Ground-state properties of nuclei from carbon to curium in the framework of the Sky3D model

The ground-state properties of 2410 nuclei from C ($Z=6$) to Cm ($Z=96$) have been systematically studied using the Sky3D model, which is based on the Skyrme-Hartree-Fock $(\mathrm{SHF})+$ Bardeen-Cooper-Schrieffer (BCS) method, with the Skyrme interactions from SV-mas07I to SV-mas07IV. The effects of spin-orbit interaction and pairing on the binding energy per nucleon, the quadrupole deformation parameter ${\ensuremath{\beta}}_{2}$, and the charge radius of nuclei have been investigated. The calculated results were compared with available experimental data from the atomic mass evaluation (AME2020), the results of the finite range droplet model (FRDM2012), and the available compiled database of the nuclear ground-state charge radius. It was shown that the spin-orbit interaction can significantly affect the magic nuclei and their neighboring nuclei, increasing the binding energy per nucleon closer to the experimental values compared to the case without spin-orbit interaction. Additionally, it can adjust the shapes of magic nuclei to the expected spherical shape and reduce the overestimated charge radii of nuclei, making them closer to the experimental measurements. Pairing has a relatively weaker impact than the spin-orbit interaction, but it can also bring the ground-state properties of nuclei closer to the experimental data or FRDM2012 results. Together, the spin-orbit interaction and pairing can enhance the accuracy of the Sky3D model in describing the ground-state properties of nuclei to a very good precision. Specifically, the root mean square (rms) deviation of the binding energy per nucleon compared to AME2020 is 0.268 MeV; the rms deviation of the quadrupole deformation parameter ${\ensuremath{\beta}}_{2}$ compared to the FRDM2012 results is 0.229; for the charge radii compared to the experimental data in the CR2013 database, the value is 0.0319 fm, and compared to the experimental data in the CR2021 database, the value is 0.0290 fm.