${\mathrm{C}}_{60}$: Interacting electrons on a spherical molecule

We study a simplified model of ${\mathrm{C}}_{60}$, where the π electrons move freely on the surface of a sphere. The total energy in the presence of an adjustable repulsive interaction is computed by first- and second-order perturbation theory. The second-order results yield an effective attraction (pair binding) between electrons which are added above a closed angular-momentum shell. For different regimes of interaction parameters, we find an L=0 singlet and an L=1 triplet ground state. Pair binding occurs at larger couplings for longer-range interactions. We estimate the third-order corrections, and define the region where the second-order predictions are expected to hold. The relevance of this model to superconductivity and ferromagnetism in doped fullerenes is discussed.