Induced interaction in a Fermi gas with a BEC-BCS crossover

Abstract

We study the effect of the induced interaction on the superfluid transition temperature of a Fermi gas with a Bose-Einstein condensation--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. The Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from the BCS side to the entire crossover and the pairing fluctuation is treated in the approach by Nozi\`eres and Schmitt-Rink. At unitarity, the induced interaction reduces the transition temperature by about 20%. In the BCS limit, the transition temperature is reduced by a factor of about 2.22, as found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the induced interaction is important both on the BCS side and in the unitary region.