Electric dipole polarizability in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>208</mml:mn></mml:msup></mml:math>Pb: Insights from the droplet model

We study the electric dipole polarizability ${\ensuremath{\alpha}}_{D}$ in ${}^{208}$Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean-field models. We adopt the droplet model as a guide to better understand the correlations between ${\ensuremath{\alpha}}_{D}$ and other isovector observables. Insights from the droplet model suggest that the product of ${\ensuremath{\alpha}}_{D}$ and the nuclear symmetry energy at saturation density $J$ is much better correlated with the neutron skin thickness $\ensuremath{\Delta}{r}_{np}$ of ${}^{208}$Pb than the polarizability alone. Correlations of ${\ensuremath{\alpha}}_{D}J$ with $\ensuremath{\Delta}{r}_{np}$ and with the symmetry energy slope parameter $L$ suggest that ${\ensuremath{\alpha}}_{D}J$ is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of the nuclear energy density functional by comparing our theoretical predictions against measurements of both ${\ensuremath{\alpha}}_{D}$ and the parity-violating asymmetry in ${}^{208}$Pb. We find that the recent experimental determination of ${\ensuremath{\alpha}}_{D}$ in ${}^{208}$Pb in combination with the range for the symmetry energy at saturation density $J=[31\ifmmode\pm\else\textpm\fi{}{(2)}_{\mathrm{est}}]$ MeV suggests $\ensuremath{\Delta}{r}_{np}({}^{208}\mathrm{Pb})=0.165\ifmmode\pm\else\textpm\fi{}{(0.009)}_{\mathrm{expt}}\ifmmode\pm\else\textpm\fi{}{(0.013)}_{\mathrm{theor}}\ifmmode\pm\else\textpm\fi{}{(0.021)}_{\mathrm{est}}\phantom{\rule{4pt}{0ex}}\mathrm{fm}$ and $L=43\ifmmode\pm\else\textpm\fi{}{(6)}_{\mathrm{expt}}\ifmmode\pm\else\textpm\fi{}{(8)}_{\mathrm{theor}}\ifmmode\pm\else\textpm\fi{}{(12)}_{\mathrm{est}}$ MeV.