Equations for Green functions with the use of the exact Hamiltonian in the quasiparticle-phonon nuclear model

Abstract

A set of equations for Green functions based on the exact Hamiltonian of the Quasiparticle-Phonon Model (QPM) for spherical even-even nuclei is obtained. The relation between this new set and the usual equations employed so far in the QPM is discussed. In particular a comparison between the obtained secular equation for excited state energy and the one used so far in the QPM for the case, when the excited state wave function consists of one- and two-phonon components, is made. The numerical evaluation performed in the schematic two level model showed that the difference between the results given by the calculation with the exact Hamiltonian and those based on the approximated Hamiltonian was remarkable in nonmagic nuclei.