dimers. At a magnetic field of $730$ G, the $23$-dimer crosses the $12$-dimer and the relaxation channel into $12$-dimers opens up. As the crossing is approached from above, the rate vanishes as $\sqrt{a_1-a_3}$ in agreement with the analytical result from Sec. \[sec:relaxation\]. Between 790 and 810 G, the condition $a_1 \gg a_3$ with $a_2$ non-resonant is satisfied approximately. The rate into the shallow dimer in this region scales approximately as $a_3^2/a_1$ in agreement with the prediction of D’Incao and Esry [@DIncao:2009]. At $811$ G, the $23$-dimer disappears through the three-atom threshold and the relaxation rate vanishes.

Our results show two resonances at $B_*=672$ G and $B_*'\approx
597$ G. There is also a dramatic change in the relaxation rate at $730$ G because the relaxation channel into $12$-dimers opens and the corresponding rate into the $12$-dimer increases rapidly. Our results describe the resonances in the experimental data qualitatively. The second resonance has been measured at $B_{*}^{\rm exp}=685$ G in Ref. [@Lompe:2010; @Nakajima:2010]. This value is 13 G away from the theoretical prediction $B_*=672$ G. In terms of the scattering length, this corresponds to $a_{23}(B_{*}^{\rm exp})/a_{23}(B_{*})=1076/835\approx 1.3$, leading to a 30% shift in the resonance position. This shift is a factor three 