RADIAL VIBRATIONS OF A SODIUM-ION INSIDE ICOSAHEDRAL C-60

The very high symmetry of icosahedral C60 suggests that as a first approximation an atom trapped inside C60 would be subject to a potential that is radially symmetric about the center. All-electron local-density-functional calculations of the total energy of a sodium ion as a function of radial displacement from the center along the fivefold axis Of C60 serve to refine such a radial potential. In particular the calculations suggest studying potentials that have minima displaced from the center. An analytic functional form for a radial potential having a positive cusp at the origin is proposed, and the s-wave radial solutions of the corresponding Schrodinger equation are examined.