  The optical conductivity spectra of the rattling phonons in the clathrate
Ba$_8$Ga$_{16}$Ge$_{30}$ are investigated in detail by use of the terahertz
time-domain spectroscopy. The experiment has revealed that the lowest-lying
vibrational mode of a Ba(2)$^{2+}$ ion consists of a sharp Lorentzian peak at
1.2 THz superimposed on a broad tail weighted in the lower frequency regime
around 1.0 THz. With decreasing temperature, an unexpected linewidth broadening
of the phonon peak is observed, together with monotonic softening of the phonon
peak and the enhancement of the tail structure. These observed anomalies are
discussed in terms of impurity scattering effects on the hybridized phonon
system of rattling and acoustic phonons.
