Dynamical effects on phonon emission in a polar electron gas

We calculate the quasiparticle damping rate of energetic electrons in two- and three-dimensional electron systems due to Fr\"ohlich interaction. The dynamical screening effect is included in the theory through a mode-coupling mechanism. At high and low electron densities the dynamically screened phonon emission rate approaches the statically screened and the unscreened results, respectively. Interesting structure associated with plasmon threshold is seen in the phonon emission rate at characteristic electron energies. The total electronic damping rate in the coupled electron-phonon-plasmon GaAs system is obtained numerically for both two and three dimensions and is related to recent experiments on hot-electron spectroscopy.