  Using Fourier-transform infrared spectroscopy and optical ellipsometry, room
temperature spectra of complex conductivity of single crystals of hexaborides
Gd$_x$La$_{1-x}$B$_6$, $x$(Gd)$=0$, 0.01, 0.1, 0.78, 1 are determined in the
frequency range 30$-$35000$~cm^{-1}$. In all compounds, in addition to the
Drude free-carrier spectral component, a broad excitation is discovered with
the unusually large dielectric contribution $\Delta$$\varepsilon$=5000 -- 15000
and non-Lorentzian lineshape. It is suggested that the origin of the excitation
is connected with the dynamic cooperative Jahn-Teller effect of B$_6$ clusters.
Analysis of the spectra together with the results of DC and Hall resistivity
measurements shows that only 30$-$50$\%$ of the conduction band electrons are
contributing to the free carrier conductivity with the rest being involved in
the formation of an overdamped excitation, thus providing possible explanation
of remarkably low work function of thermoemission of Gd$_x$La$_{1-x}$B$_6$ and
non-Fermi-liquid behavior in GdB$_6$ crystals.
