Electron-phonon coupling in the C<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>60</mml:mn></mml:msub></mml:math>fullerene within the many-body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>approach

We study the electron-phonon coupling in the C${}_{60}$ fullerene within the first-principles $GW$ approach, focusing on the lowest unoccupied ${t}_{1u}$ threefold electronic state which is relevant for the superconducting transition in electron-doped fullerides. It is shown that the strength of the coupling is significantly enhanced as compared to standard density functional theory calculations with (semi)local functionals, with a 48$%$ increase of the electron-phonon potential ${V}^{ep}$ with respect to the LDA value. The calculated $GW$ value for the contribution from the ${H}_{g}$ modes of 93 meV comes within 4$%$ of the most recent experimental values. The present results call for a reinvestigation of previous density functional based calculations of electron-phonon coupling in covalent systems in general.