Feshbach resonances in the presence of inelastic scattering: threshold behavior and suppression of poles in scattering lengths

In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross sections. However, inelastic scattering removes the poles. Even for quite weak inelastic scattering the peaks in cross sections are dramatically suppressed. A resonant scattering length is defined to characterize the strength of the resonance, and is shown to be small for most collisions of ultracold molecules. The results suggest that cross sections for ultracold molecular inelastic collisions are much less sensitive to details of the potential than has been believed.