COMPUTATION OF THE ULTRAVIOLET-ABSORPTION AND ELECTRON INELASTIC-SCATTERING CROSS-SECTION OF MULTISHELL FULLERENES

We develop a model in which the ultraviolet dielectric tenser of plana r graphite is transported to the spherical geometry of a nanoscale mul tishell fullerene with a central cavity. This is accomplished by assig ning to every point of the multishell fullerene a local dielectric ten ser identical to that of graphite with its c axis aligned along the lo cal radial direction. The dynamic, multipolar polarizabilities of the model fullerene are obtained from the exact solutions of the nonretard ed Maxwell equations. The ultraviolet absorption spectrum of the hollo w fullerene is calculated as a function of the ratio of the inner and outer radii. Comparisons of the theoretical absorption spectra with th e 2175-Angstrom interstellar extinction hump and with recent absorptio n measurements for synthetic multishell fullerenes indicate that the d ielectric properties of graphite are qualitatively adequate for unders tanding the optical data. However, difficulties persist with both the astrophysical and laboratory absorption peaks which lead us to conside r 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 difficult ies of the graphitic multishell model. Finally theoretical electron-en ergy-loss spectra (EELS) of these structures with an empty or filled c avity are calculated from the multipolar polarizabilities of the model . The results indicate that spatially resolved EELS measurements shoul d be ideally suited to study the dielectric properties of individual m ultishell fullerenes and to ascertain to what extent they differ from those of planar graphite.