dorsal/arxiv
View SchemaEquivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods
| Authors | D. Baye, J. Goldbeter, J. -M. Sparenberg |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201021 |
| URL | https://arxiv.org/abs/quant-ph/0201021 |
| DOI | 10.1103/PhysRevA.65.052710 |
| Journal | Phys. Rev. A 65 (2002) 052710 |
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.
{
"annotation_id": "19e79fda-84a9-419f-aaff-97edeb7a6c1b",
"date_created": "2026-03-02T18:01:48.826000Z",
"date_modified": "2026-03-02T18:01:48.826000Z",
"file_hash": "65994499c135ff09f43235a486466156412272e2b60b1aea1665cf8047431908",
"private": false,
"record": {
"abstract": "Siegert pseudostates are purely outgoing states at some fixed point expanded\nover a finite basis. With discretized variables, they provide an accurate\ndescription of scattering in the s wave for short-range potentials with few\nbasis states. The R-matrix method combined with a Lagrange basis, i.e.\nfunctions which vanish at all points of a mesh but one, leads to simple\nmesh-like equations which also allow an accurate description of scattering.\nThese methods are shown to be exactly equivalent for any basis size, with or\nwithout discretization. The comparison of their assumptions shows how to\naccurately derive poles of the scattering matrix in the R-matrix formalism and\nsuggests how to extend the Siegert-pseudostate method to higher partial waves.\nThe different concepts are illustrated with the Bargmann potential and with the\ncentrifugal potential. A simplification of the R-matrix treatment can usefully\nbe extended to the Siegert-pseudostate method.",
"arxiv_id": "quant-ph/0201021",
"authors": [
"D. Baye",
"J. Goldbeter",
"J. -M. Sparenberg"
],
"categories": [
"quant-ph",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevA.65.052710",
"journal_ref": "Phys. Rev. A 65 (2002) 052710",
"title": "Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods",
"url": "https://arxiv.org/abs/quant-ph/0201021"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b67cd1f3-5bde-4533-bf19-c812edfa1ca3",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}