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 $L$ alongwith that for neutron skin can be put in tighter bounds. The value of $L$ is found to be $L$= 64$\pm $5 MeV. For $^{208}$Pb, the neutron skin thickness comes out to be 0.188 $\pm $0.014 fm. Knowing $L$, the method can be applied to predict neutron skins of other nuclei.