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Collective Modes of Trapped Fermi Gases in the Normal Phase

We consider the collective mode spectrum of a normal Fermi gas in a spherical harmonic trap. Using a self-consistent random-phase-approximation, we systematically examine the effects of the two-body interactions on the modes of various symmetries. For weak coupling where the spectrum is shifted very little away from the ideal gas case, a sum-rule approach is shown to work well. For stronger coupling, the interplay between the single particle and the collective excitations causes effects such as mode splitting and Landau damping. A finite low frequency response present at stronger coupling is predicted for the quadrupole mode. Finally, we briefly discuss the effect of a finite temperature on the spectrum and the excitation of higher collective modes.