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Title: Description of the continuous spectrum of a three-body Coulomb system within the J-matrix approach

Abstract

The contribution of the continuous spectrum of two-body Coulomb sybsystems to reaction matrix elements is studied. The respective Faddeev-Merkuriev differential equations are solved within the J-matrix 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.

Authors:
;  [1];  [2]
  1. Pacific National University (Russian Federation), E-mail: knyr@fizika.khstu.ru
  2. Moscow State University (Russian Federation), E-mail: popov@srd.sinp.msu.ru
Publication Date:
OSTI Identifier:
21075899
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 4; Other Information: DOI: 10.1134/S1063778807040084; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; 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; ELECTRON BEAMS; ELECTRONS; FADDEEV EQUATIONS; HELIUM; HELIUM IONS; IONIZATION; MATRICES; MATRIX ELEMENTS; SPECTRA; THREE-BODY PROBLEM; TWO-BODY PROBLEM

Citation Formats

Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V. Description of the continuous spectrum of a three-body Coulomb system within the J-matrix approach. United States: N. p., 2007. Web. doi:10.1134/S1063778807040084.
Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., & Popov, Yu. V. Description of the continuous spectrum of a three-body Coulomb system within the J-matrix approach. United States. doi:10.1134/S1063778807040084.
Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V. Sun . "Description of the continuous spectrum of a three-body Coulomb system within the J-matrix approach". United States. doi:10.1134/S1063778807040084.
@article{osti_21075899,
title = {Description of the continuous spectrum of a three-body Coulomb system within the J-matrix approach},
author = {Zaytsev, S. A., E-mail: zaytsev@fizika.khstu.ru and Knyr, V. A. and Popov, Yu. V.},
abstractNote = {The contribution of the continuous spectrum of two-body Coulomb sybsystems to reaction matrix elements is studied. The respective Faddeev-Merkuriev differential equations are solved within the J-matrix 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.},
doi = {10.1134/S1063778807040084},
journal = {Physics of Atomic Nuclei},
number = 4,
volume = 70,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • A version of the J-matrix method for solving three-body differential Faddeev-Merkuriev equations is proposed. This version permits taking into account the full spectrum of a two-body 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.
  • A semiclassical S-Matrix theory is described for electron--atom or electron--ion scattering. The development of semiclassical approximations is briefly reviewed and the justification for semiclassical perspectives in electronic problems is discussed and contrasted with the situation of nucleus--nucleus scattering. Special properties of classical {ital N}--electron atoms are derived. On their basis quantitative results are presented for electron and positron impact ionization of hydrogen close to threshold. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
  • A method for expanding a three-particle T matrix at energies above the two-particle threshold as an infinite series of separable terms, based on the Schmidt theorem, is presented. The Yamaguchi-type separable potential is assumed for the two-nucleon interaction. The application of this expansion to the calculation of a four-body resonance is studied by giving a numerical example. The convergence of the Schmidt expansion is comparable to that of the Hilbert-Schmidt expansion at energies below the two-particle threshold.
  • A simple approach is proposed which makes it possible to obtain good results in the two-level approximation of the adiabatic method for the problem of three bodies. Binding energies of mesic molecules and various characteristics of p..mu..+p and d..mu..+d scattering processes are calculated with this approach. The results are compared with those of previous calculations.
  • The S-matrix formalism is used in the problem of interaction of two nuclear fragments with J{sup {pi}}=const at variable nuclear masses and charges in order to demonstrate that the decay energies of the ground states of composite systems are linear functions of the Coulomb coupling constant. 18 refs., 2 figs.