  The effective isospin-density dependent pairing interaction (P1) [S. S.
Zhang, U. Lombardo and E. G. Zhao, Sci. Chin. Phys. Mech. Astro. {\bf 54}, 236
(2011)] extracted from neutron pairing gaps for $^1$S$_0$ in asymmetric nuclear
matter calculations [S. S. Zhang, L. G. Cao, U. Lombardo, et al. Phys. Rev. C
{\bf 81}, 044313 (2010)] is employed to study the bulk properties of Ca, Ni, Zr
and Sn isotopes. The odd-even mass (OEM) staggering is calculated by the Skyrme
Hartree-Fock plus BCS method (SHF + BCS) with the SkP interaction. For
comparison, we study two other types of isovector effective pairing
interactions. One is also extracted from pairing gaps of infinite nuclear
matter by the Brueckner-Hartree-Fock (BHF) method but for free spectrum (P2).
The other is obtained by fitting the empirical OEM (P3). An isoscalar effective
pairing interaction (P4) is also adopted which is determined by fitting the
empirical OEM. We find that interaction P1 can better describe the OEM
staggering of Ni, Zr and Sn isotopes by $14.3 \%, 41 \%, 30.4 \%$ compared with
interaction P2, in terms of root mean square deviations to the empirical OEM,
respectively. On the other hand, the performance of P1 and P2 is comparable for
Ca isotopes. For Ca and Ni isotopes, P1 behaves similarly as P3, but for Zr
isotopes P1 is better than P3 by $\sim 34 \%$. Among the four pairing
interactions studied, P4 performs the worst. Therefore, one may conclude that
for neutron pairings in finite nuclei, the isovector pairings are preferred
than the isoscalar one. It is quite interesting to note that the pairing
interaction P1 extracted from nuclear matter calculations can describe pairing
gaps of finite nuclei as well as or even better than the interaction P3
directly fitted to finite nuclei.
