Frequency dependence of the optical relaxation time in metals

The optical relaxation times for electron-phonon and for impurity scattering are shown to have the form ${\ensuremath{\tau}}^{\ensuremath{-}1}(\ensuremath{\omega})={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}+b{\ensuremath{\omega}}^{2}$, and values of $b$ for impurity and electron-phonon effects (including umklapp processes) are calculated. The values of $b$ for electron-phonon scattering are compared with estimates for electron-electron scattering and with experiment for the alkali and noble metals. It appears that the observed frequency dependence in these materials at room temperature derives from correction terms of higher order in $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{{E}_{F}}$ to the electron-phonon interaction. For impurity scattering $b$ is predicted to be negative.