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

The empirical pairing gaps derived from four different odd–even mass staggering formulas are compared. By performing single-j   shell and multi-shell seniority model calculations as well as by using the standard HFB approach with Skyrme force we show that the simplest three-point formula ΔC(3)(N)=12[B(N,Z)+B(N−2,Z)−2B(N−1,Z)] can provide a good measure of the neutron pairing gap in even-N   nuclei. It removes to a large extent the contribution from the nuclear mean field as well as contributions from shell structure details. It is also less contaminated by the Wigner effect for nuclei around N=ZN=Z. We also show that the strength of ΔC(3)(N) can serve as a good indication of the two-particle spatial correlation in the nucleus of concern and that the weakening of ΔC(3)(N) in some neutron-rich nuclei indicates that the di-neutron correlation itself is weak in these nuclei.