We study the wavevector- and frequency- dependent exchange-correlation local-field factor, [Formula: see text], of the dynamical spin susceptibility, [Formula: see text], of a homogeneous electron gas. For high frequencies we calculate [Formula: see text] diagrammatically to second order in the Coulomb interaction, and consequently find that [Formula: see text] varies as q−2 ω−1/2 for large ω and finite q. We also consider an interpolation formula for [Formula: see text], that yields the exact small- and large- wave-number limits. Making use of these results and the Kramers–Kronig relation, we construct an approximate local-field factor that has the correct limiting behavior for both low and high frequencies.
Long-wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid
