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 like 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 \sigma _ { pp } ^ { inel } = 51 mb at E _ { 0 } = 10 ^ { 6 } GeV to \sigma _ { pp } ^ { inel } = 64 mb at E _ { 0 } = 10 ^ { 8 } GeV and an elasticity , additionally increased by 10 % to 15 % , describes the data best .
Using these parameters , the mean logarithmic mass \langle \ln A \rangle derived from X _ { max } measurements is compatible with the extrapolations of the results of direct measurements to high energies using the poly-gonato model .