Small angle scattering in quantum electrodynamics

A problem is formulated of particle scattering on small angles within the framework of the perturbation theory. The main term of the scattering amplitude expansion is calculated by adding Feynman diagrams. Particles with spin 1/2 are considered. An accurate formulation of the problem at the small values of momentum transfer squared receives primary attention. The principal result of the paper is obtaining the correction term in the Rutherford formula for the scattering cross section in all the orders of the constant of fine structure. The relation between the results obtained and nonrelativistic and relativistic quantum mechanics is discussed