  The impact of the short-range interaction on the resonances occurrence in the
anisotropic dipolar scattering in a plane was numerically investigated for the
arbitrarily oriented dipoles and for a wide range of collision energies. We
revealed the strong dependence of the cross section of the 2D dipolar
scattering on the radius of short-range interaction, which is modeled by a hard
wall potential and by the more realistic Lennard-Jones potential, and on the
mutual orientations of the dipoles. We defined the critical (magic) tilt angle
of one of the dipoles, depending on the direction of the second dipole for
arbitrarily oriented dipoles. It was found that resonances arise only when this
angle is exceeded. In contrast to the 3D case, the energy dependencies of the
boson (fermion) 2D scattering cross section grows (is reduced) with an energy
decrease in the absence of the resonances. We showed that the mutual
orientation of dipoles strongly impacts the form of the energy dependencies,
which begin to oscillate with the tilt angle increase, unlike the 3D dipolar
scattering. The angular distributions of the differential cross section in the
2D dipolar scattering of both bosons and fermions are highly anisotropic at
non-resonant points. The results of the accurate numerical calculations of the
cross section agree well with the results obtained within the Born and eikonal
approximations.
