  We investigate the localization of charged particles by the image potential
of spherical shells, such as fullerene buckyballs. These "spherical image
states" exist within surface potentials formed by the competition between the
attractive image potential and the repulsive centripetal force arising from the
angular motion. The image potential has a power law rather than a logarithmic
behavior for a nanotube, leading to fundamental differences in the forms for
the effective potential for the two geometries. The sphere has localized stable
states close to its surface. At low temperatures, this results in long
lifetimes for the image states. We predict the possibility of creating image
states with binding energies of a few meV around metallic/non-metallic
spherical shells by photoionization. Applications and related phenomena are
discussed.
