Evidence for Rapidly Risingρ−ρTotal 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 ${\sigma }_{\mathrm{pp}}$ rises at least as rapidly as $38.8+0.4{\ln }^2\left(\frac{s}{s_0}\right)$ from $E\sim {10}^3 \mathrm{to} 3\times {10}^4$ GeV incident energy, corresponding to ${\sigma }_{\mathrm{pp}}\gg 60$ mb at the highest energy available. In view of large experimental errors at the highest energies, a value of ${\sigma }_{\mathrm{pp}}\gg 48$ mb can be estimated at 95% confidence level at $E\sim {10}^4$ GeV.