We study the properties of non-rotating and rotating neutron stars for a new set of equations of state (EOSs) with different high density behaviour obtained using the extended field theoretical model. The high density behaviour for these EOSs are varied by varying the ω−meson self-coupling and hyperon-meson couplings in such a way that the quality of fit to the bulk nuclear observables, nuclear matter incompressibility coefficient and hyperon-nucleon potential depths remain practically unaffected. We find that the largest value for maximum mass for the non-rotating neutron star is 2.1M ⊙ . The radius for the neutron star with canonical mass is 12.8 − 14.1 km provided only those EOSs are considered for which maximum mass is larger than 1.6M ⊙ as it is the lower bound on the maximum mass measured so far. Our results for the very recently discovered fastest rotating neutron star indicate that this star is supra massive with mass 1.7 − 2.7M ⊙ and circumferential equatorial radius 12 − 19 km.

We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass (∼ 1.4M ⊙ ). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the same set of the data as employed to determine the parameters of the GSEF. We find that the GSEF yields larger values for the neutron skin thickness which are closer to the recent predictions based on the isospin diffusion data. The Skyrme parameters so obtained are employed to compute the strength function for the isoscalar giant monopole, dipole and quadrupole resonances. It is found that in the case of GSEF, due to the the larger value of the nucleon effective mass the values of centroid energies for the isoscalar giant resonances are in better agreement with the corresponding experimental data in comparison to those obtained using the SSEF. We also present results for some of the key properties associated with the neutron star of "canonical" mass and for the one with the maximum mass. 21.65+f,24.30.Cz,21.60jz,26.60.+c