Second-order distorted wave calculation for electron impact ionization of helium to He$^{+}$(n=1 and 2)

Second-order distorted wave calculations are presented for electron impact ionization of helium with the residual ion left in n=1 and 2 states at intermediate energies in coplanar asymmetric geometry. Whereas previous second-order calculations have used the plane wave Born approximation and have used approximations to simplify the evaluation of the second-order term, we perform a full distorted wave calculation and make no approximations in the evaluation of the second-order amplitude (i.e. we sum over all contributing intermediate states). The triple differential cross sections are compared with experimental measurements and other theoretical results.