Can a simple model describe the collisions in Erbium spin mixtures?

The collisional properties of lanthanides exhibit remarkable complexity due to their strong long-ranged dipole-dipole interactions, anisotropic short-ranged interactions and complex magnetic structure, leading to an extraordinarily dense Feshbach spectrum showing signs of quantum chaos. Nevertheless, certain qualitative features of two-body collisions recently observed in spin mixtures of bosonic Erbium can be reproduced by a simple phenomenological multichannel square-well model. Unlike Feshbach resonances observed in collisions of alkali atoms, the resonance profiles observed in spin-resolved atom loss measurements exhibit a pronounced Fano asymmetry that is a result of interference between two collision pathways.  We identify a sequence of resonances that we believe to be caused by a single molecular state. Five independent model parameters are tuned to reproduce a single resonance and the resulting model is used to quantitatively predict the atom-loss profiles for six other resonances in different spin states.  We discuss the Fano asymmetry in the atom-loss profiles, as well as the observed exponential scaling of the resonance widths with respect to increasing (less negative) values of the magnetic quantum number.