Highest Energy Proton-Nucleus Cross Sections

TL;DR

This paper extends the black disc model for high energy proton-proton interactions to proton-nucleus collisions, predicting cross section growth with energy and implications for cosmic ray physics.

Contribution

It introduces a generalized model for proton-nucleus cross sections at high energies, including specific energy-dependent terms based on nucleus size.

Findings

Predicts a ln^2 W growth term in cross sections

Identifies a significant ln W term with a nucleus-dependent coefficient

Suggests observable effects in cosmic ray interactions with atmospheric nuclei

Abstract

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.