Abstract

The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R-matrix but rather by the equation 1 − R_nnL_n = 0, relating R-matrix element R_nn to decay channel logarithmic derivative L_n. Extension of Siegert state equation to multichannel system results in the replacement of channel R- matrix element R_nn by its reduced counterpart R_nn. One proves the Siegert state is a pole, (1 − R_nnL_n)⁻¹, of multichannel collision matrix. The Siegert equation 1 − R_nnL_n = 0, (n – Rydberg channel), implies basic results of Quantum Defect Theory as Seaton’s theorem, complex quantum defect, channel resonances and threshold continuity of averaged multichannel collision matrix elements.

Graphical abstract

中文翻译：

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Siegert态的量子缺陷理论方法

摘要

在Bloch-Lane-Robson形式主义的框架中，对Siegert态进行量子碰撞。Siegert状态不是由Wigner R矩阵的极点描述，而是由等式1-  R _nn L _n  = 0来描述，将R矩阵元素R _nn与衰减通道对数导数L _n相关。Siegert状态方程到多通道系统的扩展导致通道R-矩阵元素R _nn被其缩减的对应R _nn取代。一个证明齐格特态是极点，（1-  R _nn L _n）^-1多通道碰撞矩阵。Siegert方程1-  R _nn L _n  = 0，（n -Rydberg通道），隐含了以西顿定理，量子缺陷，通道共振和平均多通道碰撞矩阵元素的阈值连续性为基础的量子缺陷理论的基本结果。

图形概要