Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient

Our family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled BSk19, BSk20, and BSk21, is here extended by (a) refitting to the 2012 Atomic Mass Evaluation (AME), and (b) varying the symmetry coefficient $J$. Five new models, labeled BSk22 to BSk26, along with their mass tables, HFB-22 to HFB-26, respectively, are presented. These models are characterized by unconventional Skyrme forces containing ${t}_{4}$ and ${t}_{5}$ terms, i.e., density-dependent generalizations of the usual ${t}_{1}$ and ${t}_{2}$ terms, respectively. Highly realistic contact pairing forces are used. The Skyrme forces are constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614$\ensuremath{-}$2230 and PSR J0348+0432. Unphysical spin and spin-isospin instabilities of homogeneous nuclear matter, including the transition to a polarized state in neutron-star matter, are eliminated with the new forces. The best fits to the new database of 2353 nuclei are found for models BSk24 ($J=30$ MeV) and BSk25 ($J=29$ MeV), for which the root-mean square (rms) deviations are 0.55 and 0.54 MeV, respectively. Despite the larger database this is even better than the rms deviation of 0.58 MeV that we found with our fits to the 2003 AME. With $J=32$ MeV the rms deviation rises to 0.63 MeV. The neutron-skin thicknesses derived from antiproton scattering are shown to be consistent with the conclusions that we have drawn from masses.