  We study fermions in two dimensions interacting via a long-ranged 1/r
potential for small particle separations and a short-ranged 1/r^3 potential for
larger separations in comparison to a length scale \xi. We compute the energy
of the Wigner crystal and of the homogeneous Fermi liquid phases using a
variational approach, and determined the phase diagram as a function of density
and \xi at zero temperature. We discuss the collective modes in the Fermi
liquid phase, finite temperature effects on the phase diagram, and possible
experimental realizations of this model.
