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Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods
D. Baye, J. Goldbeter, J. -M. Sparenberg
abstract: Siegert pseudostates are purely outgoing states at some fixed point expanded
over a finite basis. With discretized variables, they provide an accurate
description of scattering in the s wave for short-range potentials with few
basis states. The R-matrix method combined with a Lagrange basis, i.e.
functions which vanish at all points of a mesh but one, leads to simple
mesh-like equations which also allow an accurate description of scattering.
These methods are shown to be exactly equivalent for any basis size, with or
without discretization. The comparison of their assumptions shows how to
accurately derive poles of the scattering matrix in the R-matrix formalism and
suggests how to extend the Siegert-pseudostate method to higher partial waves.
The different concepts are illustrated with the Bargmann potential and with the
centrifugal potential. A simplification of the R-matrix treatment can usefully
be extended to the Siegert-pseudostate method.
- oai_identifier:
- oai:arXiv.org:quant-ph/0201021
- categories:
- quant-ph physics.comp-ph
- comments:
- 19 pages, 1 figure
- doi:
- 10.1103/PhysRevA.65.052710
- arxiv_id:
- quant-ph/0201021
- journal_ref:
- Phys. Rev. A 65 (2002) 052710
- created:
- 2002-01-07
Full article ▸
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