  A variant of the basic Skyrme-Hartree-Fock (SHF) functional is considered
dealing with a new form of density dependence. It employs only integer powers
and thus will allow a more sound basis for projection schemes (particle number,
angular momentum). We optimize the new functional with exactly the same
adjustment strategy as used in an earlier study with a standard Skyrme
functional. This allows direct comparisons of the performance of the new
functional relative to the standard one. We discuss various observables: bulk
properties of finite nuclei, nuclear matter, giant resonances, super-heavy
elements, and energy systematics. The new functional performs at least as well
as the standard one, but offers a wider range of applicability (e.g. for
projection) and more flexibility in the regime of high densities.
