Large momentum transfer collisions off simple atoms

A detailed analytic examination of the Born series is presented for large momentum transfer electron-hydrogen and electron-helium collisions. Comparison of the differential cross sections is made with recent fully numerical calculations and experiments for both elastic and inelastic collisions. The initial state is chosen to be a ground state as well as some of the lower lying excited bound states. The final state is one of the lower lying excited bound states. The agreement is remarkable at even incident energies below where one might expect the Born series would be accurate.