Determining the Density Content of Symmetry Energy and Neutron Skin: An Empirical Approach

The density dependence of nuclear symmetry energy remains poorly constrained. Starting from precise empirical values of the nuclear volume and surface symmetry energy coefficients and the nuclear saturation density, we show how in the ambit of microscopic calculations with different energy density functionals, the value of the symmetry energy slope parameter $L$ along with that for neutron skin can be put in tighter bounds. The value of $L$ is found to be $L=64\pm 5\mathrm{MeV}$. For ${}^{208}\mathrm{Pb}$, the neutron skin thickness comes out to be $0.188\pm 0.014\mathrm{fm}$. Knowing $L$, the method can be applied to predict neutron skin thicknesses of other nuclei.

Figure 1

Blue triangles representing $L$ calculated using Eq. (1) with different RMF interactions. They are plotted as a function of corresponding $R_{\mathrm{skin}}$ for ${}^{208}\mathrm{Pb}$. The shaded region represents the envelope of possible $L$ values with different RMF interactions obtained using Eqs. (7, 9). The acceptable window for the values of $L$ and $R_{\mathrm{skin}}$ for ${}^{208}\mathrm{Pb}$ is represented by the magenta box.

Figure 2

Values of $L$ shown as a function of $R_{\mathrm{skin}}$ for ${}^{124}\mathrm{Sn}$ (blue stars), ${}^{90}\mathrm{Zr}$ (magenta triangles), and ${}^{48}\mathrm{Ca}$ (green squares) calculated with different RMF interactions. The shaded region corresponds to the projected-out range in the values of $L$ as obtained from Fig. 1.