  The dynamic Jahn-Teller splitting of the six equivalent $D_{5d}$ polarons due
to quantum fluctuations is studied in the framework of the Bogoliubov-de Gennes
formalism. The tunneling induced level splittings are determined to be $^2
T_{1u} \bigoplus ^2 T_{2u}$ and $^1 A_g \bigoplus ^1 H_g$ for $C_{60}^{1-}$ and
$C_{60}^{2-}$, respectively, which should give rise to observable effects in
experiments.
