Universality of the froissart limit of [formula omitted] for colliding hadrons or nuclei

Abstract

Making use of the supercritical pomeron model it is shown that at s → ∞ the ratio σ tot(s) ln 2 ( s m N 2 ) approaches the Froissait limit 2 πa 2 = const. which is independent of the kind of colliding particles, and increases slowly from the value of ∼ 0.25 mb to 0.5–0.6 mb in the region s > 10 10 GeV of superhigh energies. The multipomeron exchange graphs have been estimated using the two-channel model. In far asymptotics the threshold singularity at f = 4 m π 2 in the pomeron trajectory α p( t) and the interaction between pomerons are essential factors which result in the slow increase of the quantity σ tot ln 2 ( s m N 2 ) ⋍ 2πa 2 up to 0.5 mb, where a = 2 α′ p s ⋍ 0.06 fm at s ≳ 10 6 GeV, and a = Δ 2 m π + α′ p 2m π ⋍0.09 fm at s > 10 10 GeV ; Δ = α p (0) −1- 0.11, α′ p ⋍0.22( GeV) −2 . At superhigh energies, where the rising radius of hadron interaction R 0 = a ln ( s m N 2 ) , exceeds the nuclear radius R A = r 0A 1 3 , the nucleon-nucleus cross section σ NA tot ln 2 ( s m N 2 ) and even the nucleus-nucleus one σ A 1 A 2 tot ln 2 ( s m N 2 ) are shown to have the same limit 2 πα 2, a = 0.06–0.09 fm.