Finite range corrections near a Feshbach resonance and their role in the Efimov effect

We have measured the binding energy of $^7$Li Feshbach molecules deep into the non-universal regime by associating free atoms in a Bose-Einstein condensate by modulating the magnetic field. We extract the scattering length from these measurements, correcting for non-universal short-range effects using several different methods. We find that field-dependent effective range corrections agree well with the data. With this more precise determination of the scattering length vs. field we reanalyze our previous data on the location of atom loss features produced by the Efimov effect \cite{PollackSci09} and investigate effective range corrections to universal theory.