Abstract
It is shown that the third-order second Born approximation, in which the second Born cross section is evaluated correct to only third order in the interaction potential, gives poor results for electron impact excitation of the 11S to 21S transition. The full second Born approximation, in which cross sections are calculated by squaring the modulus of the full second Born amplitude, is better but still not quite satisfactory. A corrected simplified second Born approximation is proposed in which couplings between the 11S and 21S states are given special treatment. The new approximation is in good agreement with experiment except at low energies and large angles.
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