Effect of electron-phonon interaction on the shift and attenuation of optical phonons

Using the Boltzmann equation for electrons in metals, we show that the optical phonons soften and have a dispersion due to screening in agreement with the results reported recently [M. Reizer, Phys. Rev. B {\bf 61}, 40 (2000)]. Additional phonon damping and frequency shift arise when the electron--phonon interaction is properly included.Comment: 4 pages, late