52][53].…”