Nuclear Symmetry Energy Probed by Neutron Skin Thickness of Nuclei

We describe a relation between the symmetry energy coefficients $c_{\mathrm{sym}}(\rho )$ of nuclear matter and $a_{\mathrm{sym}}(A)$ of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of $c_{\mathrm{sym}}(\rho )$. Here, we take advantage of this relation to explore the prospects for constraining $c_{\mathrm{sym}}(\rho )$ of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.

Figure 1

Correlation of the quantal self-consistent $S$ value in ${}^{208}\mathrm{Pb}$ with the slope of the symmetry energy $L$ (a), the ratio $L/J$ (b), and with $J-a_{\mathrm{sym}}(A)$ (c), for various nuclear models (DD and PC stand for density dependent and point coupling models). From left to right, the correlation factors are $r=0.961$, 0.945, and 0.970.

Figure 2

Comparison of the fit described in the text of Eq. (2) with the experimental neutron skins from antiprotonic measurements and their linear average $S=(0.9\pm 0.15)I+(-0.03\pm 0.02)\mathrm{fm}$ [20]. Results of the modern Skyrme SLy4 and relativistic FSUGold forces are also shown.

Figure 3

Constraints on $L$ and $K_{\tau }$ from neutron skins and their dependence on the $S_{\mathrm{sw}}$ correction of Eq. (2). The crosses express the $L$ and $K_{\tau }$ ranges compatible with the uncertainties in the skin data. The shaded regions depict the constraints on $L$ and $K_{\tau }$ from isospin diffusion [6, 7] and on $K_{\tau }$ as determined in 13 from the GMR of Sn isotopes.