The relativistic quasi-particle random phase approximation and applications in exotic nuclei P. Ring, N. Paar Physikdepartment der Technischen Universit¨ at M¨ unchen, D-85748 Garching, Germany T. Nikˇ si´ c and D. Vretenar Physics Department, Faculty of Science, University of Zagreb, Croatia Abstract Collective Vibrations of nuclei far from the valley of stability are in- vestigated within the quasi-particle random phase approximation based on relativistic Hartree-Bogoliubov theory with non-linear meson cou- plings. Pairing correlations are described in by a finite range effective particle-particle interaction of Gogny type. The quasi-particle random phase equations are solved in the canonical basis and collective strength distributions are discussed. 1 Introduction In recent years the investigation of nuclei far from stability has gained world- wide interest as well on the experimental as on the theoretical side. These nuclei are characterized by unique structure properties: the weak binding of the outermost nucleons and the effects of the coupling between bound states and the particle continuum. On the neutron rich side, in particular, the mod- ification of the effective nuclear potential leads to the formation of nuclei with very diffuse neutron densities, to the occurrence of the neutron skin and halo structures. These phenomena will also affect collective vibrations of unstable nuclei, in particular the electric dipole and quadrupole excitations, and new modes of excitations might arise in nuclei near the drip line. A quantitative description of ground-states and properties of excited states in nuclei characterized by the closeness of the Fermi surface to the particle continuum, necessitates a unified description of mean-field and pairing cor- relations, as for example in the framework of the Hartree-Fock-Bogoliubov (HFB) theory. In order to describe transitions to low-lying excited states in