  We study the BCS superfluid transition in a single-component fermionic gas of
dipolar particles loaded in a tight bilayer trap, with the electric dipole
moments polarized perpendicular to the layers. Based on the detailed analysis
of the interlayer scattering, we calculate the critical temperature of the
interlayer superfluid pairing transition when the layer separation is both
smaller (dilute regime) and of the order or larger (dense regime) than the mean
interparticle separation in each layer. Our calculations go beyond the standard
BCS approach and include the many-body contributions resulting in the mass
renormalization, as well as additional contributions to the pairing
interaction. We find that the many-body effects have a pronounced effect on the
critical temperature, and can either decrease (in the very dilute limit) or
increase (in the dense and moderately dilute limits) the transition temperature
as compared to the BCS approach.
