Abstract
A computation of $^{87}\mathrm{\ensuremath{-}}^{87}$Rb spin-exchange rate constants as functions of the two-body singlet scattering length ${\mathrm{a}}_{\mathrm{s}}$ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for ${\mathrm{a}}_{\mathrm{s}}$. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the $^{87}\mathrm{Rb}$ singlet scattering length (74--102 a.u.).
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