Contradicting effective mass scalings within the Skyrme energy density functional method

TL;DR

This paper investigates the complex and often contradictory effective mass scaling in Skyrme energy density functionals, revealing that parameter interdependencies undermine predictable single-particle energy calculations.

Contribution

It demonstrates that the expected isoscalar effective mass scaling is canceled by implicit parameter effects, and shows how including specific splittings can restore proper scaling.

Findings

The isoscalar effective mass scaling is often canceled by other parameters.

Including certain spin-orbit splittings improves the functional's predictability.

The unphysical properties are linked to the fitting strategies and datasets used.

Abstract

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.