Effects of density-dependent spin-orbit interactions in Skyrme-Hartree-Fock-Bogoliubov calculations of the charge radii and densities of Pb isotopes
I have investigated the -dependence of the charge radii across in the Pb isotopes and the surface densities of Pb using new Skyrme interactions that contain a density-dependent spin-orbit term, which I have named the Skyrme-ddso interactions. I have compared the results obtained using Skyrme-Hartree-Fock-Bogoliubov calculations that employ the Skyrme-ddso interactions with the original Skyrme results and have discussed the effects of including the density-dependent spin-orbit term. The results for the kink behavior of at in the Pb isotopes were improved by the inclusion of the density-dependent spin--orbit term. Moreover, the new Skyrme calculations yield better results for the inner part of the surface proton density of Pb at fm. The change in the potentials from the original Skyrme calculation contributes to the kink behavior through its effects on the splitting of the neutron orbitals. It also affects the inner part of the surface proton density through its effect on the proton orbitals. I have further demonstrated that the change in the isoscalar-to-isovector ratio of the spin--orbit term makes only a minor contribution to the single-particle energies and to the kink behavior in the Pb isotopes. In addition, I have investigated Ca using Skyrme-Hartree-Fock calculations with the new Skyrme interactions and have determined the effects of the density-dependent spin--orbit term on its radii and densities.