Sum rule for a Schiff-like dipole moment

Details Sum rule for a Schiff-like dipole moment Sum rule for a Schiff-like dipole moment

2009-06-16

arxiv.org/abs/0906.2911v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

arXiv admin note: substantial text overlap with arXiv:1004.3159

Scientific paper

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, ${\cal N}$. The deviations are evaluated by two distinct approaches. One of them is based on the charge density expansion around an uniform distribution and provides an analytical ${\cal N}$ dependence for the sum rule while, the other one hinges of the RPA approach and yields compact expressions for corrections as function of the RPA amplitudes. Although the formalism might be considered for any many body system, we applied it for illustration, to the case of $Na$ clusters. One concludes that the RPA results for $Na$ clusters obey the modified TRK sum rule.

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