Exact second Born amplitude for elastic electron-hydrogen scattering

An exact calculation of the second Born amplitude for elastic electron-hydrogen scattering at 30 eV is reported. Comparison is made with various forms of the closure approximation to the amplitude and it is concluded that failure of the closure approximation cannot account for the existing discrepancies between theories employing the second Born approximation and experimental data on elastic electron-atom scattering. It is suggested that the principal cause of the disagreement lies in the neglect of second- and higher-order exchange terms. (author)