  An accurately calibrated relativistic parametrization is introduced to
compute the ground state properties of finite nuclei, their linear response,
and the structure of neutron stars. While similar in spirit to the successful
NL3 parameter set, it produces an equation of state that is considerably softer
-- both for symmetric nuclear matter and for the symmetry energy. This
softening appears to be required for an accurate description of several
collective modes having different neutron-to-proton ratios. Among the
predictions of this model are a symmetric nuclear-matter incompressibility of
K=230 MeV and a neutron skin thickness in 208Pb of Rn-Rp=0.21 fm. Further, the
impact of such a softening on the properties of neutron stars is as follows:
the model predicts a limiting neutron star mass of Mmax=1.72 Msun, a radius of
R=12.66 km for a ``canonical'' M=1.4 Msun neutron star, and no (nucleon) direct
Urca cooling in neutrons stars with masses below M=1.3 Msun.
