Energy weighted sum rule in Na clusters

TL;DR

This paper investigates the energy-weighted sum rule for electric dipole transitions in Na clusters, showing that RPA results conform to a modified Thomas-Reiche-Kuhn sum rule with corrective terms depending on the number of components.

Contribution

It introduces a modified sum rule for Na clusters and demonstrates that RPA calculations adhere to this revised rule.

Findings

RPA results obey the modified TRK sum rule

Corrective terms depend on the number of system components

Formalism applicable to Na clusters

Abstract

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.