Gluon saturation effects at the nuclear surface: Inelastic cross section of proton–nucleus in the ultra-high-energy cosmic ray domain

Considering the high-energy limit of the QCD gluon distribution inside a nucleus, we calculate the proton–nucleus total inelastic cross section using a simplified dipole model. We show that, if gluon saturation occurs in the nuclear surface region, the total cross section of proton–nucleus collisions increases more rapidly as a function of the incident energy compared to that of a Glauber-type estimate. We discuss the implications of this with respect to recent ultra-high-energy cosmic ray experiments.