The microscopic structure of the surface plasmon is investigated in th
e fullerenes C-60 and C-70, in particular the contribution to its line
shape and linewidth arising from the coupling to the normal modes of
vibration of the ions, both at zero and at finite temperature. This co
upling is found to be negligible in C-60 at all temperatures, but size
able for C-70 already at T = 0, evidencing a weak temperature dependen
ce, a feature which is due to the lower equilibrium symmetry of C-70.
As a result, Landau damping is found to be the dominant relaxation mec
hanism contributing to the large width observed experimentally.