Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\sum_{n}\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually.
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机译：对于两个能量分离的阈值，研究了Siegert伪状态（SPS）的摄动理论[Phys.Rev.A 58，2077（1998）和Phys.Rev.A 67，032714（2003）]。推导了一个阈值情况的摄动公式作为极限情况，由此我们为衰减状态重构了More's理论[Phys.Rev.A 3,1217（1971）]并修正了一个误差。由于Siegert伪状态的非标准正交关系，两阈值情况的摄动公式具有其他项。我们将该理论应用于2通道模型问题，并发现扰动展开的收敛速度应在方差$ D = || E- \ sum_ {n} \ lambda ^ n E ^ { （n）} || $代替单独的摄动能量的实部和虚部。
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