  The low-lying dipole and quadrupole states in neutron rich nuclei, are
studied within the fully self-consistent relativistic quasiparticle
random-phase approximation (RQRPA), formulated in the canonical basis of the
Relativistic Hartree-Bogoliubov model (RHB), which is extended to include the
density dependent interactions. In heavier nuclei, the low-lying E1 excited
state is identified as a pygmy dipole resonance (PDR), i.e. as a collective
mode of excess neutrons oscillating against a proton-neutron core. Isotopic
dependence of the PDR is characterized by a crossing between the PDR and
one-neutron separation energies. Already at moderate proton-neutron asymmetry
the PDR peak is calculated above the neutron emission threshold, indicating
important implications for the observation of the PDR in (gamma,gamma')
scattering, and on the theoretical predictions of the radiative neutron capture
rates in neutron-rich nuclei. In addition, a novel method is suggested for
determining the neutron skin of nuclei, based on measurement of excitation
energies of the Gamow-Teller resonance relative to the isobaric analog state.
