To Bogolubov's method in superconductivity

The Frohlich Hamiltonian with electron-boson interaction of the fourth degree in fermion operators is studied. The Hamiltonian takes into account the exchange interaction of electron magnetic moments of conductivity. The boson spectrum consists of normal modes of connected phonon-magnon oscillations. The system of equations describing the compensation of “dangerous” diagrams that correspond to birth from vacuum two (bivertexes) and four (tetravetrexes) electron excitements is obtained by using Bogolubov's method. The modification of bivertex compensation equation stimulated by four-fermion interactions leads to the possibility of increasing the constant of the electron-boson connection and the energetic split. The numerical investigation of this system of equations is carried out. Considerable increasing of the energetic split in comparison with the Frohlich model is revealed.