Title: On the solution of a pairing problem in the continuum Show Chinese title

Title: 关于连续介质中配对问题的解

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. Show Chinese abstract

Abstract: 我们提出了一个广义的Richardson解，用于描述费米子与离散部分和连续部分都相互作用的配对相互作用的单粒子(s.p.)谱。 配对哈密顿量基于有理Gaudin(RG)模型，该模型在Berggren系综中表述。 我们证明，广义Richardson方程在两种极限情况下解是精确的：(i) 在极点近似下和(ii) 在单粒子连续谱下。 如果单粒子谱同时包含离散和连续部分，则广义Richardson方程为Gamow壳模型提供了准确的解。