Cooper instability in the Jellium model: Implicit renormalization approach

We study superconducting properties of the jellium model by the implicit renormalization approach, which enables us to reliably determine the exponentially low transition temperatures in s-, p-, and d-channels. Existence of superconducting states at r_s>2.0 within the RPA approximation indicates that dynamic screening may lead to an effective attractive Cooper-channel coupling, in disagreement with the notion of repulsive pseudopotential. Going beyond RPA, we consider an effective KO interaction, as well as the effects of higher-order diagrams accounting for renormalization of the electron self-energy and the vertex function with the projection renormalization method.