On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials

We study some formal aspects of the exterior complex scaling (ECS) approach when implemented for both short and long-range potentials. In particular, we focus on the inconsistencies related to the requirement of an artificial cut-off of the potential in order to avoid exponential divergencies due to...

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Publicado: 2012
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346060_v66_n4_p_Gasaneo
http://hdl.handle.net/20.500.12110/paper_14346060_v66_n4_p_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_14346060_v66_n4_p_Gasaneo2023-06-08T16:15:33Z On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials We study some formal aspects of the exterior complex scaling (ECS) approach when implemented for both short and long-range potentials. In particular, we focus on the inconsistencies related to the requirement of an artificial cut-off of the potential in order to avoid exponential divergencies due to the complex rotation. For the pure two-body Coulomb potential we demonstrate analytically and numerically that the ECS inner solution is indeed the correct one, thus reinforcing the method; the extraction of the transition amplitude, however, remains problematic. We also show that a consistent application of the ECS method requires a distorted wave formulation, and two variants are proposed. Finally, we will propose an approach equivalent to the original ECS but that avoids all formal difficulties. It is based on performing the complex rotation on the basis functions rather than on the driven equation itself, and makes use of Sturmian functions with appropriately chosen outgoing boundary conditions. Our proposal differs from one of the original versions of the ECS method, through the use of physically based basis functions rather than pure numeric ones. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346060_v66_n4_p_Gasaneo http://hdl.handle.net/20.500.12110/paper_14346060_v66_n4_p_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 study some formal aspects of the exterior complex scaling (ECS) approach when implemented for both short and long-range potentials. In particular, we focus on the inconsistencies related to the requirement of an artificial cut-off of the potential in order to avoid exponential divergencies due to the complex rotation. For the pure two-body Coulomb potential we demonstrate analytically and numerically that the ECS inner solution is indeed the correct one, thus reinforcing the method; the extraction of the transition amplitude, however, remains problematic. We also show that a consistent application of the ECS method requires a distorted wave formulation, and two variants are proposed. Finally, we will propose an approach equivalent to the original ECS but that avoids all formal difficulties. It is based on performing the complex rotation on the basis functions rather than on the driven equation itself, and makes use of Sturmian functions with appropriately chosen outgoing boundary conditions. Our proposal differs from one of the original versions of the ECS method, through the use of physically based basis functions rather than pure numeric ones. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.
title On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
spellingShingle On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
title_short On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
title_full On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
title_fullStr On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
title_full_unstemmed On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials
title_sort on the applicability of the exterior complex scaling method for scattering problems including coulombic potentials
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346060_v66_n4_p_Gasaneo
http://hdl.handle.net/20.500.12110/paper_14346060_v66_n4_p_Gasaneo
_version_ 1768544334989230080

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