Spin-dependent part of $p\bar{p}$ interaction cross section and Nijmegen potential

Low energy $p\bar{p}$ interaction is considered taking into account the polarization of both particles. The corresponding cross sections are calculated using the Nijmegen nucleon-antinucleon optical potential. Then they are applied to the analysis of the polarization buildup which is due to the interaction of stored antiprotons with polarized protons of a hydrogen target. It is shown that, at realistic parameters of a storage ring and a target, the filtering mechanism may provide a noticeable polarization in a time comparable with the beam lifetime.