  Nanomaterials made of the cerium oxides CeO$_2$ and Ce$_2$O$_3$ have a broad
range of applications, from catalysts in automotive, industrial or energy
operations to promising materials to enhance hadrontherapy effectiveness in
oncological treatments. To elucidate the physico-chemical mechanisms involved
in these processes, it is of paramount importance to know the electronic
excitation spectra of these oxides, which are obtained here through
high-accuracy linear-response time-dependent density functional theory
calculations. In particular, the macroscopic dielectric response functions
$\bar\epsilon$ of both bulk CeO$_2$ and Ce$_2$O$_3$ are derived, which compare
remarkably well with the available experimental data. These results stress the
importance of appropriately accounting for local field effects to model the
dielectric function of metal oxides. Furthermore, we reckon the materials
energy loss functions $\mbox{Im} (-1/\bar{\epsilon})$, including the accurate
evaluation of the momentum transfer dispersion from first-principles. In this
respect, by using a Mermin-type parametrization we are able to model the
contribution of different electronic excitations to the dielectric loss
function. Finally, from the knowledge of the electron inelastic mean free path,
together with the elastic mean free path provided by the relativistic Mott
theory, we carry out statistical Monte Carlo (MC) charge transport simulations
to reproduce the major features of the reported experimental reflection
electron energy loss (REEL) spectra of cerium oxides. The good agreement with
REEL experimental data strongly supports our approach based on MC modelling
informed by ab initio calculated electronic excitation spectra in a broad range
of momentum and energy transfers.
