Processes leading to possible anharmonic dipole-plasmon oscillations in alkali-metal clusters are investigated. The electronic excitation spectrum of sodium clusters including highly excited states with more than one plasmon is calculated with an approach based on the separation of center of mass and intrinsic motion of delocalized electrons. The spectrum is analyzed in terms of collective plasmon oscillations, intrinsic electron motion, and their interaction. The latter is of primary importance. It is responsible for the anharmonicity of giant dipole oscillations. The predicted nonlinear blueshift of the dipole resonance is comparable with its spreading width, and therefore ought to be observed in photoabsorption experiments.

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.

An analytical investigation is made of semiconductor quantum-well subband structures using the three-band Kane model. The analysis is based on the assumption, that electron and light hole masses are much smaller than heavy hole mass in the heterostructure. It is demonstrated, that some anomalies in the subband spectrum are due to the interaction with interface states, others are generated by the repulsion between the subbands near the points of their quasiintersections. For the heterostructure, composed of the gapless layer in a finite-gap bulk material, the interface state is found to cause a nonmonotonous dependence of the gap on the layer thickness.Es wird eine analytische Untersuchung von Halbleiter-Quantenwell-Subbandstrukturen mit dem Kaneschen Dreibandermodell durchgefuhrt. Die Analyse beruht auf der Annahme, daR Elektronen-und Leichte-Locher-Massen vie1 kleiner sind als die Masse schwerer Locher in der Heterostruktur. Es wird gezeigt, daR einige Anomalien im Subbandspektrum durch die Wechselwirkung mit Grenzflachenzustanden hervorgerufen werden, andere werden durch die AbstoDung zwischen den Subbandern in der Nahe ihrer Quasiuberschneidungspunkte generiert. Fur die Heterostrukturen, die aus einer gaplosen Schicht in einem Volumenmaterial mit endlicher Bandlucke zusammengesetzt sind, wird gefunden, daD die Grenzflache eine monotone Abhangigkeit der Bandlucke von der Schichtdicke verursacht.

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We demonstrate that the electron energy loss spectrum in collision with metal clusters or fullerenes depends strongly on the scattering angle of the electron. This results from the fact that the excitation probability of the surface plasmon modes of different multipolarity is correlated with the scattering angle of the electron. We derive the kinematic conditions under which the plasmon excitation with the given angular momentum dominates in the cross section. We perform our treatment in the resonance plasmon approximation and also in the random phase approximation with exchange using the wavefunctions of the Hartree-Fock jellium model. We compare the predictions of these two quite different approaches for the cluster Na 40 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.