The energy limit of Coulomb wave functions in angular distribution in (e, 3e) reactions on helium

Abstract We have studied the fivefold differential cross section (FDCS) for the electron-impact double ionization of helium for moderate incident energy less than 1 keV . The calculation is based on the first Born approximation and non relativistic regime. The wave functions of the incident and scattered electrons are treated as plane waves, while that of the ejected electron moving in the Coulomb field of the residual nucleus He 2+ and the other electron leaving the target atom is represented by Coulomb wave function or plane wave function depending on their energy. On the other hand, the coupling between the two ejected electrons is approximated by the Gamow factor. The influence of the scattering angle and the energies of the leaving electron of the target atom is analyzed and several illustrative examples are discussed. We find that in general the FDCS are strongly dependant on the choice of the model of the ejected wave functions, i.e. of energies of the electrons leaving the target-atom and presents a deep destructive interference between the various contributing Coulomb wave functions.