  The Green function formalism with a consistent account for phonon coupling
(PC), based on the self-consistent theory of finite Fermi-systems, is applied
for pygmy- and giant multipole resonances in magic nuclei with the aim to
consider particle-hole (ph) and complex 1p1h phonon configurations. A new
equation for the effective field, which describes nuclear polarizability, is
obtained. It contains new PC contributions which are of interest in the energy
region under consideration. They are due to: i)the tadpole effect in the
standard ph-propagator, ii)two new induced interactions (caused by the exchange
of ph-phonon) in the second ph-channel and in the particle-particle channels,
and iii) the first and second variations of the effective interaction in the
phonon field. The general expressions for energies and probabilities of
transitions between the ground and excited states are obtained. The qualitative
analysis and discussion of the new terms are performed.
