The properties of the scattering solutions obtained as poles of the $S$ and $K$ matrices are analyzed in terms of pairing effects in the framework of the Hartree-Fock-Bogoliubov (HFB) Jost function. As a result of our analysis, we found the following: in order for the poles of the $S$ matrix to form a resonance, there must be a pole of the $K$ matrix nearby. Within the framework of HFB theory, there are three types of resonance states; shape resonances, particle-type, and hole-type quasiparticle resonances. Other scattering states that can be classified are independent $K$- and $S$-matrix poles. It is shown both numerically and qualitatively using the Jost function that the pair-correlation effect is hardly observed in the shape resonance state, and that the appearance of the pair-correlation effect is different in the particle-type and hole-type quasiparticle resonance. We also found a noteworthy correlation effect that independent $K$-matrix poles break the metastable structure of the wave function of the quasiparticle resonance and turn it into an independent $S$-matrix pole. The correlation effect that the poles of the independent $S$ matrix break the metastable structure of the inner wave function without breaking the resonance structure of the outer wave function when a pole of the independent $S$ matrix is near the hole-type resonance state was also revealed. This is considered to be another aspect of the Fano effect.

中文翻译：

---

Hartree-Fock-Bogoliubov 框架内对 n−Ascattering 的共振和配对效应的分类

作为极点获得的散射溶液的性质 $秒$ 和 $钾$在 Hartree-Fock-Bogoliubov (HFB) Jost 函数的框架中，根据配对效应分析矩阵。作为我们分析的结果，我们发现了以下内容：为了使极点$秒$ 矩阵要形成共振，必须有一个极点 $钾$矩阵附近。在 HFB 理论的框架内，存在三种类型的共振态：形状共振、粒子型和空穴型准粒子共振。其他可分类的散射状态是独立的$钾$- 和 $秒$-矩阵极点。使用Jost函数从数值上和定性上都表明，在形状共振状态下几乎观察不到对相关效应，并且在粒子型和空穴型准粒子共振中对相关效应的出现是不同的。我们还发现了一个值得注意的相关效应，即独立的$钾$- 矩阵极点打破了准粒子共振波函数的亚稳态结构，使其成为独立的 $秒$-矩阵极点。独立极点的相关效应$秒$ 矩阵破坏内部波函数的亚稳态结构而不破坏外部波函数的共振结构，当独立的极点时 $秒$基体附近的空穴型共振状态也被揭示。这被认为是法诺效应的另一个方面。