Highest Energy Proton-Nucleus Cross Sections

The description of very high energy proton-proton cross sections in terms of a `black disc' with an `edge' allows of a simple generalization to highest energy proton-nucleus cross sections. This results in a leading $ln^2W$ term and a $ln\, W$ term whose coefficient depends linearly on the radius of the nucleus ($W$ the c.m. energy). The necessary parameters are determined from the fits to p-p data. Since the coefficient of the $ln W$ term is rather large, it is doubtful that the regime of $ln^2W$ dominance can be reached with available energies in accelerators or cosmic rays. However, the $ln W$ term can be relevant for highest energy cosmic rays in the atmosphere, where a large increase for the cross section on nitrogen is expected. Tests of the theory should be possible by studying the coefficient of $ln W$ at p-nucleus colliders.