Isovector neutron-proton pairing with particle number projected BCS

TL;DR

This paper evaluates the particle number projected BCS approximation for isovector neutron-proton pairing by comparing it with exact solutions in a model system, highlighting its strengths and limitations.

Contribution

It introduces and tests two isovector PBCS wave functions against exact solutions in a non-degenerate single-particle orbit model.

Findings

PBCS improves over BCS but less accurately than in like-particle pairing models.

The agreement between PBCS and exact solutions is moderate, indicating limitations.

Two different PBCS wave functions were analyzed for isovector pairing.

Abstract

The particle number projected BCS (PBCS) approximation is tested against the exact solution of the SO(5) Richardson-Gaudin model for isovector pairing in a system of non-degenerate single particle orbits. Two isovector PBCS wave functions are considered. One is constructed as a single proton-neutron pair condensate, while the other corresponds to a product of a neutron pair condensate and a proton pair condensate. The PBCS equations are solved using a recurrence method and the analysis is performed for systems with an equal number of neutrons and protons distributed in a sequence of equally spaced 4-fold (spin-isospin) degenerate levels. The results show that although PBCS improves significantly over BCS, the agreement of PBCS with the exact solution is less satisfactory than in the case of the SU(2) Richardson model for pairing between like particles.