Superconductivity of Rb3C60: breakdown of the Migdal-Eliashberg theory

In this paper, through an exhaustive analysis within the Migdal-Eliashberg theory, Ne show the incompatibility of experimental data of Rb3C60 With the basic assumptions of the standard theory of superconductivity. For differe nt models of the electron-phonon spectral function alpha F-2(Omega) we solv e numerically the Eliashberg equations to find which values of the electron -phonon coupling lambda of the logarithmic phonon frequency Omega (ln) and of the Coulomb pseudopotential mu* reproduce the experimental data of Rb3C6 0 We find that the solutions are essentially independent of the particular shape of alpha F-2(Omega) and that, to explain the experimental data of Rb3 C60, one has to resort to extremely large couplings: lambda = 3.0 +/- 0.8. This results differs from the usual partial analyses reported up to now and we claim that this value exceeds the maximum allowed lambda compatible wit h the crystal lattice stability. Moreover, we show quantitatively that the obtained values of lambda and Omega (ln) strongly violate Migdal's theorem and consequently are incompatible with the Migdal-Eliashberg theory. One ha s therefore to consider the generalization of the theory of superconductivi ty in the nonadiabatic regime to account for the experimental properties of fullerides.