Kohn-luttinger effect and the instability of a repulsive Fermi-liquid at T=0

I consider the possibility for a pairing instability in a 2D repulsive Fermi-liquid due to the singularity in the scattering amplitude Γ(q) at the momentum transfer q ≈2p_F (Kohn-Luttinger effect). For arbitrary Fermi-liquid, Γ(q) for the particles at the Fermi surface is found to have a singular part, Γ^sing(q) ∼ {Mathematical expression}. For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi-liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing.