  By taking into account the surface diffuseness correction for unstable
nuclei, the accuracy of the macroscopic-microscopic mass formula is further
improved. The rms deviation with respect to essentially all the available mass
data falls to 298 keV, crossing the 0.3 MeV accuracy threshold for the first
time within the mean-field framework. Considering the surface effect of the
symmetry potential which plays an important role in the evolution of the
"neutron skin" toward the "neutron halo" of nuclei approaching the neutron drip
line, we obtain an optimal value of the symmetry energy coefficient J=30.16
MeV. With an accuracy of 258 keV for all the available neutron separation
energies and of 237 keV for the alpha-decay Q-values of super-heavy nuclei, the
proposed mass formula is particularly important not only for the reliable
description of the r-process of nucleosynthesis but also for the study of the
synthesis of super-heavy nuclei.
