Space structure of hadrons in elastic scattering at high energy

Abstract

We have confirmed and complemented previous conclusions from studies of the impact parameter profiles, relative to $pp$ and $\bar pp$ scattering, using a generalized eikonalized amplitude. In particular, the transition from the grey to the black disk is followed, when the energy increases beyond $\sim 3$ TeV and for the inelastic process, by a black ring surrounding the antishadow scattering mode at the center. The ranges of hadronic forces responsible for the elastic and inelastic processes are estimated by means of root-mean-squares of the impact parameter. Predictions at the LHC energy are explicitly given. The effect of eikonalization is discussed.