  The three-body force is indispensable in nuclear energy density functionals
which leads to a density dependent two-body term in the Hartree-Fock approach.
Usually a single factional power of density dependency has been adopted. We
consider the possibility of an additional higher-order density dependence in
extended Skyrme forces. As a result, new extended Skyrme parametertizations
based on the SLy4 force are obtained and the improvements in descriptions of
global nuclei have been demonstrated. The higher-order term can also
substantially affect nuclear properties in the high density region in general
ways.
