Scattering of electrons on metal clusters and fullerenes

Abstract

It is shown that the main contribution to the elastic cross section of fast electrons on metal clusters and fullerenes results from scattering on the frozen cluster potential, which is determined by the electron density distribution of the ground state of the target cluster. The specific shape of the electron distribution in fullerenes and metal clusters manifests itself in the diffraction behaviour of the elastic differential cross section. The analysis of the total elastic cross section dependence upon projectile velocity, the number of atoms in the cluster and its size is provided. The cross section of elastic scattering on a cluster surpasses the sum of the individual scattering cross sections on the equivalent number of isolated atoms. This occurs because of the coherent interaction of the projectile electron with electrons delocalized in the cluster volume. We have demonstrated that collective electron excitations sensitive to the many-electron correlations dominate inelastic scattering. The surface plasmon resonances can be observed in the differential cross section for inelastic scattering. We found a condition for the quadrupole and higher multipole plasmon excitations to contribute relatively little to the electron energy loss spectrum. The results obtained have been compared with experimental data for the electron - fullerene collision. Reasonable agreement between theoretical and experimental results is reported. We have also demonstrated that plasmon excitations provide the main contribution to the total inelastic cross section over a wide energy range. We have calculated the dependence of the total inelastic cross section on collision energy and compared the result obtained with the experimental data available, giving an interpretation for the plateau region in the cross section as caused by plasmon excitations rather than the cluster fragmentation process. We have shown that the single-particle jellium approximation fails to describe this experiment. Our analysis is performed for metal clusters and fullerenes, However, it can also be applied to other polarizable systems, possessing plasmon or giant collective resonances.

Structure and properties of small sodium clusters

“…The jellium model provides a very useful basis for studying various collision processes, such as photabsorption [43], photoionization [5,44,45], elastic [46,47] and inelastic scattering [47][48][49][50], electron attachment [51,52], photon emission [53,54] and others, involving metal clusters,. On the basis of the jellium model one can develop ab initio many-body theories, such as the random phase approximation with exchange or the Dyson equation method and effectively solve many-electron correlation problem even for relatatively large cluster systems containing up to 100 atoms or even more.…”

Interplay of the volume and surface plasmons in the electron energy loss spectra of C60

“…Therefore, the plasmon resonance approximation utilized and further advanced in the present work turns out to be also a very useful tool for the interpretation of the results of such quantum simulations. The validity of the plasmon resonance approximation was proved by the comparison of its results with those following from ab initio quantum calculations for the case of metal clusters [11,27], and also by the comparison with available experimental data [19,21].…”

“…, is defined only by the single surface plasmon, and (1) and (2) transform into the following expression [19,20,21]:…”

Formalism for multiphoton plasmon excitation in jellium clusters

“…It is easy to estimate the relative value of the first and the second terms on the left hand side of (17). We see that the second term is negligible, provided the condition E ≪ mω 2 R/e is fulfilled.…”

“…For nearly-spherical fullerenes C 20 or C 60 , the plasmon resonance frequency is equal to (see [11,17])…”