  Low energy $p\bar p$ interaction is considered taking into account the
polarization of both particles. The corresponding cross sections are calculated
using the Paris 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 provides a noticeable polarization in a time comparable with the beam
lifetime.
