We investigate theoretically the quasiparticle properties of a trapped gas
of fermionic atoms in both the normal and the superfluid phases. Our analys
is, which accounts for the shell structure of the normal phase spectrum, sh
ows that the single-particle response of the gas to a modulation of the tra
pping frequency should indicate the onset of superfluidity. The results are
discussed in the context of current experiments on trapped Fermi gases.