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We discuss the structural properties and optical response of a small Na cluster inside rare gas (RG) matrices of Ne, Ar, or Kr atoms. The mixed systems are described with a hierarchical model, treating the cluster at a quantum mechanical level and the matrix atoms classically in terms of their positions and polarizations. We pay special attention to the differences caused by the different matrix types. These differences can be explained by the interplay of core repulsion and dipole attraction in the interaction between the cluster electrons and the RG atoms.

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