Prediction of Feshbach resonances from three input parameters

We have developed a model of Feshbach resonances in gases of ultracold alkali
metal atoms using the ideas of multichannel quantum defect theory. Our model
requires just three parameters describing the interactions - the singlet and
triplet scattering lengths, and the long range van der Waals coefficient - in
addition to known atomic properties. Without using any further details of the
interactions, our approach can accurately predict the locations of resonances.
It can also be used to find the singlet and triplet scattering lengths from
measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and
$^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental
results, and with the more computationally intensive coupled channels
technique.