Noneikonal approach to the scattering of hadrons from nuclei I. General theory

Abstract

A procedure is given and utilized for the exact computation of multiple scattering amplitudes in the case of nonoverlapping, frozen, and singly struck target nucleons. Relaxing the condition of frozen scatterers, we essentially rederive the expressions mentioned above starting from relativistic Feynman diagrams which include the effect of nucleon recoil. By a heuristic procedure we also account for overlap and reflections to all orders. We show that all multiple scattering amplitudes thus calculated contain on-shell propagation parts close, but not identical, to their Glauber (eikonal) limits. Contributions due to off-shell propagation vanish in the eikonal limit, but constitute for finite energy and nonforward scattering angles the main corrections to this limit. The effect of the corrections in differential cross sections should be substantial in interference regions for low | t |, in particular, and for increasing | t |, in general. A numerical comparison among various predictions for the double scattering amplitude on a deuteron is given for a Gaussian wave function and Gaussian elementary amplitudes.