a Lennard-Jones 6-10 potential.

![(Color online) (a) Transmission coefficients ${T_{0}^{(0)}},{T_{1}^{(0)}},{T_{2}^{(0)}}$ versus the scaled $s$-wave scattering length ${\bar{a}_{0}}$, for the first, second and third open channel (solid, dashed and dotted lines), respectively, at energy $\Delta{\epsilon}=0.95$. Higher lying curves for a particular number of open channels correspond to a lower entrance channel. Panel (b) shows ${T_{0}^{(1)}},{T_{1}^{(1)}},{T_{2}^{(1)}}$ at $\Delta{\epsilon}=0.05$ for the case $\ell=1$.[]{data-label="fig:transmission_t123_boson_fermion"}](figures/figure1.eps){width="45.00000%"}

First we show a typical case of the transmission coefficients $T_n^{(\ell)}$ for $\ell=0,1$ versus the corresponding scaled scattering length $\bar{a}^{2\ell+1}_\ell$ in panels (a) and (b) of Fig.\[fig:transmission\_t123\_boson\_fermion\], respectively. In particular we observe the asymmetric line shape of the transmission spectra for $\ell=0$. The scaled energy above the corresponding channel threshold $\Delta\epsilon=0.95$ is chosen such that the CIRs, identified as the minima of the respective transmission coefficients are best pronounced, i.e. we aim at a large difference between the transmission values taken for large $|\bar{a}_0|$ and the specific value of $\bar{a}_0$ leading to a CIR. This relative difference maximizes especially at energies below every threshold which can be readily seen in panel (a) of Fig. \[fig:transmission\_bounds\], where the transmission coefficient values for $|\bar{a}_0|\to \infty$ ($T_{\infty,i}^{(0)}$ - black lines) and for $\bar{a}_0$ at a CIR ($T_{\rm{CIR},i}^{(0)}$ - red lines) are displayed. Furthermore, 