The Gauss theorem in potential scattering theory and semi-classical corrections to the eikonal scattering amplitude

A method is proposed for the calculation of the amplitude of high-energy spinor particle potential scattering, based on the Gauss theorem application. We demonstrate the possibility of the scattering amplitude being expressed in terms of an integral over arbitrary surfaces, surrounding the external field influence domain. This representation enables to develop a simple and general method of calculating the semi-classical corrections to the eikonal scattering amplitude.