  A semi-classical model describing the charge transfer collisions of $C_{60}$
fullerene with different slow ions has been developed to explain available
experimental data. This data reveals multiple Breit-Wigner like peaks in the
cross sections, with subsequent peaks of reactive cross sections decreasing in
magnitude. Calculations of the charge transfer probabilities and cross sections
for quasi-resonant and reactive collisions have been performed using
semi-empirical potentials of interaction between fullerenes and ion
projectiles. All computations have been carried out with realistic wave
functions for $C_{60}$'s valence electrons derived from the simplified jellium
model. The quality of these electron wave functions have been successfully
verified by comparing theoretical calculations and experimental data on the
small angle cross sections of resonant $C_{60}+ C_{60}^+$ collisions. Using the
semi-empirical potentials to describe resonant scattering phenomena in $C_{60}$
collisions with ions and Landau-Zener charge transfer theory, we calculated
theoretical cross sections for various $C_{60}$ charge transfer and
fragmentation reactions which agree with experiments.
