The BCS Critical Temperature for Potentials with Negative Scattering Length

Abstract

We prove that the critical temperature for the BCS gap equation is given by $T_c = \mu (8/\pi e^{\gamma -2} + o(1)) e^{\pi/(2\sqrt \mu a)}$ in the low density limit $\mu\to 0$. The formula holds for a suitable class of interaction potentials with negative scattering length $a$ in the absence of bound states.