The effective chiral model is extended by introducing the contributions from the cross-couplings between isovector and isoscalar mesons. These cross-couplings are found to be instrumental in improving the density content of the nuclear symmetry energy. The nuclear symmetry energy as well as its slope and curvature parameters at the saturation density are in harmony with those deduced from a diverse set of experimental data. The equation of state for pure neutron matter at sub-saturation densities is also in accordance with the ones obtained from different microscopic models. The maximum mass of neutron star is consistent with the measurement and the radius at the canonical mass of the neutron star is within the empirical bounds.
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