On the first-order approximations for positronium formation in atomic hydrogen

A class of first-order approximations-the first Born approximation, the first-order exchange approximation and the modified Born approximation-are applied to study the rearrangement collision process: e + +H(1s) to (e + e - )(1s)+H + . Numerical results for the differential and total cross sections are presented for the positron energy range 8.704-2000 eV. The differential cross section in the first Born approximation shows quite different features from that given by the other two cases. It is believed from a comparison of the results at 2000 eV that the high-energy dependence of the cross sections may not be determined by the first Born approximation.