  We consider the density response of a trapped two-component Fermi gas.
Combining the Bogoliubov-deGennes method with the random phase approximation
allows the study of both collective and single particle excitations.
Calculating the density response across a wide range of interactions, we
observe a crossover from a weakly interacting pair vibration mode to a strongly
interacting Goldstone mode. The crossover is associated with a depressed
collective mode frequency and an increased damping rate, in agreement with
density response experiments performed in strongly interacting atomic gases.
