On the solution of a pairing problem in the continuum

TL;DR

This paper extends the Richardson solution to include continuum states in fermionic pairing problems, enabling exact solutions in models combining discrete and continuum spectra, relevant for nuclear physics.

Contribution

It introduces a generalized Richardson approach based on the rational Gaudin model formulated in the Berggren ensemble, providing exact solutions in continuum and pole approximations.

Findings

Exact solutions in pole approximation and continuum limit

Accurate modeling of Gamow Shell Model with discrete and continuum spectra

Extension of Richardson solution to continuum in fermionic pairing

Abstract

We present a generalized Richardson solution for fermions interacting with the pairing interaction in both discrete and continuum parts of the single particle (s.p.) spectrum. The pairing Hamiltonian is based on the rational Gaudin (RG) model which is formulated in the Berggren ensemble. We show that solutions of the generalized Richardson equations are exact in the two limiting situations: (i) in the pole approximation and (ii) in the s.p. continuum. If the s.p. spectrum contains both discrete and continuum parts, then the generalized Richardson equations provide accurate solutions for the Gamow Shell Model.