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Siegert pseudostate perturbation theory: one- and two-threshold cases
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
instead of the real and imaginary parts of
the perturbation energy individually
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