  The density dependent term in Skyrme forces is essential, which simulates
three-body and many-body correlations beyond the low-momentum two-body
interaction. We speculate that a single density term may be insufficient and a
higher-order density dependent term is added. The present work investigates the
influences of higher-order density dependencies based on extended UNEDF0 and
SkM* forces. The global descriptions of nuclear masses and charge radii have
been presented. Consequently the extended UNEDF0 force gives a global rms error
on binding energies of 1.29 MeV. The influences on fission barriers and
equation of state have also been investigated. The perspectives to improve
Skyrme forces have also been discussed, including global center-of-mass
corrections and Lipkin-Nogami pairing corrections.
