dorsal/arxiv
View SchemaSiegert pseudostate perturbation theory: one- and two-threshold cases
| Authors | Koudai Toyota, Toru Morishita, Shinichi Watanabe |
|---|---|
| Categories | |
| ArXiv ID | physics/0508140 |
| URL | https://arxiv.org/abs/physics/0508140 |
| DOI | 10.1103/PhysRevA.72.062718 |
Abstract
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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"abstract": "Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077\n(1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two\nenergetically separated thresholds. The perturbation formulas for the\none-threshold case are derived as a limiting case whereby we reconstruct More\u0027s\ntheory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error.\nThe perturbation formulas for the two-threshold case have additional terms due\nto the non-standard orthogonality relationship of the Siegert Pseudostates. We\napply the theory to a 2-channel model problem, and find the rate of convergence\nof the perturbation expansion should be examined with the aide of the variance\n$D= ||E-\\sum_{n}\\lambda^n E^{(n)}||$ instead of the real and imaginary parts of\nthe perturbation energy individually.",
"arxiv_id": "physics/0508140",
"authors": [
"Koudai Toyota",
"Toru Morishita",
"Shinichi Watanabe"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.72.062718",
"title": "Siegert pseudostate perturbation theory: one- and two-threshold cases",
"url": "https://arxiv.org/abs/physics/0508140"
},
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