Dynamical exchange effects on the plasmon dispersion in aluminum

In the dielectric function, obtained from the dynamical exchange decoupling method, exchange effects are described by a frequency‐dependent local field correction G(q, ω). From the behaviour of G(q, ω) in the static limit ω = 0, it follows that the compressibility sum rule is satisfied, and that the pair correlation function g(r) equals 1/2 at the origin. Also, in the static limit, G(q, 0) shows a sharp peak near q = 2kF. The dynamical behaviour of G(q, ω) at high frequencies fulfills the condition imposed by the third frequency moment sum rule, and it also implies that g(0) = 1/2. The same g(0) thus derives from both the static and the dynamical behaviour of G(q, ω), in contrast to earlier theories. The influence of the dynamical exchange effects on the plasmon dispersion is examined. It is found that, compared to RPA, the plasmon is almost unaffected by exchange outside the continuum, but that in the particle‐hole excitation region exchange effects drastically lower the peak position of the structure factor. This tendency has been experimentally observed in Al, where the RPA peak positions at finite wave vector are found at too large frequencies, but where the dynamical exchange decoupling method yields relatively good agreement with the experimental data.