Contradicting effective mass scalings within the Skyrme energy density functional method

The problem of the effective mass scaling in the single particle spectra calculated within the Skyrme energy density functional (EDF) method is studied. It is demonstrated that for specific pairs of orbitals the commonly anticipated isoscalar effective mass (m*) scaling of the single-particle level splittings is almost canceled by an implicit m*-scaling due to other parameters in the Skyrme EDF. This holds in particular for an indirect m*-scaling of the two-body spin-orbit strength making the theory essentially unpredictable with respect to single particle energies. It is argued that this unphysical property of the Skyrme EDF is a mere consequence of the strategies and datasets used to fit these functionals. The inclusion of certain single-particle spin-orbit splittings to fit the two-body spin-orbit and the tensor interaction strengths reinstates the conventional m*-scaling and improves the performance of the Skyrme EDF.