Some remarks on off-shell scattering in the eikonal approximation and applications to semi-inclusive reactions

Abstract Using the Abel inversion for the eikonal phase as function of the interaction we derive simple integral relations between half and on-shell eikonal phases. A frequently used short-range approximation for the half off-shell phase and profile appears supported by the above-mentioned relation. We work out some examples and also address the half off-shell eikonal phase pertinent to a diffractive amplitude. The latter is relevant for a calculation of selected transparencies T of nuclei for a proton, knocked-out in selected semi-inclusive A ( e , e ′ p ) X reactions. Some numerical results for T are given.