Applicability of the Plasmon Theory to Clusters

The first depletion spectra obtained for neutral sodium clusters N = 2-40 were characterized by structureless broad features containing one or two bands. The results were interpreted in terms of collective resonances of valence electrons (plasmons) for all clusters larger than tetramers [2, 52-55]. The analogies between findings for metallic clusters and observations of giant dipole resonances in nuclei have attracted a large attention. Therefore the methods employed in nuclear physics, such as different versions of RPA in connection with the jellium model, have also been applied for studying the optical properties of small clusters. Another aspect was the onset of conductivity in metal-insulator transitions. 

In contrast, the quantum-chemical approach has been suitable for the description of changes caused by the addition of each single atom influencing the structural and optical properties. Question has been raised as to whether a size regime can be found in which transition from optical properties of individual cluster size can go over to metallic ones. Therefore we first present the theoretical background of the plasmon energy and examine under what conditions the plasmon-like excitations can be present in systems such as small clusters. The existence conditions for collective excitations are exactly formulated in the quantum theory of plasmons and the aim is to show under what assumptions they can be fulfilled for small finite systems. 

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