Electric dipole polarizability and the neutron skin

The recent high-resolution measurement of the electric dipole (E1) polarizability alpha(D) in Pb-208 [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(skin) of Pb-208 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(D) and r(skin), we carry out systematic calculations for Pb-208, Sn-132, and Ca-48 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(D) and r(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(skin) and alpha(D) for the nuclei under consideration. We conclude that precise measurements of r(skin) in both Ca-48 and Pb-208-combined with the recent measurement of alpha(D)-should significantly constrain the isovector sector of the nuclear energy density functional.