Model dependence of the $I^4$ term in the symmetry energy for finite nuclei

In this paper we investigate the model dependence of $I^4$ term in theoretical symmetry energy for a few popular mass models. Our results show that, interestingly and unexpectedly, the coefficients of the $I^4$ term in finite nuclei extracted from different mass models correlate strongly with the corresponding root-mean-square deviations from the experimental binding energies and also with the number of bound nuclei in the nuclear landscape predicted by theoretical models. This feature suggests that the main uncertainty of symmetry energy in finite nuclei is related to the $I^4$ term.

Figure 1

(a) Symmetry-energy coefficients of the $I^4$ term $\left(c_4^{\left(\mathrm{V}\right)}\right)$ and (b) the rmsDs of binding energies in mass models $\left(\sigma \right)$ versus Pearson product-moment correlation coefficients between $R_{i\mathrm{p}-j\mathrm{n}}^{\mathrm{theor}}$ and the $I^4$ term $\left(P_{X_4^{\left(\mathrm{V}\right)}}\right)$, for two forms of the Wigner energies.

Figure 2

Symmetry-energy coefficients of the $I^4$ term $\left(c_4^{\left(\mathrm{V}\right)}\right)$ versus the rmsDs $\left(\sigma \right)$ from experimental binding energies [28] for different mass models. Panels (a) and $({\text{a}}^{\prime })$ show $c_4^{\left(\mathrm{V}\right)}$ for the whole database of mass model, and the selected database of known nuclei, respectively, by adopting form (1) of the Wigner energy. Panels (b) and $({\text{b}}^{\prime })$ show the same as panels (a) and $({\text{a}}^{\prime })$ but for form (2). The red curve is plotted by using linear polynomial fitting based on the results of global mass models.

Figure 3

Symmetry-energy coefficients of the $I^4$ term $\left(c_4^{\left(\mathrm{V}\right)}\right)$ versus the number of bound nuclei $\left(N_{\mathrm{bound}}\right)$ with $10\le Z\le 110$ and $10\le N\le 200$ predicted in global mass models, for two forms of the Wigner energies. Panels (a) and (b) correspond to the total and even-even bound nuclei, respectively. The red and green lines are linear polynomial fits for form (1) and form (2), respectively.