Microscopic theory of pygmy- and giant resonances: accounting for complex 1p1h

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$$\otimes $$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: (1) the tadpole effect in the standard ph-propagator, (2) two new induced interactions (caused by the exchange of the ph-phonon) in the second ph-channel and in the particle–particle channels, and (3) 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