Effects of the GMB correction on the critical temperature throughout the BCS-BEC crossover

It has long been known that the critical temperature of a BCS weak-coupling superfluid gets considerably reduced when the Gorkov-Melik-Barkhudarov (G-MB) correction is considered, whereby particle-hole excitations affect the two-fermion scattering in the medium responsible the formation of Cooper pairs. Here, by a careful analysis which takes into account the wave-vector and frequency dependence of the pair propagator (which gets increasingly important away from the weak coupling limit where the G-MB correction was originally derived) we extend the effects of the G-MB correction throughout the BCSBEC crossover. In particular, the Feynman diagram responsible for the G-MB correction is inserted in a partially self-consistent T-matrix scheme; the resulting equations are solved numerically and yield a curve for the critical temperature which agrees very well with the Quantum Monte Carlo data available in the crossover region.