Mathematical models and algorithms for analysis of ionization processes of helium atom and hydrogen molecules with variational functions

Algorithms for calculations of the variational functions for ground state of helium atom slaved by Kato conditions, and wave function presented in product of two continuous spectrum Coulumb functions modified by second argument describing motion of ejected electron in the field of two Coulumb centers are presented. Calculations of differential ionization cross sections of helium atom and hydrogen ion by fast electron impact are compared with modern experiments. Originating of calculations multifold integrals with the above functions are reduced to triple integrals by means of Fourier transforms. Integrals kernel contains the hypergeometric functions ${}_2F_1(a,2;c,x)$, effective algorithm for their calculation is proposed.