Interactions, pair binding and ferromagnetism on spherical molecules

The energy of a system of electrons on a sphere with purely repulsive interactions is computed by perturbation theory. Second-order results yield an effective attraction between added electrons, in the L = 0 singlet state or in the L = 1 triplet state, which depends on the magnitude and range of the interaction. An estimate of third-order corrections bounds the regime where these predictions are expected to hold. We discuss the relevance of this model to superconductivity and ferromagnetism in doped fullerenes.