2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174908The numerical calculations of the standard Eliashberg-Nambu strong coupling theory and a formula of isotope effect derived in this paper provide direct evidences that an-harmonic vibrations of lattice enhance isotope effect with anomalous coefficient $α>1/2$. The results in this paper explain very well the wide distributed $α$ values for the samples with different ratios of substitutions of $^{12}$C by $^{13}$C of fulleride superconductor Rb$_{3}$C$_{60}$. The calculations of isotope effects indicate that the intra-molecule radial modes have more important contributions to superconductivity than the intra-molecule tangential modes with higher phonon frequenciesAccepted by International of Modern Physics B (13pages, 2eps figure)SuperconductivityMaterials Sciencetext