Absorption by cold Fermi atoms in a harmonic trap

We study the absorption line shape of a strongly degenerate Fermi gas confined in a harmonic trap. The absorption spectrum is calculated using both the exact summation and also the Thomas-Fermi approximation. In the latter case, relatively simple analytical expressions are obtained for the absorption line shape for a large number of trapped atoms. At zero temperature, the approximated line shape is characterized by a $(1\mathrm{}-z^2{)}^{5/2}$ dependence, which agrees well with the exact numerical calculations. At nonzero temperature, the spectrum becomes broader, although remains non-Gaussian as long as the fermion gas is degenerate. The changes in the trap frequency for an electronically excited atom can introduce an additional line broadening.