We develop two variational wave functions of helium which give accurate energy values and satisfy Kato's cusp conditions adapted to the variational procedure. These wave functions are utilized in calculations for reproducing the electron-helium double-ionization experimental data involving both the small and large momentum transfer. A comparison of the present numerical results for the differential cross sections with experiment indicates a minor role of the cusp conditions.

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In this review, a generalization of few body quantum scattering theory is given for the case of Cou lomb interaction. Since in this specific case the scattering amplitude, which is a solution to a resolvent type equation, possesses a singularity when the complex parameter z tends to the energy shell, a definition of the physical amplitude is provided. A recipe for regularizing integrals (eliminating divergences), which describe the terms of a perturbation theory series for different perturbing potentials, is formulated. As an example, the general theory is applied to the calculations of differential cross sections for a quasi elastic electron impact ionization reaction on atomic hydrogen.

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