A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC-BCS crossover

By including the effect of a trap with characteristic energy given by the Fermi temperatureT_Fin a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a⁴⁰K atomic Fermi gas. We also reproduce the experimental closed-channel fractionZacross the BEC-BCS crossover and into the BCS regime of a⁶Li atomic Fermi gas. We obtain the expected behaviorZ∝TFat unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of theZdependency onT_Fon the BCS side, where a significant quantitative discrepancy between experimental data and theory's predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity betweenZandTFpredicted by our model for a⁴⁰K atomic Fermi gas.