Treatment of the two-body Coulomb problem as a short-range potential

Autores
Gasaneo, Gustavo; Ancarani, L. U.
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia
Materia
Coulomb Interactions
Born Series
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/68862
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Treatment of the two-body Coulomb problem as a short-range potentialGasaneo, GustavoAncarani, L. U.Coulomb InteractionsBorn Serieshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Ancarani, L. U.. Université Paul Verlaine-Metz; FranciaAmerican Physical Society2009-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68862Gasaneo, Gustavo; Ancarani, L. U.; Treatment of the two-body Coulomb problem as a short-range potential; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 80; 6; 12-2009; 062717/1-062717/111050-2947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.062717info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.80.062717info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:44:17Zoai:ri.conicet.gov.ar:11336/68862instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:44:17.511CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Treatment of the two-body Coulomb problem as a short-range potential
title Treatment of the two-body Coulomb problem as a short-range potential
spellingShingle Treatment of the two-body Coulomb problem as a short-range potential
Gasaneo, Gustavo
Coulomb Interactions
Born Series
title_short Treatment of the two-body Coulomb problem as a short-range potential
title_full Treatment of the two-body Coulomb problem as a short-range potential
title_fullStr Treatment of the two-body Coulomb problem as a short-range potential
title_full_unstemmed Treatment of the two-body Coulomb problem as a short-range potential
title_sort Treatment of the two-body Coulomb problem as a short-range potential
dc.creator.none.fl_str_mv Gasaneo, Gustavo
Ancarani, L. U.
author Gasaneo, Gustavo
author_facet Gasaneo, Gustavo
Ancarani, L. U.
author_role author
author2 Ancarani, L. U.
author2_role author
dc.subject.none.fl_str_mv Coulomb Interactions
Born Series
topic Coulomb Interactions
Born Series
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia
description The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.
publishDate 2009
dc.date.none.fl_str_mv 2009-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/68862
Gasaneo, Gustavo; Ancarani, L. U.; Treatment of the two-body Coulomb problem as a short-range potential; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 80; 6; 12-2009; 062717/1-062717/11
1050-2947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68862
identifier_str_mv Gasaneo, Gustavo; Ancarani, L. U.; Treatment of the two-body Coulomb problem as a short-range potential; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 80; 6; 12-2009; 062717/1-062717/11
1050-2947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.062717
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.80.062717
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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