On the solution of a pairing problem in the continuum

Abstract

International audienceWe present a generalized Richardson solution for fermions interacting with the pairing interactionin both discrete and continuum parts of the single particle (s.p.) spectrum. The pairing Hamiltonianis based on the rational Gaudin (RG) model which is formulated in the Berggren ensemble. Weshow 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 bothdiscrete and continuum parts, then the generalized Richardson equations provide accurate solutionsfor the Gamow Shell Model