Siegert pseudostates (SPS) are a finite basis representation of Siegert states (SS) for finite-range potentials. This paper presents a generalization of the SPS formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A 58, 2077 (1998)] for s-wave scattering in the one-channel case, to s-wave scattering in the two-channel case. This includes the investigation of the properties of orthogonality and completeness of two-channel SPS and the derivation of the SPS expansions for the two-channel Green function, wave function, and scattering matrix. Similar to the one-channel case, two types of expansions for the scattering matrix are obtained: one has a form of a sum and requires the knowledge of both the SPS eigenvalues and eigenfunctions, while the other has a form of a product and involves the eigenvalues only. As the size of the basis tends to infinity, the product formulas obtained here in terms of SPS coincide with those given by Le Couteur [Proc. R. Soc. London, Ser. A 256, 115 (1960)] in terms of SS; all the other relations, as far as we know, have no counterparts in the literature. Partial widths of resonances in the case when both channels are open for decay are identified in terms of SPS-a feature that is absent in the one-channel case. The results are illustrated by numerical calculations for two model potentials. [References: 23]
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机译：Siegert伪状态（SPS）是Siegert状态（SS）在有限范围内的势的有限基础表示。本文介绍了散射理论的SPS公式的概括，该理论最初由Tolstikhin，Ostrovsky和Nakamura [Phys。 Rev. A 58，58，2077（1998）]，用于在单通道情况下的s波散射，在两通道情况下的s波散射。这包括对两通道SPS正交性和完整性的研究，以及对两通道Green函数，波动函数和散射矩阵的SPS展开的推导。与单通道情况类似，散射矩阵获得两种类型的展开：一种具有求和形式，并且需要SPS特征值和特征函数的知识，而另一种具有乘积形式，并且涉及仅特征值。由于基数的大小趋于无穷大，因此此处根据SPS得出的产品公式与Le Couteur [Proc.Natl.Acad.Sci.USA 90：5873-5877]给出的公式一致。 R. Soc。伦敦，序列A 256，115（1960）]。据我们所知，所有其他关系在文献中都没有。根据SPS来确定两个通道都打开以进行衰减的情况下的谐振的局部宽度，这是单通道情况下不存在的特征。通过两个模型电位的数值计算来说明结果。 [参考：23]
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