  A simple model of electron-vibron interactions in buckminsterfullerene ions
is solved semiclassically. Electronic degeneracies of C$_{60}$$^{n-}$ induce
dynamical Jahn-Teller distortions, which are unimodal for $n\!\ne\!3$ and
bimodal for $n\!=\!3$. The quantization of motion along the Jahn-Teller
manifold leads to a symmetric-top rotator Hamiltonian. I find Molecular
Aharonov-Bohm effects where electronic Berry phases determine the vibrational
spectra, zero point fluctuations, and electrons' pair binding energies. The
latter are relevant to superconductivity in alkali-fullerenes.
