  An analysis of p-air cross section data from Extensive Air Shower (EAS)
measurements is presented, based on an analytical representation of the pp
scattering amplitudes that describes with high precision all available
accelerator data at ISR, SPS and LHC energies. The theoretical basis of the
representation, together with the very smooth energy dependence of parameters
controlled by unitarity and dispersion relations, permits reliable
extrapolation to high energy cosmic ray and asymptotic energy ranges.
Calculations of the p-air production cross section based on Glauber formalism
are made using the input values of the pp forward scattering parameters at high
energies, with attention given to the independence of the real and imaginary
slope parameters. The influence of contributions of diffractive intermediate
states, according to Good-Walker formalism, is examined. The comparison with
cosmic ray data is very satisfactory in the whole pp energy interval from 1 to
100 TeV. High energy asymptotic behavior of p-air cross sections is
investigated in view of the geometric scaling property of the pp amplitudes.
The observed energy dependence of the ratio between p-air and pp cross sections
in the data is shown to be related to the nature of the pp cross section at
high energies, that does not agree with the black disk image.
