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.

References in corpus (10)

• Neutron Star Observations: Prognosis for Equation of State Constraints
• Nuclear symmetry energy probed by neutron skin thickness of nuclei
• Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment
• Constraints on neutron star radii based on chiral effective field theory interactions
• Neutron skin thickness in droplet model with surface width dependence: indications of softness of the nuclear symmetry energy
• Giant Quadrupole Resonances in 208Pb, the nuclear symmetry energy and the neutron skin thickness
• A new Skyrme interaction with improved spin-isospin properties
• Pygmy Resonances and Neutron Skins
• Origin of the neutron skin thickness of 208Pb in nuclear mean-field models
• Asymmetric nuclear matter and neutron-skin in extended relativistic mean field model

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