Energy structure of weakly bound molecules near Feshbach resonances

Recent experiments on ultracold molecules created near a Feshbach resonance have allowed high precision measurements on molecular binding energy near the continuum.~ To date, measurements on molecules such as~ 6Li$_2$, 40K$_2$, 87Rb$_2$, 133Cs$_2$ and 40K-87Rb have been reported and provided the critical information to pin down the long-range interaction parameter of atoms and to test atomic scattering theories. We show that binding energies of molecules near the continuum can be well-approximated based on simplified interaction models, such as the van der Waals potential or a square-well potential. These simplified models allow for self-consistent, analytic expressions for molecular binding energies and scattering lengths near Feshbach resonances. We report excellent agreement between our results and the full multi-channel calculation within and beyond the quantum threshold regime.~ Examples include 6Li$_2$, 40K$_2$, 133Cs$_2$ and 40K-87Rb. In the latter two cases, we will present the comparison in the regime where several resonances overlap.