  The semi-empirical macroscopic-microscopic mass formula is further improved
by considering some residual corrections. The rms deviation from 2149 known
nuclear masses is significantly reduced to 336 keV, even lower than that
achieved with the best of the Duflo-Zuker models. The alpha-decay energies of
super-heavy nuclei, the Garvey-Kelson relations and the isobaric multiplet mass
equation (IMME) can be reproduced remarkably well with the model, and the
predictive power of the mass model is good. With a systematic study of 17
global nuclear mass models, we find that the quadratic form of the IMME is
closely related to the accuracy of nuclear mass calculations when the
Garvey-Kelson relations are reproduced reasonably well. Fulfilling both the
IMME and the Garvey-Kelson relations seems to be two necessary conditions to
improve the quality of the model prediction. Furthermore, the alpha-decay
energies of super-heavy nuclei should be used as an additional constraint on
the global nuclear mass models.
