We make use of isospin constraints to study the parametric coupling model and
the properties of asymmetric nuclear matter. Besides the usual constraints for
nuclear matter - effective nucleon mass and the incompressibility at saturation
density - and the neutron star constraints - maximum mass and radius - we have
studied the properties related with the symmetry energy. These properties have
constrained to a small range the parameters of the model. We have applied our
results to study the thermodynamic instabilities in the liquid-gas phase
transition as well as the neutron star configurations.Comment: 11 pages, 10 figure