  A relativistic mean field description of collective excitations of atomic
nuclei is studied in the framework of a fully self-consistent relativistic
random phase approximation (RRPA). In particular, results of RRPA calculations
of multipole giant resonances and of low-lying collective states in spherical
nuclei are analyzed. By using effective Lagrangians which, in the mean-field
approximation, provide an accurate description of ground-state properties, an
excellent agreement with experimental data is also found for the excitation
energies of low-lying collective states and of giant resonances. Two points are
essential for the successful application of the RRPA in the description of
dynamical properties of finite nuclei: (i) the use of effective Lagrangians
with non-linear terms in the meson sector, and (ii) the fully consistent
treatment of the Dirac sea of negative energy states.
