Solving a three-body continuum Coulomb problem with quasi-Sturmian functions

The scattering problem of three particles interacting via Coulomb potentials is studied using generalized parabolic coordinates. The scattering solutions are obtained by solving a driven equation. The 'perturbation' operator appearing in the driven term is the non-orthogonal part of the kinetic energy operator. The approximated solution appearing in the driven term is the product of two two-body Coulomb wave functions. As a test for our proposal, a simple two-dimensional model problem has been solved numerically by using so called parabolic quasi-Sturmian basis representation. Convergence of the solution has been obtained as the basis set is enlarged.