Energy Dependence of the Ratio of the Elastic-to-Total Cross Sections for Proton—Proton and Antiproton—Proton Collisions

The results obtained from a phenomenological analysis of the ratio of the elastic-to-total cross sections for proton-proton (pp) and antiproton-proton ($\left(\overline{p}p\right)$) scattering as a function of energy are presented. Analytic functions proposed on the basis of studying low- and high-energy experimental data for various scattering parameters make it possible to obtain a statistically acceptable quantitative description of the energy dependence of this ratio over a broad energy region of $\sqrt{s}\ge 3$ GeV for individual samples of pp and $\overline{p}p$ collisions and over the region of $\sqrt{s}\ge 5$ GeV for a combined ensemble of experimental data. On the basis of the resulting approximations, the ratio of the elastic-to-total cross sections for pp collisions are estimated at various values of $\sqrt{s}$ up to an ultrahigh energy of $\sqrt{s}=10$ PeV. The resulting estimates may prove to be useful for experiments at currently operating and future hadron colliders, as well as for measurements of ultrahigh-energy cosmic rays. An indication of the onset of the asymptotic region for the cross-section ratio in question is observed in the region of $\sqrt{s}\gtrsim 5-10$ PeV.