Correlated continuum wave functions for three particles with Coulomb interactions

We present an approximate solution of the Schrödinger equation for the three-body Coulomb problem. We write the Hamiltonian in parabolic curvilinear coordinates and study the possible separation of the wave equation as a system of coupled partial differential equations. When two of the particles are...

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Publicado: 1997
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v55_n4_p2809_Gasaneo
http://hdl.handle.net/20.500.12110/paper_10502947_v55_n4_p2809_Gasaneo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_10502947_v55_n4_p2809_Gasaneo2023-06-08T16:01:43Z Correlated continuum wave functions for three particles with Coulomb interactions We present an approximate solution of the Schrödinger equation for the three-body Coulomb problem. We write the Hamiltonian in parabolic curvilinear coordinates and study the possible separation of the wave equation as a system of coupled partial differential equations. When two of the particles are heavier than the others, we write an approximate wave equation that incorporates some terms of the Hamiltonian that before had been considered as a perturbation. Its solution can be expressed in terms of a confluent hypergeometric function of two variables. We show that the proposed wave function includes a correlation between the motion of the light particle relative to the heavy particles and verifies the correct asymptotic behavior when all particles are far from each other. Finally, we discuss the possible uses of this function in the calculation of transition matrices and differential cross sections in ionizing collisions. © 1997 The American Physical Society. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v55_n4_p2809_Gasaneo http://hdl.handle.net/20.500.12110/paper_10502947_v55_n4_p2809_Gasaneo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We present an approximate solution of the Schrödinger equation for the three-body Coulomb problem. We write the Hamiltonian in parabolic curvilinear coordinates and study the possible separation of the wave equation as a system of coupled partial differential equations. When two of the particles are heavier than the others, we write an approximate wave equation that incorporates some terms of the Hamiltonian that before had been considered as a perturbation. Its solution can be expressed in terms of a confluent hypergeometric function of two variables. We show that the proposed wave function includes a correlation between the motion of the light particle relative to the heavy particles and verifies the correct asymptotic behavior when all particles are far from each other. Finally, we discuss the possible uses of this function in the calculation of transition matrices and differential cross sections in ionizing collisions. © 1997 The American Physical Society.
title Correlated continuum wave functions for three particles with Coulomb interactions
spellingShingle Correlated continuum wave functions for three particles with Coulomb interactions
title_short Correlated continuum wave functions for three particles with Coulomb interactions
title_full Correlated continuum wave functions for three particles with Coulomb interactions
title_fullStr Correlated continuum wave functions for three particles with Coulomb interactions
title_full_unstemmed Correlated continuum wave functions for three particles with Coulomb interactions
title_sort correlated continuum wave functions for three particles with coulomb interactions
publishDate 1997
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v55_n4_p2809_Gasaneo
http://hdl.handle.net/20.500.12110/paper_10502947_v55_n4_p2809_Gasaneo
_version_ 1768542278432849920

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