Vacuum polarization effects on meson propagators

The stability of uniform nuclear matter in the relativistic Hartree approximation to the Walecka model is investigated by calculating the meson propagators in the one-loop approximation. In this renormalizable model, Dirac nucleons interact with neutral scalar and vector mesons. At the one-loop level, nuclear matter is found to be unstable to short-wavelength modes because of vacuum polarization effects. This occurs at momenta greater than twice the free-nucleon mass. The onset of instability is pushed to larger momenta with increasing baryon density as the nucleon effective mass decreases. The implications of short-range correlations and vertex corrections are discussed.