Exact solutions of relativistic two-particle equations for scattering *s*-states are obtained in cases of the -function potential and superpo-sition of two
-function potentials. Scattering amplitudes and phase shifts are calculated on the basis of wave functions found. The analysis of values obtained was carried out. As a result, the unitarity condition and vanishing conditions of scattering amplitudes are proved. It is shown that the non-relativistic limit of relativistic expressions obtained yields results which coincide with corresponding expressions which were found in the process of solving the Schrodinger equation.

Keywords: relativistic two-particle equation, relativistic configurational representation, delta-function potential, scattering amplitude, *S*-matrix, phase shift, unitarity condition, Ramsauer – Townsend effect.

V.N. Kapshai – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus

Yu.A. Grishechkin – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus