Atomic Fermi gases provide an ideal platform for studying the pairing and superfluid physics, using a Feshbach resonance between closed channel molecular states and open channel scattering states. Of particular interest is the strongly interacting regime. We show that the closed-channel fraction $Z$ provides an effective probe for the important many-body interacting effects, especially through its density dependence, which is absent from two-body theoretical predictions. Here we measure $Z$ as a function of interaction strength and the Fermi temperature $T_F$ in a trapped $^6$Li superfluid throughout the entire BCS--BEC crossover. Away from the deep BEC regime, the fraction $Z$ is sensitive to $T_F$. In particular, our data show $Z propto T_F^{alpha}$ with $alpha=1/2$ at unitarity, in quantitative agreement with calculations of a two-channel pairing fluctuation theory, and $alpha$ increases rapidly into the BCS regime, reflecting many-body interaction effects as predicted.
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