  We consider a bilayer setup with two parallel planes of cold fermionic polar
molecules when the dipole moments are oriented perpendicular to the planes. The
binding energy of two-body states with one polar molecule in each layer is
determined and compared to various analytic approximation schemes in both
coordinate- and momentum-space. The effective interaction of two bound dimers
is obtained by integrating out the internal dimer bound state wave function and
its robustness under analytical approximations is studied. Furthermore, we
consider the effect of the background of other fermions on the dimer state
through Pauli blocking, and discuss implications for the zero-temperature
many-body phase diagram of this experimentally realizable system.
