  We have examined the properties of neutron-rich matter and finite nuclei in
the modified relativistic Hartree approximation for several values of the
renormalization scale, $\mu$, around the standard choice of $\mu$ equal to the
nucleon mass $M$. Observed neutron star masses do not effectively constrain the
value of $\mu$. However for finite nuclei the value $\mu/M=0.79$, suggested by
nuclear matter data, provides a good account of the bulk properties with a
sigma mass of about 600 MeV. This value of $\mu/M$ renders the effective three
and four body scalar self-couplings to be zero at 60\% of equilibrium nuclear
matter density, rather than in the vacuum. We have also found that the matter
part of the exchange diagram has little impact on the bulk properties of
neutron stars.
