Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XV: The spin–orbit coupling

We construct two new Hartree–Fock–Bogoliubov mass models, labeled HFB-28, HFB-29, which in addition to the generalized Skyrme form containing t4t4 and t5t5 terms, also include now a modified spin–orbit force. This alternative spin–orbit force allows for an unconventional isospin and/or density dependence relative to the traditional form included in Skyrme functionals. The new forces underlying these models are fitted to essentially all mass data and at the same time to a realistic equation of state of neutron matter. The inclusion of the modified spin–orbit terms allows us to reduce the rms deviation with respect to all the 2353 known masses with Z,N≥8Z,N≥8 by 20 keV, leading to a final model error of 0.52 MeV. It is shown that the newly optimized spin–orbit forces do not conform with the one deduced from the relativistic mean field theory, and consequently that the relativistic spin–orbit force might not be optimum to reproduce experimental masses. The spin–orbit splittings are shown to be reduced and in better agreement with empirical values when including a density-dependent form of the spin–orbit interaction. However, the new mass models with such modified spin–orbit terms still fail to reproduce the kink seen in the isotopic shift of the K or Pb charge radii around the neutron magic numbers, despite the fact that such generalizations of the spin–orbit terms were also introduced to improve the description of the isotopic shifts. Shell effects, in particular far away from stability, are shown to remain unaffected by the new spin–orbit terms, except at the N=184N=184 magic number.