Polarization effects in non-relativistic $ep$ scattering

The cross section which addresses the spin-flip transitions of a proton (antiproton) interacting with a polarized non-relativistic electron or positron is calculated analytically. In the case of attraction, this cross section is greatly enhanced for sufficiently small relative velocities as compared to the result obtained in the Born approximation. However, it is still very small, so that the beam polarization time turns out to be enormously large for the parameters of $e^{\pm }$ beams available now. This practically rules out a use of such beams to polarize stored antiprotons or protons.