Central and peripheral interactions of hadrons

TL;DR

This paper explores how the ratio of elastic to inelastic proton cross sections increases with energy, revealing spatial interaction features of hadrons through phenomenological models and impact parameter analysis.

Contribution

It introduces a detailed analysis of central and peripheral hadron collisions using impact parameters and elastic scattering data, highlighting the spatial structure of inelastic regions at high energies.

Findings

Elastic to inelastic cross section ratio increases with energy.

Differential cross section shape is influenced by intermediate impact parameter collisions.

Elastic scattering at small momenta probes peripheral processes with large impact parameters.

Abstract

Surprisingly enough, the ratio of elastic to inelastic cross sections of proton interactions increases with energy in the interval correspond- ing to ISR - LHC (i.e. from 10 GeV to 10 TeV). That leads to special features of their spatial interaction region at these and higher ener- gies. Within the framework of some phenomenological models, we show how the particular ranges of the transferred momenta measured in elastic scattering experiments expose the spatial features of the in- elastic interaction region according to the unitarity condition. The difference between their predictions at higher energies is discussed. The notion of central and peripheral collisions of hadrons is treated in terms of the impact parameters description. It is shown that the shape of the differential cross section in the diffraction cone is mostly determined by collisions with intermediate impact parameters. Elastic scattering at very small transferred momenta is sensitive to peripheral processes with large impact parameters. The role of central collisions in formation of the diffraction cone is less significant.