Application of sum rules to the response of small metal particles

Abstract

Sum rules for the response of small spherical systems are derived and compared to the response calculated in the time-dependent local-density approximation by Ekardt. The ${\omega }^3$ sum rule, which can be expressed in closed form, is useful as a supplement to the polarizability sum in locating the plasmon. Explicit formulas are obtained for the shifts in the plasmon frequency resulting from the diffusivity of the charge density and from the potential field of the ground state. We show on quite general grounds that the plasmon in a jellium model is red-shifted from the Mie frequency.