First-order eikonal exchange amplitudes

A detailed derivation of a first-order analytic approximation to the electron-hydrogen charge-exchange amplitude in both the Glauber approximation and eikonal approximmations in both post and prior forms is presented. The results are applicable to arbitrary initial states. The approximation is applied to elastic scattering by hydrogen in its ground state, and numerical results for both the modulus and phase of the exchange amplitude are obtained. the analytic approximation converges rapidly to the exact eikonal result with increasing energy. The techniques used in approximating the contribution to the exchange amplitude arising from the electron-nucleus part of the interaction potential are discussed in detail