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

X. Roca-Maza, M. Centelles, X. Viñas, M. Brenna, G. Colò, B. K. Agrawal, N. Paar, J. Piekarewicz, D. Vretenar
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 slope of the symmetry energy $L$ 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 $\Delta r_{np}({}^{208}{\rm Pb}) = 0.168 \pm (0.009)_{\rm exp.} \pm (0.019)_{\rm theo.} \pm (0.021)_{\rm est.} {\rm fm}$ and $L= 43 \pm(6)_{\rm exp.} \pm (12)_{\rm theo.}\pm(12)_{\rm est.}$ MeV.
View original: http://arxiv.org/abs/1307.4806