On total inelastic cross sections and the average depth of the maximum of extensive air showers

The model dependence of the development of extensive air showers generated by high-energy cosmic-ray particles in the atmosphere is studied. The increase of proton–proton and proton–air inelastic cross sections and values for the elasticity are varied in the hadronic interaction model QGSJET. Using the CORSIKA simulation program, the impact of these changes is investigated on air shower observables such as the average depth of the shower maximum X_max and the number of muons and electrons at ground level. Calculating the mean logarithmic mass from experimental X_max values, it is found that a moderate logarithmic increase of the proton–proton inelastic cross section from σ^inel_pp = 51 mb at E₀ = 10⁶ GeV to σ^inel_pp = 64 mb at E₀ = 10⁸ GeV, and an elasticity, additionally increased by 10%–15%, describe the data best. Using these parameters, the mean logarithmic mass 〈ln A〉 derived from X_max measurements is compatible with the extrapolations of the results of direct measurements to high energies using the poly-gonato model.