Total Proton-Proton Cross Section ats12=30TeV

Abstract

We have measured the proton-air inelastic cross section at ${s}^{\frac{1}{2}}=30$ TeV by observing the distribution of extensive-air-shower maxima as a function of atmospheric depth. This distribution has an exponential tail whose slope is $\ensuremath{\lambda}=72\ifmmode\pm\else\textpm\fi{}9$ g ${\mathrm{cm}}^{\ensuremath{-}2}$ which implies that ${\ensuremath{\sigma}}_{p\ensuremath{-}\mathrm{air}}^{\mathrm{inel}}=530\ifmmode\pm\else\textpm\fi{}66$ mb. Using Glauber theory and assuming that the elastic-scattering slope parameter $b$ is proportional to ${\ensuremath{\sigma}}_{\mathrm{pp}}^{\mathrm{tot}}$, we infer a value of ${\ensuremath{\sigma}}_{\mathrm{pp}}^{\mathrm{tot}}=120\ifmmode\pm\else\textpm\fi{}15$ mb which lies between a $logs$ and a ${log}^{2}s$ extrapolation of the total $\mathrm{pp}$ cross section as measured at lower energies.