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Plasmon dispersion and dynamic exchange - correlation potentials from two-pair excitations in degenerate plasmas

Electron energy-loss experiments have shown a rapid softening of the bulk plasmon dispersion across the series of the alkali metals. Motivated by these observations, we reconsider the evaluation of the dynamic, long-wavelength exchange - correlation potential in the electron fluid, which is of interest for applications in time-dependent density functional theory. The value of at the plasma frequency determines the exchange - correlation contribution to the leading plasmon dispersion coefficient in the homogeneous electron fluid. Whereas an interpolation scheme originally proposed by Gross and Kohn assumes a monotonic increase of across the plasma frequency, we examine the possibility of strongly non-monotonic behaviour arising from a resonance process between plasmons and two-pair excitations. This process is evaluated with the help of sum rules and selfconsistency requirements within a single-pole approximation for the dielectric function. The cases of a fermion plasma and of a boson plasma are treated in parallel and the reliability of the results for the fermion plasma at low coupling is tested by calculations within a random-phase approximation for the dielectric function. In all cases it is found that the resonance process accumulates oscillator strength in the neighbourhood of , thus decreasing the value of below the static value fixed by the compressibility sum rule. Although this lowering does not suffice to account by itself for the measured plasmon dispersion coefficient in the low-density alkali metals, our results provide useful input for combined band-structure and exchange - correlation calculations.