Influence of Induced Interactions on the Superfluid Transition in Dilute Fermi Gases

We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor $(4e{)}^{1/3}\approx 2.2$, and for $\nu$ fermion species, the transition temperature is increased by a factor $(4e{)}^{\nu /3-1}\approx {2.2}^{\nu -3\mathrm{}}$. For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.