Asymptotic form of the electron capture cross section in the impulse approximation

It is shown that the high energy limit of the impulse approximation developed by Pradhan in 1957 is not uniquely defined for the process H + +H(1s) → H(1s)+H + . It is argued that the correct limit is identical with that of the first Born approximation. That this result differs from the high energy limit obtained by Bransden and Cheshire in 1963 is a consequence of a discontinuity in the matrix element at this limit. It is also shown how the impulse approximation can be deduced from the sum of the first and second Born matrix elements. This particular form of the second Born matrix element is compared with another form, and the differences are discussed.