Exact solution of the pairing problem for spherical and deformed systems

TL;DR

This paper introduces a robust hybrid polynomial method to solve the Richardson pairing model efficiently, applicable to both spherical and deformed nuclei, and demonstrates its effectiveness through studying shape coexistence in neutron-rich Ni isotopes.

Contribution

A new hybrid polynomial approach is developed to solve the nonlinear Richardson pairing equations for spherical and deformed systems, improving numerical stability and initial guess generation.

Findings

Method is robust for deformed and spherical nuclei.

Provides effective initial guesses for large degeneracy systems.

Successfully applied to neutron-rich Ni isotopes for shape coexistence analysis.

Abstract

There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this paper we tackle this problem by employing a simple hybrid polynomial approach. The method is found to be robust and is valid for both deformed and nearly spherical nuclei. It also provides important and convenient initial guesses for spherical systems with large degeneracy. As an example, we apply the method to study the shape coexistence in neutron-rich Ni isotopes.