  We consider a three dimensional Wigner crystal of electrons lying in a host
ionic dielectric. Owing to their interaction with the lattice polarization,
each localized electron forms a polaron. We study the collective excitations of
such a polaronic Wigner crystal at zero temperature, taking into account the
quantum fluctuations of the polarization within the Feynman harmonic
approximation. We show that, contrary to the ordinary electron crystal, the
system undergoes a polarization catastrophe when the density is increased. An
optical signature of this instability is derived, whose trend agrees with the
experiments carried out in Nd-based cuprates.
