A simple model for electron-vibron interactions on charged fullerenes
C-60(n-) n = 1,...,5, is solved both at weak and strong couplings. We
consider a single H(g) vibrational multiplet interacting with t1u elec
trons. At strong coupling the semiclassical dynamical Jahn-Teller theo
ry is valid. The Jahn-Teller distortions are unimodal for n = 1, 2,4,5
electrons, and bimodal for 3 electrons. The distortions are quantized
as rigid-body pseudorotators which are subject to geometrical Berry p
hases. These impose ground-state degeneracies and dramatically change
zero-point energies. Exact diagonalization shows that the semiclassica
l level degeneracies and ordering survive well into the weak-coupling
regime. At weak coupling, we discover an enhancement factor of 5/2 for
the pair binding energies over their classical values. This has poten
tially important implications for superconductivity in fullerides, and
demonstrates the shortcoming of Migdal-Eliashberg theory for molecula
r crystals.