Theory of Hyperspherical Sturmians for Three-Body Reactions

Autores
Gasaneo, Gustavo; Mitnik, Dario Marcelo; Frapiccini, Ana Laura; Colavecchia, Flavio Dario; Randazzo, Juan Martin
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schro ̈dinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.
Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Fil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Fil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Materia
Sturmian Functions
Hyperspherical
Three Body Reactions
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:11336/21924
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Theory of Hyperspherical Sturmians for Three-Body ReactionsGasaneo, GustavoMitnik, Dario MarceloFrapiccini, Ana LauraColavecchia, Flavio DarioRandazzo, Juan MartinSturmian FunctionsHypersphericalThree Body Reactionshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schro ̈dinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaFil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaFil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaAmerican Chemical Society2009-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/21924Gasaneo, Gustavo; Mitnik, Dario Marcelo; Frapiccini, Ana Laura; Colavecchia, Flavio Dario; Randazzo, Juan Martin; Theory of Hyperspherical Sturmians for Three-Body Reactions; American Chemical Society; Journal of Physical Chemistry A; 113; 52; 12-2009; 14573-145821089-5639CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1021/jp9040869info:eu-repo/semantics/altIdentifier/url/http://pubs.acs.org/doi/abs/10.1021/jp9040869info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:42:20Zoai:ri.conicet.gov.ar:11336/21924instacron: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:34982025-10-15 15:42:20.5CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Theory of Hyperspherical Sturmians for Three-Body Reactions
title Theory of Hyperspherical Sturmians for Three-Body Reactions
spellingShingle Theory of Hyperspherical Sturmians for Three-Body Reactions
Gasaneo, Gustavo
Sturmian Functions
Hyperspherical
Three Body Reactions
title_short Theory of Hyperspherical Sturmians for Three-Body Reactions
title_full Theory of Hyperspherical Sturmians for Three-Body Reactions
title_fullStr Theory of Hyperspherical Sturmians for Three-Body Reactions
title_full_unstemmed Theory of Hyperspherical Sturmians for Three-Body Reactions
title_sort Theory of Hyperspherical Sturmians for Three-Body Reactions
dc.creator.none.fl_str_mv Gasaneo, Gustavo
Mitnik, Dario Marcelo
Frapiccini, Ana Laura
Colavecchia, Flavio Dario
Randazzo, Juan Martin
author Gasaneo, Gustavo
author_facet Gasaneo, Gustavo
Mitnik, Dario Marcelo
Frapiccini, Ana Laura
Colavecchia, Flavio Dario
Randazzo, Juan Martin
author_role author
author2 Mitnik, Dario Marcelo
Frapiccini, Ana Laura
Colavecchia, Flavio Dario
Randazzo, Juan Martin
author2_role author
author
author
author
dc.subject.none.fl_str_mv Sturmian Functions
Hyperspherical
Three Body Reactions
topic Sturmian Functions
Hyperspherical
Three Body Reactions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schro ̈dinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.
Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Fil: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
Fil: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina
description In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schro ̈dinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.
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/11336/21924
Gasaneo, Gustavo; Mitnik, Dario Marcelo; Frapiccini, Ana Laura; Colavecchia, Flavio Dario; Randazzo, Juan Martin; Theory of Hyperspherical Sturmians for Three-Body Reactions; American Chemical Society; Journal of Physical Chemistry A; 113; 52; 12-2009; 14573-14582
1089-5639
CONICET Digital
CONICET
url http://hdl.handle.net/11336/21924
identifier_str_mv Gasaneo, Gustavo; Mitnik, Dario Marcelo; Frapiccini, Ana Laura; Colavecchia, Flavio Dario; Randazzo, Juan Martin; Theory of Hyperspherical Sturmians for Three-Body Reactions; American Chemical Society; Journal of Physical Chemistry A; 113; 52; 12-2009; 14573-14582
1089-5639
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1021/jp9040869
info:eu-repo/semantics/altIdentifier/url/http://pubs.acs.org/doi/abs/10.1021/jp9040869
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
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Chemical Society
publisher.none.fl_str_mv American Chemical 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 13.22299

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