[@Lompe:2010] compared to the value from recombination data is not understood. However, we note that a similar discrepancy between the values of $\eta_*$ from atom-dimer relaxation and three-body recombination occurs in the bosonic system of $^{133}$Cs atoms [@Knoop:2008; @Helfrich:2009uy].

Nakajima [*et al.*]{} [@Nakajima:2010] performed a numerical analysis for $\beta_1$ based on the universal theory and on a two-channel model. Their results obtained with the universal theory agree with our calculation. Within the two-channel model they derived energy-dependent scattering lengths which introduce non-universal effects in the two-body amplitudes. Because this model cannot resolve the discrepancy between the universal results and the measurements they concluded that the three-body parameters $\Lambda$ and $\eta_*$ depend on the magnetic field.

![(Color online) The relaxation rate constant for the 13-dimer and atom 2 as a function of the magnetic field $B$. The squares are data points from Ref. [@Lompe:2010]. The curves are our results for the total rate $\beta_2$ (solid line) and the partial rates into an atom 3 and a 12-dimer $\beta^{\rm sh}_{2\to 3}$ (dashed line), into an atom 1 and a 23-dimer $\beta^{\rm sh}_{2\to 1}$ (dashed-dotted line), and into an atom and a deep dimer $\beta^{\rm deep}_2$ (dotted line). The light solid line gives 