  We study relativistic nuclear matter in the $\sigma - \omega$ model including
the ring-sum correlation energy. The model parameters are adjusted
self-consistently to give the canonical saturation density and binding energy
per nucleon with the ring energy included. Two models are considered,
mean-field-theory where we neglect vacuum effects, and the relativistic Hartree
approximation where such effects are included but in an approximate way. In
both cases we find self-consistent solutions and present equations of state. In
the mean-field case the ring energy completely dominates the attractive part of
the energy density and the elegant saturation mechanism of the standard
approach is lost, namely relativistic quenching of the scalar attraction. In
the relativistic Hartree approach the vacuum effects are included in an
approximate manner using vertex form factors with a cutoff of 1 - 2 GeV, the
range expected from QCD. Due to the cutoff, the ring energy for this case is
significantlysmaller, and we obtain self-consistent solutions which preserve
the basic saturation mechanism of the standard relativistic approach.
