of the loss channel do not influence the loss rate as long as its threshold energy is far below the threshold energy of the entrance channel, so that the high energy limit can be applied. This observation motivates replacing the problem with the effective single-channel model with a complex potential [@Idziaszek2010], which gives the same results. Apart from the MQDT functions which depend on the energy, partial wave and the long-range potential, the only remaining parameters in our model are the coupling term $y$ and the phase shift $\xi$ introduced by the full interaction potential. This phase shift determines the background scattering length $a$, which we will express in units of the mean scattering length $\bar{a}$, defined as [@Gribakin1993] $$\bar{a}=\frac{\pi(n-2)^{(n-4)/(n-2)}}{\Gamma^2\left(\frac{1}{n-2}\right)}R_n.$$

Low energy limits
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MQDT functions
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We calculated analytically the threshold behavior of MQDT functions directly from their definitions for arbitrary $1/r^n$ potential, extending the previous results derived for $n=6$ [@Mies2000] and $n=4$ [@NJP2011]. For $s$-wave scattering ($\ell=0$) we obtain $$C^{-2}(E,\ell=0)\stackrel{E\to 0}{\longrightarrow} k\bar{a}\left(1+(s-\nu)^2\right),$$ $$\tan\lambda(E,\ell=0)\stackrel{E\to 0}{\longrightarrow} \nu-s,$$ and by definition $\tan\xi\to-k\bar{a}s$, where $s=a/\bar{a}$ and $\nu=\cot\frac{\pi}{n-2}$. Results for the $p$-wave ($\ell=1$), relevant for scattering of ultracold fermions, read $$C^{-2}(E,\ell=1)\stackrel{E\to 0}{\longrightarrow} k^3 \overline{V} \frac{(1 + (s - \nu)^2) (1 + \nu^2)}{(s - 