Constraining the symmetry energy content of nuclear matter from nuclear masses: A covariance analysis

Elements of nuclear symmetry energy evaluated from different energy density functionals parametrized by fitting selective bulk properties of few representative nuclei are seen to vary widely. Those obtained from experimental data on nuclear masses across the periodic table, however, show that they are better constrained. A possible direction in reconciling this paradox may be gleaned from comparison of results obtained from use of the binding energies in the fitting protocol within a microscopic model with two sets of nuclei, one a representative standard set and another where very highly asymmetric nuclei are additionally included. A covariance analysis reveals that the additional fitting protocol reduces the uncertainties in the nuclear symmetry energy coefficient, its slope parameter, as well as the neutron-skin thickness in ${}^{208}\mathrm{Pb}$ nucleus by $\sim 50\%\mathrm{.}$ The central values of these entities are also seen to be slightly reduced.

Figure 1

The binding energy difference $\mathrm{\Delta }B(X,Y)=B\left(X\right)-B\left(Y\right)$ for four different pairs of isotopes are plotted against neutron-skin thickness $\mathrm{\Delta }{r}_{np}$ in the ${}^{208}\mathrm{Pb}$ nucleus for 16 different RMF models (see text for details). The values of Pearson's correlation coefficients $r$ are also displayed.

Figure 2

The covariance ellipsoids for the parameters $g_{\rho }-{\eta }_{2\rho }$ (upper panel) and the corresponding $L_0-\mathrm{\Delta }{r}_{np}$ (lower panel) for the model I (blue, long oval) and model II (red, short oval). The area inside the ellipsoids indicate the reasonable domain of the parameters.