The recent high-resolution measurement of the electric dipole ( E 1 ) polarizability \alpha _ { \raisebox { -1.0 pt } { \tiny D } } in ^ { 208 } Pb [ 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 ^ { 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 _ { \raisebox { -1.0 pt } { \tiny D } } and r _ { skin } , we carry out systematic calculations for ^ { 208 } Pb , ^ { 132 } Sn , and ^ { 48 } Ca based on the nuclear density functional theory ( DFT ) using both non-relativistic and relativistic energy density functionals ( EDFs ) .
Our analysis indicates that whereas individual models exhibit a linear dependence between \alpha _ { \raisebox { -1.0 pt } { \tiny 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 _ { \raisebox { -1.0 pt } { \tiny D } } for the nuclei under consideration .
We conclude that precise measurements of r _ { skin } in both ^ { 48 } Ca and ^ { 208 } Pb—combined with the recent measurement of \alpha _ { \raisebox { -1.0 pt } { \tiny D } } —should significantly constrain the isovector sector of the nuclear energy density functional .