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This work aims at a systematic investigations of the pairing properties andFermi properties from the proton drip-line to the neutron drip-line. In orderto provide more accurate mass formula with skyrme SKI3 force, the globaldescriptive power of the SKI3-HFB model for pairing properties are made in thisstudy. Systematic Skyrme SKI3-Hartree-Fock-Bogoliubov calculations with a mixedvolume-surface pairing force are carried out to study the ground-state neutronand proton pairing gap, neutron and proton pairing energy and neutron andproton Fermi energy for about 2095 even-even nuclei ranging from $2\le{Z}\le110$ to $2\le{N}\le236$. The calculated results of neutron and proton pairing gapare compared with experimental data using the difference-point formulas$\Delta^{(3)}, \Delta^{(4)}$ and $\Delta^{(5)}$, and also compared with theneutron and proton pairing gap of Lipkin-Nogami model. It is shown that theSkyrme-SKI3 functional with the mixed volume-surface pairing force can besuccessfully used for describing the ground-state pairing and Fermi propertiesof the investigated nuclei, in particularly the neutron-rich nuclei and theexotic nuclei near the neutron drip-line. On the other hand, the calculatedneutron and proton pairing gap are in good agreement with the availableexperimental values of the neutron and proton pairing gap of thedifference-point formulas $\Delta^{(3)}, \Delta^{(4)}$ and $\Delta^{(5)}$ andwith the data of Lipkin-Nogami model over the whole nuclear chart.

Proton and Neutron Pairing Properties within a mixed volume-surface pairing force using SKI3-HFB Theory