The BCS energy gap at low density

We show that the energy gap for the BCS gap equation is = μ( 8 e^-2 + o(1)) exp( π/2√(μ) a) in the low density limit μ→ 0 . Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V . The results hold for a class of potentials with negative scattering length a and no bound states.