For calculating integrals involving four confluent hypergeometric functions, a general theoretical method is presented, which is valid for both symmetric and asymmetric geometries to determine the triple differential cross sections (TDCS) for electron impact ionization of ions. The TDCS for the ionization of hydrogenic ion at high and intermediate energies have also been calculated and compared with the existing theoretical results.

The triple differential cross sections (TDCS) in coplanar equal energy sharing and fixed relative angle geometry for electron impact ionization of He⁺ are calculated (by using a modified BBK model) at incident electron energies of 58.4,68,81.6,108.8 and 174.4 eV.Dominant ionization mechanisms are identified and the contributions of different scattering amplitudes are discussed.It concludes that Coulomb interaction in the initial channel,exchange effects,correlation and the coherence between electron electron and electron nucleus scattering are all important at these energies.

A general method to calculate the triple differential cross sections(TDCS) for electron impact ionization of hydrogen atom,hydrogenicion He⁺, helium atom and helium-like ion Li⁺is given by generalizing the theoretical framework developed by Brauner et al. The present TDCS results of H, He⁺, He and Li⁺are compared with those of other theoretical models and/or experiment, and good agreements have been found.