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

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.