The suppressed NMR coherence peak in the fullerene superconductors is
explained in terms of the dampings induced by the Coulomb interaction
between conduction electrons. The Coulomb interaction, modeled in term
s of the on-site Hubbard repulsion, is incorporated into the Eliashber
g theory of superconductivity with its frequency dependence considered
self-consistently at all temperatures. The vertex correction is also
included via the method of Nambu. The frequency dependent Coulomb inte
raction induces the substantial dampings in the superconducting state
and, consequently, suppresses the anticipated NMR coherence peak of fu
llerene superconductors as found experimentally.