Pygmy resonances: what's in a name?

The centroid, width and percentage of energy weighted sum rule of dipole resonances can be strongly affected by dynamical fluctuations and static deformations of the nuclear surface, deformations and fluctuations which, in turn, depend on pairing, and thus on Cooper pairs. Because of angular momentum conservation, such insight is restricted, to lowest order, to deformations of quadrupole and monopole type. The latter being closely connected with the neutron (excess) skin and thus with soft dipole modes. From the values $(N-Z)/A \approx 0.18$, 0.21, and 0.45 for the nuclei $^{122}$Sn, $^{208}$Pb, and $^{11}$Li, it is expected that the latter system, which is weakly bound by pairing effects (spatially extended single Cooper pair and odd proton acting as spectator), constitutes an attractive laboratory to study the properties of soft $E1$--modes and thus of isospin nuclear deformation. From the calculation of the full dipole response function in QRPA, discretizing the continuum in a spherical box of radius of 40 fm, one finds a GDR with centroid $E_x \approx 24$ MeV, width $\Gamma \approx$ 11 MeV and carrying 90\% of the EWSR, and a low--lying collective resonance characterized by $E_X = 0.75$ MeV, $\Gamma = 0.5$ MeV and $6.2\%$ EWSR The wave function of the latter resonance is built out of about fifteen components (both protons and neutrons), typical of a collective mode. The transition densities indicate this soft $E1$--mode to be generated by surface density oscillation of the neutron skin ($\Delta r_{np} \approx 1.71$ fm) relative to an approximately isospin--saturated core. Through a detailed study of the full dipole response of $^{11}$Li we will draw a comparison between the soft $E1$--mode of this halo nucleus and the PDR of heavy stable nuclei, pointing to the physical similarities and also to the basic differences.