Central and peripheral interactions of hadrons

Surprisingly enough, the ratio of elastic to inelastic cross sections of proton interactions increases with energy in the interval corresponding to ISR $\rightarrow $ LHC (i.e. from 10 to 10$^4$ GeV). That leads to special features of their spatial interaction region at these and higher energies. 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 inelastic 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-parameter 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 the formation of the diffraction cone is less significant.