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 a simple generalization to highest energy proton-nucleus cross-sections. This results in a leading ln(2) W 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(2) W 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.