Pion condensation in the Walecka model

We calculate the pion propagator in nuclear matter in a relativistic random-phase approximation to the Walecka model. We present results for the pion dimesic function for densities up to several times normal nuclear matter density. We do not observe pion condensation even in the absence of short-range correlations. Although we do observe strong pionic enhancements, these enhancements disappear at high enough nuclear density due to the strong density dependence of the effective nucleon mass ${\mathit{M}}^{\mathrm{*}}$. For a set of parameters that give a smoother behavior of ${\mathit{M}}^{\mathrm{*}}$ with density there is a lower critical density for pion condensation to set in. In contrast to nonrelativistic calculations, however, there is also an upper critical density at which the normal state is restored.