Dependence of single-particle energies on coupling constants of the nuclear energy density functional

TL;DR

This study demonstrates that single-particle energies in doubly magic nuclei depend linearly on Skyrme functional coupling constants, but current models still cannot accurately reproduce experimental energies, indicating a need for extended functionals.

Contribution

The paper shows a linear relationship between single-particle energies and coupling constants, and refits these constants to experimental data, highlighting limitations of the standard Skyrme functional.

Findings

Single-particle energies depend linearly on coupling constants.

Refitting coupling constants reduces deviations but remains large (~1.1 MeV).

Standard Skyrme functional is insufficient for spectroscopic accuracy.

Abstract

We show that single-particle energies in doubly magic nuclei depend almost linearly on the coupling constants of the nuclear energy density functional. Therefore, they can be very well characterized by the linear regression coefficients, which we calculate for the coupling constants of the standard Skyrme functional. We then use these regression coefficients to refit the coupling constants to experimental values of single-particle energies. We show that the obtained rms deviations from experimental data are still quite large, of the order of 1.1 MeV. This suggests that the current standard form of the Skyrme functional cannot ensure spectroscopic-quality description of single-particle energies, and that extensions of this form are very much required.