Diagram representation of the single-phonon propagator in the quasiparticle-phonon model of nuclei

A diagram technique is proposed for the quasiparticle-phonon model of nuclei. It is shown that restriction to single-phonon and two-phonon components in the wave functions of the excited states of even-even deformed nuclei is equivalent to summation of a definite class of single-loop diagrams. The contribution of a two-loop diagram is calculated. Further, closure of the hierarchy of equations for the Green's functions yields explicit approximations that lead to summation of the considered class of graphs.