Solving FaddeevMerkuriev equations within the Jmatrix approach: Application to coulomb problems
Abstract
A version of the Jmatrix method for solving threebody differential FaddeevMerkuriev equations is proposed. This version permits taking into account the full spectrum of a twobody Coulomb subsystem. Laguerre functions are used as a basis in expanding the total wave function of the problem being considered. In order to test the efficiency of the proposed method, the differential cross section for single ionization of a helium atom is calculated where the emerging He{sup +} ion remains in an excited state. The result agrees satisfactorily with experimental data both in the shape of the respective curve and in magnitude.
 Authors:
 Khabarovsk State Technical University (Russian Federation), Email: knyr@fizika.khstu.ru
 Moscow State University, Institute of Nuclear Physics (Russian Federation), Email: popov@srd.sinp.msu.ru
 Publication Date:
 OSTI Identifier:
 21076118
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Atomic Nuclei; Journal Volume: 69; Journal Issue: 2; Other Information: DOI: 10.1134/S1063778806020098; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; DIFFERENTIAL CROSS SECTIONS; DIFFERENTIAL EQUATIONS; EFFICIENCY; EQUATIONS; EXCITED STATES; FADDEEV EQUATIONS; HELIUM; HELIUM IONS; IONIZATION; LICENSES; MATHEMATICAL SOLUTIONS; MATRICES; SPECTRA; THREEBODY PROBLEM; TWOBODY PROBLEM; WAVE FUNCTIONS
Citation Formats
Zaitsev, S. A., Email: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V.. Solving FaddeevMerkuriev equations within the Jmatrix approach: Application to coulomb problems. United States: N. p., 2006.
Web. doi:10.1134/S1063778806020098.
Zaitsev, S. A., Email: zaytsev@fizika.khstu.ru, Knyr, V. A., & Popov, Yu. V.. Solving FaddeevMerkuriev equations within the Jmatrix approach: Application to coulomb problems. United States. doi:10.1134/S1063778806020098.
Zaitsev, S. A., Email: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V.. Wed .
"Solving FaddeevMerkuriev equations within the Jmatrix approach: Application to coulomb problems". United States.
doi:10.1134/S1063778806020098.
@article{osti_21076118,
title = {Solving FaddeevMerkuriev equations within the Jmatrix approach: Application to coulomb problems},
author = {Zaitsev, S. A., Email: zaytsev@fizika.khstu.ru and Knyr, V. A. and Popov, Yu. V.},
abstractNote = {A version of the Jmatrix method for solving threebody differential FaddeevMerkuriev equations is proposed. This version permits taking into account the full spectrum of a twobody Coulomb subsystem. Laguerre functions are used as a basis in expanding the total wave function of the problem being considered. In order to test the efficiency of the proposed method, the differential cross section for single ionization of a helium atom is calculated where the emerging He{sup +} ion remains in an excited state. The result agrees satisfactorily with experimental data both in the shape of the respective curve and in magnitude.},
doi = {10.1134/S1063778806020098},
journal = {Physics of Atomic Nuclei},
number = 2,
volume = 69,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Application of the Jmatrix method to FaddeevMerkuriev equations for (e,2e) reactions: Beyond pseudostates
A version of the Jmatrix method for solving numerically the threebody FaddeevMerkuriev differential equations is proposed. This version allows one to take into account the full spectrum of the twobody Coulomb subsystem. As a result, a discrete analog of the LippmannSchwinger equation is obtained which allows one to interpret correctly the threebody wave function in twobody domains. The scheme is applied to calculations of the fully resolved absolute differential cross sections for the He(e,2e)He{sup +} reactions leaving the residual ion in an excited state, at small energy and momentum transfer. The results are in good agreement with the experiment bothmore » 
Description of the continuous spectrum of a threebody Coulomb system within the Jmatrix approach
The contribution of the continuous spectrum of twobody Coulomb sybsystems to reaction matrix elements is studied. The respective FaddeevMerkuriev differential equations are solved within the Jmatrix approach. The differential cross sections for the double ionization of a helium atom by a direct electron impact is calculated by way of example. The results agree well with experimental data both in shape of the cross sections and in magnitude.