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

TL;DR

This study uses the droplet model to analyze the electric dipole polarizability in lead-208, revealing strong correlations with isovector properties and providing constraints on the nuclear symmetry energy and neutron skin thickness.

Contribution

It demonstrates that the product of polarizability and symmetry energy at saturation density is a better isovector indicator, aiding in constraining nuclear models using experimental data.

Findings

Correlates $ ext{α}_D J$ with neutron skin thickness and symmetry energy slope.

Provides estimates for neutron skin thickness of ${}^{208}$Pb.

Suggests $ ext{α}_D$ can constrain the isovector sector of nuclear energy density functionals.

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 $J=[31\pm (2)_{\rm est.}]$\,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.