We develop a simple numerical method that allows us to calculate the BCS superfluid transition temperature $T_c$ precisely for any interaction potential. We apply it to a polarized, ultracold Fermi gas with long-range, anisotropic, dipolar interactions and include the effects of anisotropic exchange interactions. We pay particular attention to the short-range behavior of dipolar gases and reexamine current renormalization methods. In particular, we find that dimerization of both atoms and molecules significantly hampers the formation of a superfluid. The end result is that at high density or interaction strengths, we find $T_c$ is orders of magnitude lower than previous calculations.

• Received 17 February 2016

DOI:https://doi.org/10.1103/PhysRevA.94.023603