Scattering amplitude and interaction radius at high energies

Abstract

In this paper, a theoretical study of the interaction of hadrons at high energies is carried out within the eikonal approach using a relativistic quasipotential in the Yukawa form. The application of the of two-particle unitarity conditions and analytical continuity in the high-energy region allows for an effective consideration of the structure of the scattering amplitude in the impact parameter plane. The dependence of the cross section and the ratio A(t)—the of the real part of the forward scattering amplitude to its imaginary part, on the momentum t are discussed. The slope of diffraction at a given energy depends slightly on t. In more peripheral interactions, the nature of the potential does not affect the value of A(t) to the same extent as the momentum transfer. In the Oriar region, with increasing energy, the slope of the diffraction peak increases, indicateing that particles with small transverse moment become easier to scatter. By using the total angular momentum as a relativistic dynamic variable and taking into account the minimum value of this moment, beyond which partial waves contribute negligibly to the amplitude, an expression is derived for the effective interaction radius in the relativistic case. It is shown that the interaction radius cannot increase significantly with increasing energy, since this would lead toan unrealistic swelling of the particles. The physical interpretation of the results indicates that the qualitative scattering picture is valid for a broader class of strong potentials that decay rapidly at infinity. The obtained results are applied to elastic (p,p) scattering.