Siegert pseudostate perturbation theory: one- and two-threshold cases

Details Siegert pseudostate perturbation theory: one- and two-threshold cases Siegert pseudostate perturbation theory: one- and two-threshold cases

2005-08-19

arxiv.org/abs/physics/0508140v1

Physics

Atomic Physics

Scientific paper

10.1103/PhysRevA.72.062718

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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