ON BOGOLIUBOVS METHOD IN SUPERCONDUCTIVITY

The Frolich Hamiltonian, with the addition of the electron-boson inter action of the fourth degree in fermion operators, is studied. The Hami ltonian takes into account the exchange interactions of the magnetic m oments of the conduction electrons. The boson spectrum consists of the normal modes of coupled phonon-magnon oscillations. Using the Bogoliu bov method in the theory of superconductivity and a generalized canoni c transformation, a system of equations describing the mutual compensa tion of ''dangerous'' (i.e., leading to divergences) diagrams correspo nding to the creation of two (bivertexes) and of four (tetravertexes) electron excitations from vacuum is obtained. The bivertex compensatio n equation, modified by a four-fermion interaction, indicates the poss ibility of an effective increase in the electron-boson coupling consta nt and an increase in the superconductive energy gap. Numerical invest igation of the obtained system of equations was carried out. The consi derable increase in the energy gap was revealed in comparison with the Frolich model.