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In the last years we have developed an innovative tool to deal with three body scattering problems, based on a direct solution of the Schrödinger equation with appropriate flux boundary conditions [1]. The method uses a Generalized Sturmian Function (GSF) expansion of the three body wave function, in terms of two of the inter-particle coordinates of the problem. By using spherical coordinates, a partial wave series is performed both for the wave functions and the representation of the Coulomb interaction which depends on the third inter-particle coordinate, usually named r12. The r−1 12 interaction is the only one not considered by the basis, as generally done in atomic calculations with not explicitly correlated basis functions.

New numerical techniques to determine ionization cross sections: series representation for ${r}_{12}^{-1}$ integrals and Bohm’s velocity field