An analytically solvable three-body break-up model problem in hyperspherical coordinates

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and...

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Autores principales: Ancarani, L.U., Gasaneo, G., Mitnik, D.M.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14346060_v66_n10_p_Ancarani
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_14346060_v66_n10_p_Ancarani2023-10-03T16:15:44Z An analytically solvable three-body break-up model problem in hyperspherical coordinates Ancarani, L.U. Gasaneo, G. Mitnik, D.M. An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14346060_v66_n10_p_Ancarani
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.
format JOUR
author Ancarani, L.U.
Gasaneo, G.
Mitnik, D.M.
spellingShingle Ancarani, L.U.
Gasaneo, G.
Mitnik, D.M.
An analytically solvable three-body break-up model problem in hyperspherical coordinates
author_facet Ancarani, L.U.
Gasaneo, G.
Mitnik, D.M.
author_sort Ancarani, L.U.
title An analytically solvable three-body break-up model problem in hyperspherical coordinates
title_short An analytically solvable three-body break-up model problem in hyperspherical coordinates
title_full An analytically solvable three-body break-up model problem in hyperspherical coordinates
title_fullStr An analytically solvable three-body break-up model problem in hyperspherical coordinates
title_full_unstemmed An analytically solvable three-body break-up model problem in hyperspherical coordinates
title_sort analytically solvable three-body break-up model problem in hyperspherical coordinates
url http://hdl.handle.net/20.500.12110/paper_14346060_v66_n10_p_Ancarani
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