Microscopic description of nuclear vibrations: Relativistic QRPA and its extensions with quasiparticle-vibration coupling

The recent extensions of the covariant energy density functional theory with the quasiparticle-vibration coupling (QVC) are reviewed. Formulation of the Quasiparticle Random Phase Approximation (QRPA) in the relativistic framework is discussed. Self-consistent extensions of the relativistic QRPA imply the QVC which is implemented in two-body propagators in the nuclear medium. This provides fragmentation of the QRPA states describing the damping of the vibrational motion.