  We studied numerically the Andreev scattering cross-sections of
three-dimensional isolated quantized vortex rings in superfluid 3He-B at
ultra-low temperatures. We calculated the dependence of the cross-section on
the ring's size and on the angle between the beam of incident thermal
quasiparticle excitations and the direction of the ring's motion. We also
introduced, and investigated numerically, the cross-section averaged over all
possible orientations of the vortex ring; such a cross-section may be
particularly relevant for the analysis of experimental data. We also analyzed
the role of screening effects for Andreev reflection of quasiparticles by
systems of vortex rings. Using the results obtained for isolated rings we found
that the screening factor for a system of unlinked rings depends strongly on
the average radius of the vortex ring, and that the screening effects increase
with decreasing the rings' size.
