Electric dipole polarizability and the neutron skin

The recent high-resolution measurement of the electric dipole ($E1$) polarizability ${\ensuremath{\alpha}}_{\mathrm{D}}$ 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 ${\ensuremath{\alpha}}_{\mathrm{D}}$ 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 ${\ensuremath{\alpha}}_{\mathrm{D}}$ 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 ${\ensuremath{\alpha}}_{\mathrm{D}}$ 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 ${\ensuremath{\alpha}}_{\mathrm{D}}$---should significantly constrain the isovector sector of the nuclear energy density functional.