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The isovector dipole response in $^{208}$Pb is described in the framework ofa fully self-consistent relativistic random phase approximation. The NL3parameter set for the effective mean-field Lagrangian with nonlinear mesonself-interaction terms, used in the present calculations, reproduces groundstate properties as well as the excitation energies of giant resonances innuclei. In addition to the isovector dipole resonance in $^{208}$Pb, thepresent analysis predicts the occurrence of low-lying E1 peaks in the energyregion between 7 and 11 MeV. In particular, a collective state has beenidentified whose dynamics correspond to that of a dipole pygmy resonance: thevibration of the excess neutrons against the inert core composed of equalnumber of protons and neutrons.Comment: LaTex 7 pages, 4 eps Figs, submitted to Phys. Lett.

Pygmy dipole resonances in the relativistic random phase approximation