Equations of the quasiparticle-phonon nuclear model with the phonon scattering effects at finite temperature

A generalization of the quasiparticle-phonon nuclear model (QPNM) for describing the interaction with (2p-2h) configurations at finite temperature is presented. By taking exactly into account the occupation numbers of one-phonon energy levels a closed system of approximate equations for Green functions with one- to two-phonon transition, phonon-ground state correlation and phonon scattering propagators in even-even spherical nuclei is explicitly derived. A one-to-one correspondence between this system and the system of QPNM equations of the coefficients of the excited state wave function is established. It is shown that in the zero temperature limit one obtains the standard basic equations employed so far within the QPNM. The numerical evaluation of the phonon scattering effects has shown that for temperatures T<1 MeV the zero temperature limit of the QPNM is a quite good approximation. The equivalence between the QPNM diagrams and the diagrams of the nuclear field theory and the theory of finite Fermi-systems is discussed