Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem

A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied...

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Autores principales: Mitnik, D.M., Gasaneo, G., Ancarani, L.U.
Formato: JOUR
Materias:
Analytical results
Asymptotic behaviour
Basis functions
Bound state
Computational requirements
Dinger equation
Fast convergence
Hyperspherical
Model problems
Non-homogeneous
Non-separability
S-wave models
Scattering problems
Scattering process
Spatial extension
Spherical coordinates
Sturmian
Transition amplitudes
Asymptotic analysis
Scattering
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09534075_v46_n1_p_Mitnik
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_09534075_v46_n1_p_Mitnik2023-10-03T15:51:04Z Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem Mitnik, D.M. Gasaneo, G. Ancarani, L.U. Analytical results Asymptotic behaviour Basis functions Bound state Computational requirements Dinger equation Fast convergence Hyperspherical Model problems Non-homogeneous Non-separability S-wave models Scattering problems Scattering process Spatial extension Spherical coordinates Sturmian Transition amplitudes Asymptotic analysis Scattering A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements. © 2013 IOP Publishing Ltd. Fil:Mitnik, D.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gasaneo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09534075_v46_n1_p_Mitnik
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Analytical results
Asymptotic behaviour
Basis functions
Bound state
Computational requirements
Dinger equation
Fast convergence
Hyperspherical
Model problems
Non-homogeneous
Non-separability
S-wave models
Scattering problems
Scattering process
Spatial extension
Spherical coordinates
Sturmian
Transition amplitudes
Asymptotic analysis
Scattering
spellingShingle Analytical results
Asymptotic behaviour
Basis functions
Bound state
Computational requirements
Dinger equation
Fast convergence
Hyperspherical
Model problems
Non-homogeneous
Non-separability
S-wave models
Scattering problems
Scattering process
Spatial extension
Spherical coordinates
Sturmian
Transition amplitudes
Asymptotic analysis
Scattering
Mitnik, D.M.
Gasaneo, G.
Ancarani, L.U.
Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
topic_facet Analytical results
Asymptotic behaviour
Basis functions
Bound state
Computational requirements
Dinger equation
Fast convergence
Hyperspherical
Model problems
Non-homogeneous
Non-separability
S-wave models
Scattering problems
Scattering process
Spatial extension
Spherical coordinates
Sturmian
Transition amplitudes
Asymptotic analysis
Scattering
description A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements. © 2013 IOP Publishing Ltd.
format JOUR
author Mitnik, D.M.
Gasaneo, G.
Ancarani, L.U.
author_facet Mitnik, D.M.
Gasaneo, G.
Ancarani, L.U.
author_sort Mitnik, D.M.
title Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
title_short Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
title_full Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
title_fullStr Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
title_full_unstemmed Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem
title_sort use of generalized hyperspherical sturmian functions for a three-body break-up model problem
url http://hdl.handle.net/20.500.12110/paper_09534075_v46_n1_p_Mitnik
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AT gasaneog useofgeneralizedhypersphericalsturmianfunctionsforathreebodybreakupmodelproblem
AT ancaranilu useofgeneralizedhypersphericalsturmianfunctionsforathreebodybreakupmodelproblem
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