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The self-consistent Theory of Finite Fermi Systems (TFFS) is consistentlygeneralized for the case of accounting for phonon coupling (PC) effects in theenergy region of pygmy- and giant multipole resonances (PDR and GMR) in magicnuclei with the aim to consider particle-hole (ph) and both complex 1p1h\otimesphonon and two-phonon configurations. The article is the direct continuationand generalization of the previous article [S.Kamerdzhiev, M.Shitov,Eur.Phys.J.A. 56, 265 (2020)],referred to as [I], where 1p1h- and only complex1p1h\otimes phonon configurations were considered. The newest equation for theTFFS main quantity, the effective field (vertex), which describes the nuclearpolarizability, has been obtained. It has considerably generalized the resultsof the previous article and accounts for two-phonon configurations. Twovariants of the newest vertex equation have been derived: (1)the first variantcontains complex 1p1h\otimes phonon configurations and the full1p1h-interaction amplitude \Gamma instead of the known effective interaction Fin [I], (2) the second one contains both 1p1h\otimes phonon and two-phononconfigurations. Both variants contain new, as compared to usual approaches, PCcontributions, which are of interest in the energy region under considerationand, at least, should result in a redistribution of the PDR and GMR strength,which is important for the explanation of the PDR and GMR fine structure. Thequalitative analysis and discussion of the new terms and the comparison to theknown time-blocking approximation are performed.

Microscopic theory of pygmy- and giant resonances:Accounting for complex 1p1h\otimes phonon and two-phonon configurations