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The covariant particle-vibration coupling model within the time blockingapproximation is employed to supplement the Relativistic Random PhaseApproximation (RRPA) with coupling to collective vibrations. The Bethe-Salpeterequation in the particle-hole channel with an energy dependent residualparticle-hole (p-h) interaction is formulated and solved in the shell-modelDirac basis as well as in the momentum space. The same set of the couplingconstants generates the Dirac-Hartree single-particle spectrum, the static partof the residual p-h interaction and the particle-phonon coupling amplitudes.This approach is applied to quantitative description of damping phenomenon ineven-even spherical nuclei with closed shells $^{208}$Pb and $^{132}$Sn. Sincethe phonon coupling enriches the RRPA spectrum with a multitude ofph$\otimes$phonon states a noticeable fragmentation of giant monopole anddipole resonances is obtained in the examined nuclei. The results are comparedwith experimental data and with results of the non-relativistic approach.Comment: 12 pages, 4 figures, Proceedings of the NSRT06 Conferenc

Covariant response theory beyond RPA and its application