Evaluation of the second Born amplitude as a two-dimensional integral for H++H(1s) to H(1s)+H+

The second Born amplitude (with the exact propagator replaced by the free particle propagator) for the electron capture reaction H + +H(1s) to H(1s)+H + is reduced to a two-dimensional integral. The integrand has several singularities, which are dealt with. Results of the numerical integration of the cross section for various energies in the 25-200 keV range are presented.