An effective potential operator, previously derived from a multiple-scattering series expansion of the exact transition amplitude for scattering two composite particles, is used in a high energy context to derive an approximate one-body Schrödinger equation by use of the closure approximation. The equivalent one-body equation is reduced to a set of coupled-channel equations which relates the entrance channel to the final excited states of the projectile and target. A Schrödinger equation for the coherent elastic amplitude is extracted from the coupled equations. Total and absorption cross sections are then derived on the basis of the Eikonal approximation and the assumption that the coherent scattering dominates the forward scattered amplitude. Unlike other models, the assumption that nuclear matter single-particle densities can be represented by nuclear charge distributions is not made. Instead, a method for extracting single-particle density distributions from nuclear charge distributions is presented. Comparisons with other theoretical models and with recent experimental data are also made. Finally, an experimental method for choosing between the Glauber approximation and the theory presented here is suggested.