Theoretical analysis of plasmon dispersion in simple metals

The dielectric response of an electron gas has been investigated with a view to understanding the small momentum behaviour of the plasmon peak in inelastic electron energy loss spectra. It is shown that the life-time of the plasmon and the width of the incident beam both contribute to the apparent flattening of the plasmon dispersion which has been seen to occur in some metals (magnesium,alluminium,indium) for plasmon wavevectors less than approximately 0.5A-1. Expressions, beyond the random phase approximation, are derived for the dispersion coefficients up to fourth order in the plasmon wavevector. Good agreement with experiment is obtained