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 formulacan 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 = Z. We also show that the strength of (3) C (N ) can serve as a good indication of the two-particle spatial correlation in the nucleus of concern and that the weakening of (3) C (N ) in some neutron-rich nuclei indicates that the di-neutron correlation itself is weak in these nuclei.The occurrence of a systematic odd-even staggering (OES) of the nuclear binding energy has long been identified in nuclear physics, which is associated with the pairing correlation [1,2]. It plays an important role in many nuclear phenomena and is the dominant many-body correlation beyond the nuclear mean field. Yet, in spite of the many efforts performed in the study of pairing correlations, there are still features which may be induced by the pairing interaction that are not

This work aims at a global assessment of the effect of the density dependence of the zero-range pairing interaction. Systematic Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface and mixed pairing forces are carried out to study the pairing gaps in even-even nuclei over the whole nuclear chart. Calculations are also done in coordinate representation for unstable semi-magic even-even nuclei. The calculated pairing gaps are compared with empirical values from four different odd-even staggering formulae. Calculations with the three pairing interactions are comparable for most nuclei close to β-stability line. However, the surface interaction calculations predict neutron pairing gaps in neutron-rich nuclei that are significantly stronger than those given by the mixed and volume pairing. On the other hand, calculations with volume and mixed pairing forces show noticeable reduction of neutron pairing gaps in nuclei far from the stability.

Two types of average neutron-proton interaction formulas are compared: In the first type, neutronproton interactions for even-even and odd-A nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number A and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-A and odd-A nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-A systems. We explore three possible ways to extract this additional interaction from the binding energy difference of neighboring nuclei. The extracted interactions are positive in nearly all cases and show weak dependence on the mass number. The empirical interactions are also compared with theoretical values extracted from recent nuclear mass models where large unexpected fluctuations are seen in certain nuclei. The reproduction of the residual neutron-proton interaction and the correction of those irregular fluctuations can be a good criterion for the refinement of those mass models.

We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-N isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in 120 Sn and globally to all available data on the OES of semi-magic nuclei with Z ≥ 8. In the former calculations, there is a noticeable difference between the neutron mean gaps in neutronrich O, Ca, Ni and Sn isotopes calculated with the surface pairing and those with the mixed and volume pairing. The difference gets much smaller if the globally optimized pairing strengths are employed. The heavier Pb isotopes show the opposite trend. Moreover, large differences between the mean gap and the OES may be expected in both calculations when one goes towards the neutron drip line.