  The indirect carrier-phonon vertex function is evaluated for cubic zirconia
by employing the many-body perturbation theory on top of the frozen phonon
model. The phonon-induced carrier velocity and spectral renormalization are
represented at each individual lattice vibronic mode. Our results show that for
the indirect electron-phonon scattering, optical phonons make up the dominant
contribution. It is observed that, despite the phonon-phonon interaction, there
is a substantial polaronic character for all the activated lattice optical
vibrations which is in accordance with the previous experimental and
theoretical finding concerning the crucial role of optical phonons. Eventually
our results are capable to discuss that, in the presence of optical phonons a
transition between small to large polaron is probable
