Electric dipole polarizability and the neutron skin

The recent high-resolution measurement of the electric dipole ($E1$) polarizability ${\alpha }_{\mathrm{D}}$ in ${}^{208}$Pb [A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011)] provides a unique constraint on the neutron-skin thickness of this nucleus. The neutron-skin thickness $r_{\mathrm{skin}}$ of ${}^{208}$Pb is a quantity of critical importance for our understanding of a variety of nuclear and astrophysical phenomena. To assess the model dependence of the correlation between ${\alpha }_{\mathrm{D}}$ and $r_{\mathrm{skin}}$, we carry out systematic calculations for ${}^{208}$Pb, ${}^{132}$Sn, and ${}^{48}$Ca based on the nuclear density functional theory using both nonrelativistic and relativistic energy density functionals. Our analysis indicates that whereas individual models exhibit a linear dependence between ${\alpha }_{\mathrm{D}}$ and $r_{\mathrm{skin}}$, this correlation is not universal when one combines predictions from a host of different models. By averaging over these model predictions, we provide estimates with associated systematic errors for $r_{\mathrm{skin}}$ and ${\alpha }_{\mathrm{D}}$ for the nuclei under consideration. We conclude that precise measurements of $r_{\mathrm{skin}}$ in both ${}^{48}$Ca and ${}^{208}$Pb—combined with the recent measurement of ${\alpha }_{\mathrm{D}}$—should significantly constrain the isovector sector of the nuclear energy density functional.

Figure 1

Predictions from 48 nuclear EDFs discussed in the text for the electric dipole polarizability and neutron-skin thickness of ${}^{208}$Pb. Constrains on the neutron-skin thickness from PREX [3] and on the dipole polarizability from RCNP [27] have been incorporated into the plot.

Figure 2

Predictions from the 48 nuclear EDFs used in the text for the neutron-skin thickness of ${}^{208}$Pb and ${}^{132}$Sn (a) and ${}^{48}$Ca (b). Constrains on the neutron-skin thickness from PREX [3] have been incorporated into the plot.