  We reveal a strong influence of a superfluid phase transition on the
character of single-particle excitations of a trapped neutral-atom Fermi gas.
Below the transition temperature the presence of a spatially inhomogeneous
order parameter (gap) shifts up the excitation eigenenergies and leads to the
appearance of in-gap excitations localized in the outer part of the gas sample.
The eigenenergies become sensitive to the gas temperature and are no longer
multiples of the trap frequencies. These features should manifest themselves in
a strong change of the density oscillations induced by modulations of the trap
frequencies and can be used for identifying the superfluid phase transition.
