SUPERCONDUCTIVITY IN THE STRONG ELECTRON-PHONON COUPLING SYSTEMS

The superconducting state in the strong electron-phonon coupling systems is studied. The integral Eliashberg equations are transformed to the form simplifying their analysis and numerical solution. In the limit of the large coupling constants lambda >> 1 the energy gap at T=0 is shown to have an asymptote like DELTA-0 infinity omega-lambda-1/2BAR. It is shown that the density of electron states at finite temperatures is different from zero for all omega and in the spectrum of,superconductors there are excitations with energies inside the gap. In the case of the strong coupling this results in a significant redistribution of the normal and superconducting electron numbers and the essential deviations of the properties of such superconductors from the BCS model.