Computation of the ultraviolet absorption and electron inelastic scattering cross section of multishell fullerenes

We develop a model in which the ultraviolet dielectric tensor of planar graphite is transported to the spherical geometry of a nanoscale multishell fullerene with a central cavity. This is accomplished by assigning to every point of the multishell fullerene a local dielectric tensor identical to that of graphite with its c axis aligned along the local radial direction. The dynamic, multipolar polarizabilities of the model fullerene are obtained from the exact solutions of the nonretarded Maxwell equations. The ultraviolet absorption spectrum of the hollow fullerene is calculated as a function of the ratio of the inner and outer radii. Comparisons of the theoretical absorption spectra with the 2175-Å interstellar extinction hump and with recent absorption measurements for synthetic multishell fullerenes indicate that the dielectric properties of graphite are qualitatively adequate for understanding the optical data. However, difficulties persist with both the astrophysical and laboratory absorption peaks which lead us to consider the possible role of multishell fullerene aggregation into small or large clusters. It is found that the effect of clustering is important and reduces but does not remove completely the quantitative difficulties of the graphitic multishell model. Finally theoretical electron-energy-loss spectra (EELS) of these structures with an empty or filled cavity are calculated from the multipolar polarizabilities of the model. The results indicate that spatially resolved EELS measurements should be ideally suited to study the dielectric properties of individual multishell fullerenes and to ascertain to what extent they differ from those of planar graphite.