Explicit formula for hadron-nucleus elastic scattering in the eikonal approximation

We obtain a closed form asymptotic approximation to the eikonal amplitude in hadron-nucleus scattering which agrees remarkably well with numerical evaluation of the full eikonal amplitude. The characteristic features of the scattering are dominated by the nuclear edge: its radius and thickness. The radius determines the oscillations and the thickness the exponential decrease with momentum transfer of the cross section. By developing systematic corrections to our asymptotic approximation we can separate the effects of ''hard'' and ''soft'' collisions in the multiple-scattering sense