Many-body treatment of electron inelastic scattering on metal clusters

In this paper we suggest the many-body treatment for the inelastic scattering of fast electrons on metal clusters. The accurate many-body theory for this process is necessary because electrons in the cluster experience collective excitations during the collision. We perform our calculation in the random phase approximation with exchange using the wavefunctions of the Hartre-Fock jellium model and also in the plasmon resonance approximation. The latter approach is appropriate to treat collective excitations in clusters. We analyse the differential and total inelastic scattering cross sections and elucidate the relative importance of collective electron excitations and single-electron transitions in the formation of the inelastic scattering cross section on metal clusters. We perform this calculation for the magic sodium clusters Na-20, Na-40, Na-58 and Na-92. Theoretical results are also compared with the experimental data available for electron collisions with the Na-8, Na-20 and Na-40 clusters. We report some discrepancy between theoretical and experimental results.