Phenomenological investigations of S(k,ω) of the two-dimensional electron gas in the memory-function formalism

The dynamic structure function S(k,ω) and the dielectric function ε(k,ω) of the two-dimensional electron gas is calculated phenomenologically at ${\mathit{r}}_{\mathit{s}}$=1 and 5 in the memory-function formalism. The density-density response function χ(k,ω) is expressed in terms of that of a noninteracting system and an effective potential. The interaction part of the second-order memory function that determines the effective potential is approximated by a Gaussian in time domain. We use a consistent set of highly accurate ground-state static properties as input, coming from a Green’s-function Monte Carlo calculation. The calculated S(k,ω) shows a single-broad-peak structure at intermediate k, which is from the case in three dimensions.