  We evaluate the scattering functions of a gas of spin-polarized,
non-interacting fermions confined in a quasi-onedimensional harmonic trap at
zero temperature. The main focus is on the inelastic scattering spectrum and on
the angular distribution of scattered light from a mesoscopic atomic cloud as
probes of its discrete quantum levels and of its shell structure in this
restricted geometry. The dynamic structure factor is calculated and compared
with the results of a local-density approximation exploiting the spectrum of a
one-dimensional homogeneous Fermi gas. The elastic and inelastic contributions
to the static structure factor are separately evaluated: the inelastic term
becomes dominant as the momentum transfer increases, masking a small peak at
twice the Fermi momentum in the elastic term but still reflecting the discrete
quantum levels of the cloud. A fast and accurate numerical method is developed
to evaluate the full pair distribution function for mesoscopic inhomogeneous
clouds.
