Neutron stars with isovector scalar correlations

Neutron stars with the isovector scalar $\delta$-field are studied in the framework of the relativistic mean field ($RMF$) approach in a pure nucleon plus lepton scheme. The $\delta$-field leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses. Both features are influencing the stability conditions of the neutron stars. Two parametrizations for the effective nonlinear Lagrangian density are used to calculate the nuclear equation of state ($EOS$) and the neutron star properties, and compared to correlated Dirac-Brueckner results. We conclude that in order to reproduce reasonable nuclear structure and neutron star properties within a $RMF$ approach a density dependence of the coupling constants is required.