Introducing a phase factor for the two-electron continuum representation

In the asymptotic region Omega(0) (large hyperradius), the two-electron continuum wave function presents formally a logarithmic phase term corresponding to the electron-electron interaction. The idea of this contribution is to somehow include this phase into a Convoluted Quasi Sturmian (CQS) basis whose elements already behave asymptotically as an outgoing (incoming) six-dimensional spherical wave. With an appropriately introduced phase factor, the new CQS possess an asymptotic form very close to the formal one, and hopefully constitute a suitable set of basis functions for the three-body Coulomb continuum wave function representation in the entire space. To illustrate this numerically, we have considered a first order (e, 3e) non-homogeneous Schrodinger equation for the electron impact double ionization of helium: a considerable improvement of the partial transition amplitudes' convergence rate is observed with a simple two-parameters form of the introduced phase factor.