Double ionization of helium with a convoluted quasi Sturmian approach

The double ionization of Helium by fast electron impact is investigated through an ab initio approach based on an expansion on convoluted quasi Sturmian functions. The latter are dressed with an appropriately built phase factor that allows to represent adequately the delicate Coulomb phase associated with the electron-electron interaction. In so doing, these dressed basis functions possess the correct asymptotic behavior in the double continuum channel. They are used to solve, in the whole space, the driven Schrodinger equation corresponding to a first order treatment of the scattering process. Because of the asymptotic built in property of the basis, the ionization amplitudes are extracted directly from the Coulomb three-body scattering wave function, without the need to evaluate a six-dimensional matrix element. The calculated (e ,3e ) fully differential cross sections for two electrons escaping at 10 + 10 eV or 4 + 4 eV are in good shape agreement with those obtained by two other numerical approaches. However, for certain geometrical configurations a magnitude enhancement is observed for the lower energy case, and is ascribed to the different large distance descriptions of the long range Coulomb correlation in the scattering solution.