  We study the absorption spectrum for a strongly degenerate Fermi gas confined
in a harmonic trap. The spectrum is calculated using both the exact summation
and also the Thomas-Fermi (TF) approximation. In the latter case, relatively
simple analytical expressions are obtained for the absorption lineshape at
large number of trapped atoms. At zero temperature, the approximated lineshape
is characterized by a $(1-z^2)^{5/2}$ dependence which agrees well with the
exact numerical calculations. At non-zero 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.
