Dynamical exchange-correlation potentials for the electron liquid in the spin channel

Abstract

The components of the exchange-correlation kernel tensor of an isotropic electron liquid in the spin channel have the structure f xc,2 L,T (q,v) ! q!0 A(v)/q21BL,T(v), where L denotes the longitudinal component and T the transverse component relative to the direction of the wave vector q. In this paper we calculate analytically the high- and low-frequency limits of A(v) and BL,T(v) and combine these limiting forms with the Kramers-Kro¨nig dispersion relations to obtain approximations for A(v) and BL,T(v) at all frequencies.