Contrasting the wide Feshbach resonances in $^6$Li and $^7$Li

Abstract

We compare and contrast the wide Fehbach resonances and the corresponding weakly bound states in the lowest scattering channels of ultracold $^6$Li and $^7$Li. We use high-precision measurements of binding energies and scattering properties to determine new interaction potentials, incorporating non-Born-Oppenheimer terms to account for the failure of mass scaling between $^6$Li and $^7$Li. Correction terms are needed for both the singlet and the triplet potential curves. The universal formula relating binding energy to scattering length is not accurate for either system. The $^6$Li resonance is open-channel-dominated and the van der Waals formula of Gao [J. Phys. B 37, 4273 (2004)] gives accurate results for the binding energies across much of the resonance width. The $^7$Li resonance, by contrast, is weakly closed-channel-dominated and a coupled-channels treatment of the binding energies is required. Plotting the binding energies in universal van der Waals form helps illustrate subtle differences between the experimental results and different theoretical forms near the resonance pole.