Energy weighted sum rule in Na clusters

The energy-weighted sum rule for an electric dipole transition operator of a Schiff type differs from the Thomas-Reiche-Kuhn sum rule by several corrective terms which depend on the number of system components, ${\cal N}$. For illustration the formalism was applied to the case of $Na$ clusters. One concludes that the RPA results for $Na$ clusters obey the modified TRK sum rule.