Electric Dipole Polarizability in ${}^{208}$Pb: insights from the Droplet Model

Abstract

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 $J=[31\pm (2{)}_{est.}]$\,MeV suggests $\Delta r_{np}({}^{208}\mathrm{Pb})=0.165\pm (0.009{)}_{exp.}\pm (0.013{)}_{theo.}\pm (0.021{)}_{est.}\mathrm{fm}$ and $L=43\pm (6{)}_{exp.}\pm (8{)}_{theo.}\pm (12{)}_{est.}$ MeV.

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