Generalized Sturmian Functions applied to double continuum problems

The Generalized Sturmian Functions method aims to deal with atomic physics problems. It has seen application to two and three-body problems, and its flexibility enables one to work with bound systems as well as with particles in the continuum. In the present contribution we analyze how the method expands the atomic double continuum in collision problems, using the double ionization of Helium by fast electrons as a showcase. We first test the robustness of the method in a particularly challenging situation, the zero energy case. We then present fully differential cross sections for a scattering problem which after 15 years of continued efforts has not been satisfactorily solved: the double ionization of Helium by electron impact in the fast projectile regime, as measured by the Orsay group.