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The theory of renormalized energy spectrum of a multi-level quasiparticleinteracting with polarization phonons at $T=0$ K is developed within theFeynman-Pines diagram technique in a new approach. It permits a successiveseparation of multiplicative diagrams from non-multiplicative ones for allorders of mass operator, and their partial summing as well. The obtained massoperator is presented as a sum of branched chain fractions, which effectivelytake into account the multi-phonon processes. For the two-level quasiparticleit is shown that just the interlevel (non-diagonal) interaction with phononsfundamentally changes the properties of the spectrum. In the vicinity of allthreshold energies, the quasi-equidistant phonon satellite bands (i.e., groupsof energy levels) are formed. They correspond to the complexes of bound statesof a quasi-particle with many phonons.

condensed matter physics

Method of successive separation and summing of multiplicative diagrams  of mass operator for the multi-level quasiparticle interacting with  polarization phonons