  We evaluate the effective potential for the conventional linear Walecka non
perturbatively up to one loop. This quantity is then renormalized with a
prescription which allows finite vacuum contributions to the three as well as
four 1PI Green's functions to survive. These terms, which are absent in the
standard relativistic Hartree approximation, have a logarithmic energy scale
dependence that can be tuned so as to mimic the effects of phi3 and phi4 type
of terms present in the non linear Walecka model improving quantities such as
the compressibility modulus and the effective nucleon mass, at saturation, by
considering energy scales which are very close to the nucleon mass at vanishing
density.
