Exploration of a modified density dependence in the Skyrme functional

A variant of the basic Skyrme-Hartree-Fock functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, superheavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g., for projection) and more flexibility in the regime of high densities.

Figure 1

Average errors on nuclear bulk properties for a variety of parametrizations as indicated. The errors are obtained from averaging over the reference set of SV-min [10]. (a) Errors on diffraction radius $R$, surface thickness $\sigma$, and rms radius $r$. (b) Errors on binding energy.

Figure 2

Nuclear matter properties (filled boxes) together with their extrapolation uncertainty for the selected parametrizations.

Figure 3

Binding energy per nucleon in homogeneous nuclear matter as a function of density for neutron matter (a) and symmetric matter (b). Shown are results for the “min” parametrizations as indicated. Those for the “bas” parametrizations are very similar. The values for RD-min are given together with error bars representing the uncertainty in the extrapolation.

Figure 4

Average peak energies of giant resonance excitations in ${}^{208}\mathrm{Pb}$. (a) Isoscalar giant quadrupole resonance (GQR). (b) Isovector giant dipole resonance (GDR). (c) Isoscalar giant monopole resonance (GMR). For the newly fitted forces, we show as error bars also the uncertainties in the prediction. The faint horizontal lines indicate the experimental resonance positions (taken from [33, 34, 35]).

Figure 5

Properties of superheavy elements (boxes) together with their extrapolation uncertainty for the selected parametrizations. (a) Binding energy of ${}^{264}\mathrm{Hs}$ (including a correction for the rotational zero-point energy [10]); the experimental value is indicated by a dashed horizontal line [40]. (b) $Q_{\alpha }$ value for the nucleus $Z=120$, $N=180$. (c) Binding energy of the nucleus $Z=120$, $N=180$.

Figure 6

Fission barriers (filled boxes) of two groups of SHEs for the selected parametrizations together with the experimental values. The extrapolation errors are very similar for all three forces. They are indicated for the lower group near the left margin and for the upper group near the right margin.

Figure 7

Systematics of binding energies over all known even-even nuclei for three parametrizations: (a) RM-bas, (b) RD-bas, and (c) SV-bas. Fit nuclei are indicated by filled black circles, well-deformed ones by filled red circles, and all the remainder by open green circles.