Symmetry energy of nuclear matter and properties of neutron statrs in a relativistic approach

Asymmetric nuclear matter is treated in the formalism of Dirac-Brueckner approach with Bonn one-boson-exchange nucleon-nucleon interaction. We extract the symmetry energy coefficient at the saturation to be about 31 MeV, which is in good agreement with empirical value of $30\pm 4$ MeV. The symmetry energy is found to increase almost linearly with the density, which differs considerably from the results of non-relativistic approaches. This finding also supports the linear parameterization of Prakash, Ainsworth and Lattimer. We find, furthermore, that the higher-order dependence of the nuclear equation of state on the asymmetry parameter is unimportant up to densities relevant for neutron stars. The resulting equation of state of neutron-rich matter is used to calculate the maximum mass of neutron star, and we find it to be about 2.1$M_\odot$. Possible mechanisms for the softening of the equation of state are also discussed.