Frequency moments of the dielectric function for an inhomogeneous electron gas

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Abstract
A unified treatment of the arbitrary frequency moments Iqq(n) of the longitudinal dielectric matrix epsilon qq'( omega ) and of the moments Fqq(n) of epsilon qq'-1( omega ) is given for the inhomogeneous electron gas. The Iqq(n) are in the RPA, whereas the Fqq(n) are exact in the non-relativistic limit excluding phonons. Furthermore, the author derives formulae allowing the Fqq(n) to be calculated from Iqq(n) and vice versa for a given approximation, which obeys the Kramers-Kronig relations. Using inequalities between the moments the author derives an inequality relating the static dielectric function of a non-conductor and the electron density at the nuclear sites.