  Optical conductivity of an interacting polaron gas is calculated within an
extended random phase approximation which takes into account mixing of
collective excitations of the electron gas with LO phonons. This mixing is
important for the optical response of strongly polar crystals where the static
dielectric constant is rather high: strontium titanate is the case. The present
calculation sheds light on unexplained features of experimentally observed
optical conductivity spectra in $n$-doped SrTiO$_{3}$. These features appear to
be due to dynamic screening of the electron-electron interaction by polar
optical phonons and hence do not require additional mechanisms for the
explanation.
