High-Energy Large-Angle Scattering by Singular Potentials

An attempt, based on potential scattering, to understand the recent experimental results on high-energy large-angle proton-proton scattering is presented. Potentials of the form $g e^{-i\Delta } r^{-n}$, representing strong absorption ($\pi >\Delta \ge 0$; $n\ge 2$) at short distances $r$ ($g>\mathrm{}0\mathrm{}$ may depend on the energy), are studied in order to obtain the asymptotic form of the associated scattering amplitude at high energies and fixed (nonforward) angle. This form is found to display the rapid (exponential) decrease of the (elastic) differential cross section with increasing scattering angle which is typical of the $p-p$ experiments.