  Compared to purely atomic collisions, ultracold collisions involving
molecules have the potential to support a much larger number of Fano-Feshbach
resonances due to the huge amount of ro-vibrational states available. In order
to handle such ultracold atom-molecule collisions, we formulate a theory that
incorporates the ro-vibrational Fano-Feshbach resonances in a statistical
manner while treating the physics of the long-range scattering, which is
sensitive to such things as hyperfine states, collision energy and any applied
electromagnetic fields, exactly within multichannel quantum defect theory.
Uniting these two techniques, we can assess the influence of highly resonant
scattering in the threshold regime, and in particular its dependence on the
hyperfine state selected for the collision. This allows us to explore the onset
of Ericson fluctuations in the regime of overlapping resonances, which are
well-known in nuclear physics but completely unexplored in the ultracold
domain.
