  Nonresonant inelastic light and X-ray scattering is investigated for the
spinless Falicov-Kimball model on an infinite-dimensional hypercubic lattice
with a charge-density-wave phase at half filling. The many-body density of
states (DOS) is found for different values of the Coulomb repulsion $U$,
ranging from a dirty metal to a Mott insulator. At zero temperature, the charge
gap is exactly equal to $U$; increasing the temperature rapidly fills the gap
with subgap states. The nonresonant response function for Raman and inelastic
X-ray scattering shows peaks connected with transitions over the gap and
transitions that involve subgap states. In the case of X-ray scattering (when
both energy and momentum are transferred), the response function illustrates
features of dynamical screening (vertex corrections) in the different
(nonresonant) symmetry channels ($A_{\rm 1g}$ and $B_{\rm 1g}$). We also derive
and verify the first moment sum rules for the (nonresonant) Raman and inelastic
X-ray response functions.
