  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 ($\sim 1.4
M_\odot$). 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.
