Proton-air and proton-proton cross sections from air shower data

Data on the fluctuations in depth of maximum development of cosmic ray air showers, corrected for the effects of mixed primary composition and shower development fluctuations, yield values of the inelastic proton-air cross section for laboratory energies in the range 10 to the 8th power to 10 to the 10th power GeV. From these values of proton-air cross section, corresponding values of the proton-proton total cross section are derived by means of Glauber theory and geometrical scaling. The resulting values of proton-proton cross section are inconsistent with a well known 1n(2)s extrapolation of ISR data which is consistent with SPS data; they indicate a less rapid rate of increase in the interval 540 sq root of s 100000 GeV.