Liquid-gas instability and superfluidity in nuclear matter

We study effects of the medium polarization on superfluidity in symmetric nuclear matter in a relativistic formalism. An effect of the liquid-gas instability is emphasized. We examine two types of decomposition of the nucleon propagator; the standard Feynman-density and the particle-hole-antiparticle ones. In both cases, the medium polarization effect is determined by a characteristic cancellation among the \sigma, the longitudinal \omega, and the \sigma-\omega mixed polarizations. The instability leads to increase of pairing gap. Around the saturation density that is free from the instability the medium polarization enhances pairing gap in the former case whereas reduces in the latter. At the lowest density that is also free from the instability the gap increases in both cases.