Pygmy dipole resonances in the relativistic random phase approximation

The isovector dipole response in ${}^{208}\mathrm{Pb}$ is described in the framework of a fully self-consistent relativistic random phase approximation. The NL3 parameter set for the effective mean-field Lagrangian with nonlinear meson self-interaction terms, used in the present calculations, reproduces ground state properties as well as the excitation energies of giant resonances in nuclei. In addition to the isovector dipole resonance in ${}^{208}\mathrm{Pb},$ the present analysis predicts the occurrence of low-lying $E1\mathrm{}$ peaks in the energy region between 7 and 11 MeV. In particular, a collective state has been identified whose dynamics correspond to that of a dipole pygmy resonance: the vibration of the excess neutrons against the inert core composed of an equal number of protons and neutrons.