Multipole plasmon resonances in differential cross-sections of inelastic scattering of fast electrons on metal clusters and fullerenes

We demonstrate that the electron energy loss spectrum in collision with metal clusters or fullerenes strongly depends on the electron scattering angle. This results from the fact that the excitation probability of the surface plasmon modes of different multipolarity is correlated with the electron scattering angle. We derive the kinematic conditions, under which the plasmon excitation with the given angular momentum dominates in the cross-section. We perform a treatment in the resonance plasmon approximation and also in the random phase approximation with exchange using the wave functions of the Hartree-Fock jellium model. We compare the predictions of these two quite different approaches for a Na-40 cluster and report their qualitative agreement. Theoretical results are compared with the available experimental data for the electron-fullerene C-60 collision. Reasonable agreement between theoretical and experimental results is reported.