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The Green's function method in the \emph{Quasiparticle Time BlockingApproximation} is applied to nuclear excitations in $^{132}$Sn and $^{208}$Pb.The calculations are performed self-consistently using a Skyrme interaction.The method combines the conventional RPA with an exact single-particlecontinuum treatment and considers in a consistent way the particle-phononcoupling. We reproduce not only the experimental values of low- and high-lyingcollective states but we also obtain fair agreement with the data ofnon-collective low-lying states that are strongly influenced by theparticle-phonon coupling.

Self-consistent calculations within the Green's function method including particle-phonon coupling and the single-particle continuum