Proton-air collisions in a model of soft interactions at high energies

We evaluate both the Pomeron interactions and the inelastic Gribov corrections to the Glauber-Gribov formula, which is used to extract proton-proton cross sections from proton-air collisions at high energies. We demonstrate that these corrections are compatible with the errors for proton-air cross sections measured at ultrahigh energies in cosmic ray experiments. We present the results of a calculation of these cross sections based on our model for the soft interactions at high energies, which provides a good description of available accelerator data, including that for LHC energies.