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

TL;DR

This study uses electric dipole polarizability measurements in specific nuclei to constrain the symmetry energy parameters and neutron skin thickness, enhancing understanding of nuclear structure and neutron-rich matter.

Contribution

The paper demonstrates how measured polarizabilities in three nuclei can be used to accurately predict symmetry energy parameters and neutron skin thicknesses, validating correlations from the Droplet Model.

Findings

Predicted symmetry energy at saturation: 30-35 MeV.

Predicted slope parameter L: 20-66 MeV.

Neutron skin thickness ranges: 0.15-0.19 fm in $^{68}$Ni, 0.12-0.16 fm in $^{120}$Sn, 0.13-0.19 fm in $^{208}$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.