SU(2) Chiral $\sigma$ model and the properties of neutron stars

We discuss SU(2) chiral sigma model in the nuclear matter using mean field approach at high density. In this model we include a dynamically generated isoscalar vector field and higher order terms in scalar field. With inclusion of these, we reproduce the empirical values of the nuclear matter saturation density, binding energy and the nuclear incompressibility. The desirable value of incompressibility is chosen according to the recently estimated heavy-ion collision data. We then apply the same dynamical model to neutron-rich matter in beta equilibrium relating to neutron star structure. The maximum mass and corresponding radius of the stable non-rotating neutron stars are found to be in the observational limit