Liquid-Gas Instability and Superfluidity in Nuclear Matter

We study effects of medium polarization on superfluidity in symmetric nuclear matter in a relativistic formalism. The 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 σ, the longitudinal ω, and the σ-ω mixed polarizations. The instability leads to an increase of the pairing gap. Around the saturation density, which is free from the instability, the medium polarization enhances the pairing gap in the former case and reduces it in the latter. At the lowest density, which is also free from the instability, the gap increases in both cases.