Spectroscopic Properties of Nuclear Skyrme Energy Density Functionals

We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and observations. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more or one less neutron or proton. Theoretically, bare SPEs, before being confronted with observations, must be corrected for the effects of the particle vibration coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with observations, on average, improves; nevertheless, large discrepancies still remain. We conclude that the main source of disagreement is still in the underlying mean fields, and not in including or neglecting the PVC corrections.

Figure 1

PVC corrections calculated for neutron SPEs in six doubly magic nuclei and for five parametrizations of the Skyrme EDF. For each nucleus, thin vertical lines separate hole and particle states. (a) and (b) show results for light and heavy nuclei, respectively.

Figure 2

Same as in Fig. 1 but for proton SPEs.

Figure 3

Distributions of residuals of the bare (left panels) and PVC-corrected (right panels) SPEs, determined with respect to the empirical values of data set $A$, and shown for the five parametrizations of the Skyrme EDF: SAMi (a) and (b), SLy5 (c) and (d), SIII (e) and (f), ${\mathrm{SkM}}^{*}$ (g) and (h), and SkP (i) and (j).

Figure 4

Left: (a) and (c) [right (b) and (d)] panels: rms deviations between the bare [PVC-corrected] SPEs and empirical data of set $A$. Upper: (a) and (b) and lower: (c) and (d) panels show results obtained for standard Skyrme EDFs and for refitted parametrizations, respectively. In all cases, partial contributions obtained in six doubly magic nuclei are shown.

Figure 5

Open (full) symbols: rms deviations between the bare (PVC-corrected) SPEs and empirical data of sets $A$ (a), $B$ (b), $C$ (c), $M$ (d), and $S$ (e) (see text). Results obtained for the five studied Skyrme EDFs (squares), and for the corresponding refitted parametrizations (circles), are shown in the function of the effective mass corresponding to the original Skyrme EDF parametrizations.