Radiative corrections to the cross section of $e^-+p\to\nu+n$ and the crossed processes

Born cross section and the radiative corrections to its lowest order are considered in the frame work of QED with structureless nucleons including the emission of virtual and real photons. The result is generalized to take into account radiative corrections in higher orders of perturbation theory in the leading and next-to leading logarithmic approximation. Crossing processes are considered in the leading approximation.