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We evaluate the scattering functions of a gas of spin-polarized,non-interacting fermions confined in a quasi-onedimensional harmonic trap atzero temperature. The main focus is on the inelastic scattering spectrum and onthe angular distribution of scattered light from a mesoscopic atomic cloud asprobes of its discrete quantum levels and of its shell structure in thisrestricted geometry. The dynamic structure factor is calculated and comparedwith the results of a local-density approximation exploiting the spectrum of aone-dimensional homogeneous Fermi gas. The elastic and inelastic contributionsto the static structure factor are separately evaluated: the inelastic termbecomes dominant as the momentum transfer increases, masking a small peak attwice the Fermi momentum in the elastic term but still reflecting the discretequantum levels of the cloud. A fast and accurate numerical method is developedto evaluate the full pair distribution function for mesoscopic inhomogeneousclouds.Comment: 11 pages, 7 figure

Light scattering from a degenerate quasi-one-dimensional confined gas of noninteracting fermions