Eikonal exchange amplitudes

We show that the existing and widely used results for an approximation to eikonal exchange amplitudes, which contain an indeterminate phase, are not valid. We derive a new analytic result, containing a well-defined phase, which can be used unambiguously with direct amplitudes to calculate full differential cross sections. The modulus of our result also differs from that of the previous formulations. Comparisons are made with the earlier $e^{-}$-H approximate exchange calculations and with exact eikonal exchange calculations.