The generalized hybrid derivative coupling model has been applied to explor
e various ground state properties of different nuclei. In this work we have
confined our calculation only to the model characterized by the hybridizat
ion parameter alpha = 1/4 which gives better results than the other models
of the same class, as we have seen earlier, for nuclear matter calculations
. The binding energy, single-particle energy spectra, density and charge ra
dii of different doubly closed nuclei like O-16, Ca-40, Ca-48, Zr-90, Sn-13
2, Pb-208 have been studied. The success of this model, in describing the d
oubly closed nuclei, motivates us to extend this calculation further in the
case of open shell nuclei after incorporating the pairing interaction and
using a BCS transformation. We have calculated the binding energy for such
nuclei. Mie have also studied the isotopic shift for different Pb isotopes
with respect to Pb-208. We have compared our results with the other standar
d theoretical results as well as with the experimental values.