Emergence of pygmy dipole resonances: Magic numbers and neutron skins

Abstract

The pygmy dipole resonances (PDR) for even-even nuclei in $8\ensuremath{\leqslant}Z\ensuremath{\leqslant}40$ are studied performing a systematic calculation of the random-phase approximation with the Skyrme functional of SkM*. The calculation is fully self-consistent and does not assume any symmetry in the nuclear shape of the ground state. In every isotopic chain, the PDR emerges by showing a peak of the $E1$ strength at energies less than 10 MeV. The $E1$ strength of the PDR strongly depends on the position of the Fermi level and shows a clear correlation with the occupation of the orbits with the orbital angular momenta less than $3\ensuremath{\hbar}$ ($\ensuremath{\ell}\ensuremath{\leqslant}2$). We also found a strong correlation between the isotopic dependence of the neutron skin thickness and the pygmy dipole strength. The fraction of the energy-weighted strength exhausted by the PDR and the neutron skin thickness show a linear correlation with the universal rate of about 0.2 fm${}^{\ensuremath{-}1}$.