Extension and parameterization of high-order density dependence in Skyrme forces

The three-body force is indispensable in nuclear energy density functionals which leads to a single density dependent two-body term in the Hartree-Fock approach. We consider the possibility of higher-order density dependence in extended Skyrme forces. As a result, new extended Skyrme parametertizations based on the SLy4 force are obtained in which the high-order term is about 10$\thicksim$40 percent of strength compared to the original term. This can substantially affect nuclear properties at the high density region in general ways.