Solving the Richardson equations close to the critical points

TL;DR

This paper develops a numerical method to solve Richardson equations near critical pairing strengths where divergences occur, enabling accurate solutions across all coupling regimes.

Contribution

It introduces a new set of equations to identify critical pairing strengths and non-collapsing energies, improving numerical solutions near critical points.

Findings

Derived equations for critical g values and non-collapsing energies.

Established a numerical procedure for arbitrary coupling strengths.

Enhanced understanding of Richardson equations near divergences.

Abstract

We study the Richardson equations close to the critical values of the paring strength g_c where the occurrence of divergencies preclude numerical solutions. We derive a set of equations for determining the critical g values and the non-collapsing pair energies. Studying the behavior of the solutions close to the critical points, we develop a procedure to solve numerically the Richardson equations for arbitrary coupling strength.