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A new mechanism is proposed to explain the puzzling damping of collective excitations, which was recently observed in the experiments of strongly interacting Fermi gases below the superfluid critical temperature on the fermionic (BCS) side of Feshbach resonance. Sound velocity, superfluid density and damping rate are calculated with effective field theory. We find that a dominant damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasiparticles, in contrast to the previously proposed pair-breaking mechanism. Results from our effective model are compared quantitatively with recent experimental findings, showing a good agreement.

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