High frequency dielectric function of metals taking into account Umklapp processes

An analytical model for the high-frequency dielectric function of metals accounting for electron-phonon interactions and Umklapp processes is derived using a quantum statistical approach within a linear response theory. Different limiting cases for radiation frequencies and electron temperatures, which are either low or high in comparison to the Fermi energy, are studied. New asymptotic formulas for high radiation frequencies or high electron temperatures are obtained. The application for the description of optical properties in warm dense aluminum plasma is discussed.