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Electron energy loss in carbon nanostructures

The response of fullerenes and carbon nanotubes is investigated by representing each carbon atom by its atomic polarizability. The polarization of each carbon atom produces an induced dipole that is the result of the interaction with a given external field plus the mutual interaction among carbon atoms. The polarizability is obtained from the dielectric function of graphite after invoking the Clausius-Mossotti relation. This formalism is applied to the simulation of electron energy loss spectra both in fullerenes and in carbon nanotubes. The case of broad electron beams is considered and the loss probability is analyzed in detail as a function of the electron deflection angle within a fully quantum-mechanical description of the electrons. A general good agreement with available experiments is obtained in a wide range of probe energies between 1 keV and 60 keV.