  Low energy $\bar{p}d$ interaction is considered taking into account the
polarization of both particles. The corresponding cross sections are obtained
using the Nijmegen nucleon-antinucleon optical potential with shadowing effects
taken into account. Double-scattering effects are calculated within the Glauber
approach and found to be about 10-20%. The cross sections are applied to the
analysis of the polarization buildup which is due to the interaction of stored
antiprotons with a polarized 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. The energy
dependence of the polarization rate for deuterium target is similar to that for
hydrogen one. However, the time of polarization for deuterium is much smaller
than that for hydrogen.
