Constraints on neutron skin thickness in 208Pb and density-dependent symmetry energy

Accurate knowledge about the neutron skin thickness $\mathrm{\Delta }{R}_{np}$ in ${}^{208}$Pb has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel Lead Radius Experiment (PREX) did not yield stringent constraint on the $\mathrm{\Delta }{R}_{np}$ recently. We employ a more practicable strategy currently to probe the neutron skin thickness of ${}^{208}$Pb based on a high linear correlation between the $\mathrm{\Delta }{R}_{np}$ and $J-a_{\text{sym}}$, where $J$ and $a_{\text{sym}}$ are the symmetry energy (coefficient) of nuclear matter at saturation density and of ${}^{208}$Pb. An accurate $J-a_{\text{sym}}$ thus places a strong constraint on the $\Delta R_{np}$\mathrm{.}Comparedwiththeparity-violatingasymmetry$A_{$\text{PV}$}$ in the PREX, the reliably experimental information on the $J-a_{\text{sym}}$ is much more easily available attributed to a wealth of measured data on nuclear masses and on decay energies. The density dependence of the symmetry energy is also well constrained with the $J-a_{\text{sym}}$. Finally, with a `tomoscan’ method, we find that one just needs to measure the nucleon densities in ${}^{208}$Pb starting from $R_m=7.61\pm 0.04$ fm to obtain the $\mathrm{\Delta }{R}_{np}$ in hadron scattering experiments, regardless of its interior profile that is hampered by the strong absorption.