Covariant energy density functionals: Nuclear matter constraints and global ground state properties

The correlations between global description of the ground state properties (binding energies, charge radii) and nuclear matter properties of the state-of-the-art covariant energy density functionals have been studied. It was concluded that the strict enforcement of the constraints on the nuclear matter properties (NMP) defined in Dutra et al. [Phys. Rev. C 90, 055203 (2014)] will not necessarily lead to the functionals with good description of the binding energies and other ground and excited state properties. In addition, it will not substantially reduce the uncertainties in the predictions of the binding energies in neutron-rich systems. It turns out that the functionals, which come close to satisfying these NMP constraints, have some problems in the description of existing data. On the other hand, these problems are either absent or much smaller in the functionals which are carefully fitted to finite nuclei but which violate some NMP constraints. This is a consequence of the fact that the properties of finite nuclei are defined not only by nuclear matter properties but also by underlying shell effects. The mismatch of phenomenological content, existing in all modern functionals, related to nuclear matter physics and the physics of finite nuclei could also be responsible.

Figure 1

The binding energy spreads $\mathrm{\Delta }E(Z,N)$ as a function of proton and neutron number. From Ref. [10].

Figure 2

Panel (a) is based on the results presented in Fig. 1. However, the squares are shown only for the nuclei which are currently known and which will be measured with FRIB. The regions of the nuclei with measured and measured+estimated masses are enclosed by dashed and solid black lines, respectively. The squares beyond these regions indicate the nuclei which may be measured with FRIB. For simplicity the line formed by the most neutron-rich nucleus in each isotope chain accessible with FRIB will be called as “FRIB limit”. The FRIB limit of the nuclear chart is defined by a fission yield greater than ${10}^{-6}$ that may be achieved with dedicated existence measurements [29]. The same color map as in Fig. 1 is used here, but the ranges of particle numbers for vertical and horizontal axis are different from the ones in Fig. 1. The two-neutron drip lines are shown for the CEDFs NL3* and DD-PC1 by blue dashed and solid red lines, respectively. Panel (b) is based on the same results as (a), but the spreads in relative errors in the description of the masses are shown instead of binding energy spreads $\mathrm{\Delta }E$.

Figure 3

The differences in the calculated binding energies of the Yb nuclei obtained in the RHB calculations with two functionals. The results obtained with DD-PC1 are used as a reference. The regions of measured and measured+estimated masses from Ref. [28] are indicated by arrows. The FRIB limit is shown by dashed orange line.

Figure 4

Binding energy spreads $\mathrm{\Delta }E(Z,N)$ for the pairs of indicated functionals. All even-even nuclei between the two-proton and two-neutron drip lines are included in the comparison.

Figure 5

The nuclei (solid squares), shown in the $(Z,N)$ plane, which were used in the fit of indicated CEDFs. Their total number is shown below the functional label. Magic shell closures are shown by dashed lines. The colors of the squares show the difference $E_{\mathrm{th}}-E_{exp}$ between calculated and experimental binding energies. Two-proton and two-neutron drip lines of the indicated functional are shown by solid black lines.

Figure 6

The differences $E_{\mathrm{th}}-E_{exp}$ between calculated and experimental binding energies for the indicated CEDFs. The experimental data are taken from Ref. [28] and all 835 even-even nuclei, for which measured and estimated masses are available, are included. If $E_{\mathrm{th}}-E_{exp}<0$, the nucleus is more bound in the calculations than in experiment. Two-proton and two-neutron drip lines of the indicated functional are shown by solid black lines.

Figure 7

The difference between measured and calculated charge radii $r_{ch}$ for indicated functionals. The experimental data are taken from Ref. [48]. Two-proton and two-neutron drip lines of the indicated functional are shown by solid black lines.

Figure 8

Charge radii spreads $\mathrm{\Delta }{r}_{ch}(Z,N)$ as a function of proton and neutron number. $\mathrm{\Delta }{r}_{ch}(Z,N)=|r_{ch}^{\max }(Z,N)-r_{ch}^{\min }(Z,N)|$, where $r_{ch}^{\max }(Z,N)$ and $r_{ch}^{\min }(Z,N)$ are the largest and smallest charge radii obtained either with indicated pairs of the CEDFs (a)–(c) or with four CEDFs (d) for the $(Z,N)$ nucleus.

Figure 9

The difference $r_{ch}^{\mathrm{CEDF}-1}(Z,N)-r_{ch}^{\mathrm{CEDF}-2}(Z,N)$ in the charge radii predicted by two indicated CEDFs. The second functional in the label “CEDF-1 vs CEDF-2” indicates the reference functional. All even-even nuclei between the two-proton and two-neutron drip lines are included in the comparison.