Electronic Shell Structure and Relative Abundances of Cesium-CoatedC60

The relative abundances of ${\mathrm{C}}_{60}\mathrm{Cs}\left(N\right)$, $N\le 500$, determined from mass spectra measurements, are presented and explained in terms of the successive filling of the electronic shells by the cesium valence electrons. The motion of the Cs valence electrons, confined to a metal layer surrounding the ${\mathrm{C}}_{60}$ molecule, is described within the jellium model, with Cs spread into a uniform positive background. The electronic shell structure is calculated with the local approximation to density-functional theory and is shown to correspond to measured abundances. Strong Friedel oscillations in the electronic density are found and closed forms for them are given for jellium spheres both with and without the void.