Summing over excited states of the target in atomic collisions

A new approximation is introduced for summing the first Born cross section over the final excited states of the target in atomic collisions. The new approach attempts to model energy differences between target states while at the same time preserving completeness of the target state set. Tests of the approximation against accurate first Born calculations for electron loss from H(1s) and H(2s) and discrete excitation of H(1s) to the n=2 and n=3 levels, all in collision with a He target, prove very successful. Two particular applications of the method are made, the first to electron loss in H(1s)+Xe collisions, the second to the double differential cross section for electron ejection in He + (1s)+He encounters. In the latter case an existing discrepancy between theory and experiment for near forward electron ejection is resolved. The closure approximation is also discussed with particular emphasis on electron loss collisions.