High-energy nucleon-nucleus scattering and cosmic-ray cross sections

We develop a QCD-based diffractive model for nucleon-nucleon and nucleon-nucleus cross sections in which the increase in the cross sections at high energies is driven by semihard parton-parton scattering. We use the model to calculate the absorptive cross section for protons on air at very high energies, and find excellent agreement with data from cosmic-ray experiments. The results can be used to extract ${\sigma }_{\mathrm{tot}(\mathrm{pp}}$) from ${\sigma }_{\mathrm{abs}(\mathrm{p}}$-air) in a way which is nearly independent of the input parameters. We include an approximate treatment of single-diffractive pp scattering.