In this work we report on the results of many-body quantum treatment for the inelastic scattering of fast electrons on metal clusters in the range of energies transferred above the ionization threshold. In this energy range, many-electron collective excitations provide significant contribution to the cross section. Above the cluster ionization threshold, the volume plasmon is the most significant many-electron excitation because its resonance frequency is located above the ionization threshold. We performed calculation of the electron inelastic cross sections using two different approaches. First, we calculated the cross section in the RPAE with the Hartree-Fock jellium model wave functions, accounting for both all single particle and collective excitations in the cluster. In order to extract contribution of plasmon excitations, we have also obtained the cross section in the plasmon resonance approximation.
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