Derivation of the equations of superconductivity in an electron-ion model of a metal

A simple derivation is given of the equation for the matrix electron Green's function in a superconductor for an arbitrary form of the electron-lattice interaction. A closed system of equations is obtained by ignoring the renormalization of the vertex in the mass operator; in it, the effective electron interaction is described by the total dynamical structure form factor of the lattice.