The neutron skin thickness from the measured electric dipole polarizability in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb

Abstract

The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability ${\alpha }_D$ of ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb with the predictions of the Random Phase Approximation, using a representative set of nuclear energy density functionals. The calculated values of ${\alpha }_D$ are used to validate different correlations involving ${\alpha }_D$, the symmetry energy at the saturation density $J$, the corresponding slope parameter $L$ and the neutron skin thickness $\Delta r_{np}$, as suggested by the Droplet Model. A subset of models that reproduce simultaneously the measured polarizabilities in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are employed to predict the values of the symmetry energy parameters at saturation density and $\Delta r_{np}$. The resulting intervals are: $J=30\text{-}35$ MeV, $L=20\text{-}66$ MeV; and the values for $\Delta r_{np}$ in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are in the ranges: 0.15\text{-}0.19 fm, 0.12\text{-}0.16 fm, and 0.13\text{-}0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.

12 pages, 2 tables and 6 figures

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