Jellium model vibrations

A splitting of the dipole resonance into three peaks has been observed in some sodium clusters [64], This observation is interpreted as corresponding to collective vibrations of the valence electrons in the directions of the principal axes of a triaxially deformed cluster, and has motivated an extension of the deformed jellium model to fully triaxial shapes. Lauritsch et al. [65] have applied this model to Nai2 and Nai4. 

A precise theoretical and experimental determination of polarizability would provide an important probe of the electronic structure of clusters, as a is very sensitive to the presence of low-energy optical excitations. Accurate experimental data for a wide range of size-selected clusters are available only for sodium, potassium [104] and aluminum [105, 106]. Theoretical predictions based on DFT and realistic models do not cover even this limited sample of experimental data. The reason for this scarcity is that the evaluation of polarizability by the sum rule (46) requires the preliminary computation of S(co), which, with the exception of Ref. [101], is available only for idealized models. Two additional routes exist to the evaluation of a, in close analogy with the computation of vibrational properties static second-order perturbation theory and finite differences [107]. Again, the first approach has been used exclusively for the spherical jellium model. In this case, the equations to be solved are very similar to those introduced in Ref. [108] for the computation of atomic polarizabilities. Applications of this formalism to simple metal clusters are reported, for instance, in Ref. [109]. 

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