Formalism of collective electron excitations in fullerenes

We present a detailed formalism for the description of collective electron excitations in fullerenes in the process of the electron inelastic scattering. Considering the system as a spherical shell of a finite width, we show that the differential cross section is defined by three plasmon excitations, namely two coupled modes of the surface plasmon and the volume plasmon. The interplay of the three plasmons appears due to the electron diffraction of the fullerene shell. Plasmon modes of different angular momenta provide dominating contributions to the differential cross section depending on the transferred momentum.