Pygmy resonances and neutron skins

In a study motivated by a recent experiment, the distribution of electric dipole strength in the neutron-rich $^{68}\mathrm{Ni}$ isotope was computed using a relativistic random-phase approximation with a set of effective interactions that---although well calibrated---predict significantly different values for the neutron-skin thickness in $^{208}\mathrm{Pb}$. The emergence of low-energy ``pygmy'' strength that exhausts about $5%$--$8%$ of the energy-weighted sum rule (EWSR) is clearly identified. In addition to the EWSR, special emphasis is placed on the dipole polarizability. In particular, our results suggest a strong correlation between the dipole polarizability of $^{68}\mathrm{Ni}$ and the neutron-skin thickness of $^{208}\mathrm{Pb}$. Yet we find a correlation just as strong, and an even larger sensitivity, between the neutron-skin thickness of $^{208}\mathrm{Pb}$ and the fraction of the dipole polarizability exhausted by the pygmy resonance. These findings suggest that dipole polarizability may be used as a proxy for the neutron skin.

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