Proton-nucleus cross section at high energies

Cross sections for proton inelastic collision with different nuclei are described within the Glauber and multiple scattering approximations. A significant difference between approximate `Glauber' formula and exact calculations with a geometrical scaling assumption for very high-energy cross section is shown. Experimental values of proton-proton cross sections obtained using extensive air shower data are based on the relationship of proton-proton and respective proton-air absorption cross sections. According to obtained results values reported by the Akeno and Fly's Eye experimental groups are about 10% overestimated. The proper energy dependence of absorption cross section for collisions with air nuclei is of a great importance for studies of high energy cosmic rays using the Monte Carlo technique.