Static electric polarizabilities of sodium clusters

We present pseudopotential local-spin-density calculations of the static electric polarizabilities of sodium clusters up to nine atoms. We show that the comparison of the calculated polarizabilities with the experimental average polarizabilities and with the observed collective resonance frequencies gives information on which isomer is most probably observed in the experiments. Our results indicate that the plateau in the observed polarizability between ${\mathrm{Na}}_6$ and ${\mathrm{Na}}_7$ could be related to the change from two-dimensional to three-dimensional geometries. We also present calculations for the permanent dipole moment of the clusters, and evaluate the effects of the ionic vibrations on the molecular polarizability of ${\mathrm{Na}}_2$ and ${\mathrm{Na}}_3$.