# Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems

## Abstract

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.

- Authors:

- Khabarovsk State Technical University (Russian Federation), E-mail: knyr@fizika.khstu.ru
- Moscow State University, Institute of Nuclear Physics (Russian Federation), E-mail: 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; THREE-BODY PROBLEM; TWO-BODY PROBLEM; WAVE FUNCTIONS

### Citation Formats

```
Zaitsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V..
```*Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems*. United States: N. p., 2006.
Web. doi:10.1134/S1063778806020098.

```
Zaitsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., & Popov, Yu. V..
```*Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems*. United States. doi:10.1134/S1063778806020098.

```
Zaitsev, S. A., E-mail: zaytsev@fizika.khstu.ru, Knyr, V. A., and Popov, Yu. V.. Wed .
"Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems". United States.
doi:10.1134/S1063778806020098.
```

```
@article{osti_21076118,
```

title = {Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems},

author = {Zaitsev, S. A., E-mail: zaytsev@fizika.khstu.ru and Knyr, V. A. and Popov, Yu. V.},

abstractNote = {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.},

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}

}

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