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Title: Parabolic sturmians approach to the three-body continuum Coulomb problem

Abstract

The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger-type equation, where the Green's function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the non-orthogonal part of the kinetic energy operator. As a test of this approach, the integral equation for the (e{sup -}, e{sup -}, He{sup ++}) system has been solved numerically by using the parabolic Sturmian basis representation of the (approximate) potential. Convergence of the expansion coefficients of the solution has been obtained as the basis set used to describe the potential is enlarged.

Authors:
 [1];  [2]
  1. Moscow State University, Nuclear Physics Institute (Russian Federation)
  2. Universite catholique de Louvain, Institute of Condensed Matter and Nanosciences (Belgium)
Publication Date:
OSTI Identifier:
22156398
Resource Type:
Journal Article
Journal Name:
Physics of Atomic Nuclei
Additional Journal Information:
Journal Volume: 76; Journal Issue: 3; Other Information: Copyright (c) 2013 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CONVERGENCE; EXPANSION; HELIUM IONS; INTEGRAL EQUATIONS; KINETIC ENERGY; MATHEMATICAL SOLUTIONS; POTENTIAL ENERGY; SIMULATION; THREE-BODY PROBLEM

Citation Formats

Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Popov, Yu. V., and Piraux, B. Parabolic sturmians approach to the three-body continuum Coulomb problem. United States: N. p., 2013. Web. doi:10.1134/S1063778813020178.
Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Popov, Yu. V., & Piraux, B. Parabolic sturmians approach to the three-body continuum Coulomb problem. United States. https://doi.org/10.1134/S1063778813020178
Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Popov, Yu. V., and Piraux, B. Fri . "Parabolic sturmians approach to the three-body continuum Coulomb problem". United States. https://doi.org/10.1134/S1063778813020178.
@article{osti_22156398,
title = {Parabolic sturmians approach to the three-body continuum Coulomb problem},
author = {Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru and Popov, Yu. V. and Piraux, B.},
abstractNote = {The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger-type equation, where the Green's function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the non-orthogonal part of the kinetic energy operator. As a test of this approach, the integral equation for the (e{sup -}, e{sup -}, He{sup ++}) system has been solved numerically by using the parabolic Sturmian basis representation of the (approximate) potential. Convergence of the expansion coefficients of the solution has been obtained as the basis set used to describe the potential is enlarged.},
doi = {10.1134/S1063778813020178},
url = {https://www.osti.gov/biblio/22156398}, journal = {Physics of Atomic Nuclei},
issn = {1063-7788},
number = 3,
volume = 76,
place = {United States},
year = {2013},
month = {3}
}