Bargmann型势场共振散射的Feshbach投影算符方法
Feshbach projection-operator formalism to resonance scattering on Bargmann-type potentials
摘要：
Feshbach的投影算子形式主义适用于单通道情况下的共振散射。该方法是基于完整的功能空间分为两个部分，内部（本地化）和外部（无限扩展）的划分。共振的光谱信息是从非厄米有效哈密顿算符$H_{\rm eff}$中获得的，该算符由于与外部的耦合而出现在内部。众所周知，通常由于势的截断而出现$S$矩阵的额外的所谓截止极点。我们研究的问题，虚假的$S$矩阵极点的Feshbach形式主义的框架。对有限个共振态的精确可解势进行了数值分析。这些势代表了接受共振态的Bargmann型势的推广。我们的计算表明，由Feshbach投影算符方法得到的$S$矩阵的极点与物理共振的复能量和$S$矩阵的截止极点相一致.
英文摘要：
The projection-operator formalism of Feshbach is applied to resonance scattering in a single-channel case. The method is based on the division of the full function space into two segments, internal (localized) and external (infinitely extended). The spectroscopic information on the resonances is obtained from the non-Hermitian effective Hamilton operator $H_{\rm eff}$ appearing in the internal part due to the coupling to the external part. As well known, additional so-called cut-off poles of the $S$-matrix appear, generally, due to the truncation of the potential. We study the question of spurious $S$ matrix poles in the framework of the Feshbach formalism. The numerical analysis is performed for exactly solvable potentials with a finite number of resonance states. These potentials represent a generalization of Bargmann-type potentials to accept resonance states. Our calculations demonstrate that the poles of the $S$ matrix obtained by using the Feshbach projection-operator formalism coincide with both the complex energies of the physical resonances and the cut-off poles of the $S$-matrix.
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