Siegert赝态微扰理论：单阈值和双阈值情形
Siegert pseudostate perturbation theory: one- and two-threshold cases
摘要：
研究了两个能量分离阈值下Siegert赝态（SPS）的微扰理论[Phys.Rev.A58，2077（1998）和Phys.Rev.A67，032714（2003）].作为一种极限情况，我们导出了单阈值情形的微扰公式，从而重建了莫尔的衰变态理论[Phys.Rev.A3，1217（1971）]，并修正了一个错误.由于Siegert赝态的非标准正交关系，双阈值情况下的微扰公式有附加项。我们将理论应用于一个2通道模型问题，并发现微扰展开的收敛速度应与方差$D= ||E-\sum_{n}λ^n E^{(n)}||$的帮助下，而不是单独的扰动能量的实部和虚部检查。
英文摘要：
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 $D= ||E-\sum_{n}λ^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually.
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