Evidence for rapidly rising p--p total cross section from cosmic-ray data

We give estimates of lower bounds on the p-p total cross section based on cosmic-ray data. We find that ${\sigma }_{pp}$ rises at least as rapidly as $38.8+0.4{\ln }^2\left(\frac{s}{s_0}\right)$ from E∼10³ to 3×10⁴ GeV incident energy, corresponding to ${\sigma }_{pp}\gg 60$ mb at the highest energy available. In view of large experimental errors at the highest energies, a value of ${\sigma }_{pp}\gg 48$ mb can be estimated at 95% confidence level at E∼10⁴ GeV.