The approach of panti p and pp elastic scattering to 'asymptopia'

We have previously made a model-free analysis of the t=0 amplitude for panti p and pp elastic scattering using data in the energy region 5 < √s < 62 GeV. We use our high-energy values of sigmasub(tot) and rho to fix the energy dependence of the Chou-Yang model of elastic scattering and compute the differential elastic scattering cross sections, dsigmasub(n)/dt, at large -t. In this note, we show that this model, which is dominated at low energies by the matter distribution of the panti p (pp) system, goes over at SSC energy, 40 TeV, essentially into a structureless black disk. The curvature parameter, C=(1/2)d2 [log(dsigmasub(n)/dt)]/dt2 at t=0, is a sensitive indicator of this transition to 'asymptopia', being positive at ISR energies, going through zero near √s=2TeV (the tevatron collider), and becoming very negative at √s=40 TeV (the SSC), where the predictions for the Chou-Yang model are hardly distinguishable from those for a sharp disk, after the diffraction have been filled in by the contribution of the real part. (orig.)