  The possibility of adding a D-wave term to the standard Skyrme effective
interaction has been widely considered in the past. Such a term has been shown
to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential.
The aim of the present article is to provide the necessary tools to incorporate
this term in a fitting procedure: first, a mean-field equation written in
spherical symmetry in order to describe spherical nuclei and second, the
response function to detect unphysical instabilities. With these tools it will
be possible to build a new fitting procedure to determine the coupling
constants of the new functional.
