Frequency‐dependent exchange correction to the dielectric function of the electron gas (II)

The influence of the exchange interaction on the dielectric response of the homogeneous electron gas is investigated. Starting from an expression for the dielectric function obtained earlier, the function G ( q , ω) that describes the effect of exchange, is analysed. It is shown that G ( q ,ω) has a logarithmic singularity if ω = h ( qk F ± q 2 /2), which makes the full frequency dependence of this function very significant. The dielectric function with exchange differs from the Hartree approximation by a very peaked frequency dependent structure. It even has a pole of first order. Furthermore, due to exchange, the plasmon branch is substantially changed and does not penetrate in the pair creation region. Finally, the exchange interaction induces a zero in the dynamic structure factor, where in the Hartree approximation only a discontinuous derivative with respect to frequency occurs.