  The polarized dipolar Fermi gas shows exotic properties at low temperatures,
characterized by an axially-deformed Fermi surface and anisotropic
single-particle energy, due to the long-range and anisotropic nature of
dipole-dipole interaction. In cold-atom experiments such a system has been
realized, e.g., in degenerate gas of Er and Dy atoms. In the case that
non-dipolar impurity atoms are introduced in such system, they undergoes an
induced interaction mediated by the density fluctuations of the background
dipolar Fermi gas. We derive the induced interaction potential to the
single-loop order of fluctuations and show that it becomes indeed an
anisotropic Ruderman-Kittel-Kasuya-Yosida-type potential which preserves the
axial symmetry around the polarization axis. We then solve the two-body problem
of impurity atoms interacting via the anisotropic potential and figure out the
dependence of bound state and scattering properties on the parameters of
dipolar Fermi gas.
