Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory


  • M.A. Hasan Department of Physics, College of Science, University of Kirkuk
  • A.H. Taqi Department of Physics, College of Science, University of Kirkuk



Skyrme–Hartree–Fock–Bogoliubov theory (SHFB), proton pairing gap, proton and neutron pairing energies, proton and neutron Fermi energies


This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.


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How to Cite

Hasan, M., & Taqi, A. (2023). Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory. Ukrainian Journal of Physics, 68(9), 577.



Fields and elementary particles