We study the electric dipole polarizability $\alpha_D$ in ${ }^{ 208}$Pb based on the predictions of a large and representative set of relativistic and non-relativistic nuclear mean field models. We adopt the droplet model as a guide to better understand the correlations between $\alpha_D$ and other isovector observables. Insights from the droplet model suggest that the product of $\alpha_D$ and the nuclear symmetry energy at saturation density $J$ is much better correlated with the neutron skin thickness $\Delta r_{ np}$ of ${ }^{ 208}$Pb than the polarizability alone. Correlations of $\alpha_D J$ with $\Delta r_{ np}$ and with the symmetry energy slope parameter $L$ suggest that $\alpha_D J$ is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of thenuclear energy density functional by comparing our theoretical predictions against measurements of both $\alpha_D$ and the parity-violating asymmetry in ${ }^{ 208}$Pb. We find that the recent experimental determination of $\alpha_D$ in ${ }^{ 208}$Pb in combination with the range for the symmetry energy at saturation density $J=[31\pm (2)_{ \rm est.}]$\,MeV suggests $\Delta r_{ np}({ }^{ 208}{ \rm Pb}) = 0.165 \pm (0.009)_{ \rm exp.} \pm (0.013)_{ \rm theo.} \pm (0.021)_{ \rm est.} { \rm fm}$ and $L= 43 \pm(6)_{ \rm exp.} \pm (8)_{ \rm theo.}\pm(12)_{ \rm est.}$ MeV.
Categories: nucl-th