On the Stability of Endohedral Rare Gas Fullerenes

The stability of Ne@C$_{60}$ and He@C$_{60}$ is discussed in the context of a spherical model where the carbon atoms are smeared out into a uniform shell. The electronic properties of the sixty $\pi$ electrons together with those of the central atom are treated in the Thomas-Fermi approximation. Simple electrostatic reasoning elucidates the nature of the radial stability of the complex. A method to include non-spherical corrections is outlined. Possible bonding topologies of the central atom and the C$_{60}$ cage are discussed, as well as the relevance of these topologies to incipient central atom distortions.