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The empirical pairing gaps derived from four different odd-even massstaggering formulas are compared. By performing single-$j$ shell andmulti-shell seniority model calculations as well as by using the standard HFBapproach with Skyrme force we show that the simplest three-point formula$\Delta_C^ {(3)}(N)=\frac{1}{2}\left[B(N,Z)+B(N-2,Z)-2B(N-1,Z)\right]$ canprovide a good measure of the neutron pairing gap in even-$N$ nuclei. Itremoves to a large extent the contribution from the nuclear mean field as wellas contributions from shell structure details. It is also less contaminated bythe Wigner effect for nuclei around $N=Z$. We also show that the strength of$\Delta^ {(3)}_C(N)$ can serve as a good indication of the two-particle spatialcorrelation in the nucleus of concern and that the weakening of $\Delta^{(3)}_C(N)$ in some neutron-rich nuclei indicates that the di-neutroncorrelation itself is weak in these nuclei.

Empirical pairing gaps, shell effects, and di-neutron spatial correlation in neutron-rich nuclei