  The self-consistent Theory of Finite Fermi Systems (TFFS) is consistently
generalized for the case of accounting for phonon coupling (PC) effects in the
energy region of pygmy- and giant multipole resonances (PDR and GMR) in magic
nuclei with the aim to consider particle-hole (ph) and both complex 1p1h\otimes
phonon and two-phonon configurations. The article is the direct continuation
and generalization of the previous article [S.Kamerdzhiev, M.Shitov,
Eur.Phys.J.A. 56, 265 (2020)],referred to as [I], where 1p1h- and only complex
1p1h\otimes phonon configurations were considered. The newest equation for the
TFFS main quantity, the effective field (vertex), which describes the nuclear
polarizability, has been obtained. It has considerably generalized the results
of the previous article and accounts for two-phonon configurations. Two
variants of the newest vertex equation have been derived: (1)the first variant
contains complex 1p1h\otimes phonon configurations and the full
1p1h-interaction amplitude \Gamma instead of the known effective interaction F
in [I], (2) the second one contains both 1p1h\otimes phonon and two-phonon
configurations. Both variants contain new, as compared to usual approaches, PC
contributions, which are of interest in the energy region under consideration
and, 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. The
qualitative analysis and discussion of the new terms and the comparison to the
known time-blocking approximation are performed.
