Calculation of the superconducting critical temperature in doped fullerenes

In view of experimental evidence we assume that the coupling between electrons and on-molecule phonon modes is responsible for superconductivity in doped fullerenes. Therefore, we solve the Eliashberg equations by taking properly into account that the Fermi energy is comparable to the on-molecule phonon energies. The obtained formulas for the renormalization function Z(ω) and the critical temperature ${\mathit{T}}_{\mathit{c}}$ are different from the usual ones but reduce to them when the ratio between Fermi energy and phonon frequencies is much larger than 1. We present results for the dopant and pressure dependence of ${\mathit{T}}_{\mathit{c}}$ which are in good agreement with experimental results.