  The dynamic structure factor of a normal Fermi gas is investigated by using
the moment method for the Boltzmann equation. We determine the spectral
function at finite temperatures over the full range of crossover from the
collisionless regime to the hydrodynamic regime. We find that the Brillouin
peak in the dynamic structure factor exhibits a smooth crossover from zero to
first sound as functions of temperature and interaction strength. The dynamic
structure factor obtained using the moment method also exhibits a definite
Rayleigh peak ($/omega /sim 0$), which is a characteristic of the hydrodynamic
regime. We compare the dynamic structure factor obtained by the moment method
with that obtained from the hydrodynamic equations.
