CIR, or, equivalently considering $T_{\textrm{CIR},n}^{(\ell)}=\lim_{\alpha_{\ell}\rightarrow\infty}T^{(\ell)}_n$, yields $$T_{\textrm{CIR},n}^{(\ell)}=1-\frac{({\mathbf{F}_{\ell\ell}^{\mathbf{o}}})_{nn}}{{\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}}.
\label{eq:transmission_CIR}$$ This expression in particular contains the previous statement that a CIR for a single open channel has $T^{(\ell)}_0=0$.

In the [$\ell$-SPWA]{} the smallest value the transmission coefficient can take as a function of the energy is determined by Eq. , which serves as a lower bound for the transmission coefficient. This lower bound is compared to the value of the transmission coefficient for infinite scattering length in Fig. \[fig:transmission\_bounds\]. The channel of incidence varies within the first few transversal modes, i.e. $0\le i \le 4$. As it can be easily deduced from Eq. all quasi 1D unitarity bounds tend to unity irrespective of the partial wave $\ell$ under consideration. This makes the CIR being less pronounced for increasing energies (excited channels) with respect to the corresponding suppression of the transmission. The difference between the transmission for infinite scattering length and at a CIR is largest close to the channel thresholds for $\ell=0$. Remarkably, this difference $T_{\textrm{CIR},i}^{(1)}-T_{\infty,i}^{(1)}$ for $l=1$ happens to vanish as soon as the channel threshold to the first excited mode is exceeded. This also explains the rather symmetric line shapes observed in panel (b) of Fig. \[fig:transmission\_t123\_boson\_fermion\] for $n_o\ge 2$.

