  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.
