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In the paper the non-linear generalization of the time blocking approximation(TBA) is presented. The TBA is one of the versions of the extended random-phaseapproximation (RPA) developed within the Green-function method and theparticle-phonon coupling model. In the generalized version of the TBA theself-consistency principle is extended onto the phonon space of the model. Thenumerical examples show that this non-linear version of the TBA leads to theconvergence of the results with respect to enlarging the phonon space of themodel.

Self-consistency in the phonon space of the particle-phonon coupling model