Triple differential cross section for the ionization of helium by electronic impact

We report results of analytical triple differential cross sections ( tdcs) for the single ionization of the helium iso-electronic ions by the electron impact. A two variational parameters wave function is used to evaluate the tdcs. This study shows the accuracy of the tdcs for helium atom and helium like ions in the first Born approximation ( fba) at high incident energy domain. The theory is quite acceptable as a fast calculation of the triple differential cross section, particularly at high energies where other theories and methods are cumbersome. A comparison is made of our calculations with previous results of the other theoretical methods and experiment. The fba results obtained here with the two variational parameters wave function are in good agreement with the experiment data at high incident energy. The results show that the electron correlation effects are important around the maxima and influence only the extrema magnitude but not their positions. The calculations presented here are extanded to the cases where the energies of the outgoing electrons are more equal.