Parabolic sturmians approach to the threebody continuum Coulomb problem
Abstract
The threebody continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a LippmannSchwingertype equation, where the Green's function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the nonorthogonal 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:

 Moscow State University, Nuclear Physics Institute (Russian Federation)
 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 10637788
 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; THREEBODY PROBLEM
Citation Formats
Zaytsev, S. A., Email: zaytsev@fizika.khstu.ru, Popov, Yu. V., and Piraux, B. Parabolic sturmians approach to the threebody continuum Coulomb problem. United States: N. p., 2013.
Web. doi:10.1134/S1063778813020178.
Zaytsev, S. A., Email: zaytsev@fizika.khstu.ru, Popov, Yu. V., & Piraux, B. Parabolic sturmians approach to the threebody continuum Coulomb problem. United States. https://doi.org/10.1134/S1063778813020178
Zaytsev, S. A., Email: zaytsev@fizika.khstu.ru, Popov, Yu. V., and Piraux, B. Fri .
"Parabolic sturmians approach to the threebody continuum Coulomb problem". United States. https://doi.org/10.1134/S1063778813020178.
@article{osti_22156398,
title = {Parabolic sturmians approach to the threebody continuum Coulomb problem},
author = {Zaytsev, S. A., Email: zaytsev@fizika.khstu.ru and Popov, Yu. V. and Piraux, B.},
abstractNote = {The threebody continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a LippmannSchwingertype equation, where the Green's function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the nonorthogonal 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 = {10637788},
number = 3,
volume = 76,
place = {United States},
year = {2013},
month = {3}
}
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