demonstrating that for two open channels at CIR the inelastic process are enhanced prohibiting in this manner the transmission coefficient to be zero when more than one channel is involved.

![(Color online) (a) Transmission coefficient $T_{\text{CIR},i}^{(\ell)}$ at a CIR, i.e. the confinement induced unitarity bound, versus the scaled energy ${\epsilon}$ as well as the transmission coefficient $T_{\infty,i}^{(\ell)}$ taken for large scattering length $|\bar{a}_{\ell}|$, i.e. for scattering at the free-space unitarity bound. (b) Corresponding result for $\ell=1$. Note that the two curves rapidly converge, implying a far less pronounced CIR in terms of a transmission suppression than in the case of $\ell=0$. []{data-label="fig:transmission_bounds"}](figures/figure5.eps){width="45.00000%"}

The absence of a transmission blockade at a CIR in the case of more than one open channel, can be derived quantitatively from the formal limit $\alpha_{\ell}\rightarrow\infty$ taken in Eq. . This yields $$\boldsymbol f_{\textrm{CIR}}^{(\ell)}=-\frac{{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}}{{\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}},
  \label{eq:scattering_amplitude_CIR}$$ which generalizes the well known single mode result $f_{\textrm{CIR}}^{(\ell)}=-1$. It is remarkable that for the transversal ground state a non-trivial energy dependence is not present. We note that Eq. can, by virtue of [@hess2014], also be obtained by formally equating Eq. at a vanishing closed channel coupling, i.e. $\boldsymbol
f_{\textrm{CIR}}^{(\ell)}=\boldsymbol f_{\infty}^{(\ell)}|_{{\mathfrak{U}_{\ell\ell}}=0}$. Writing down the transmission coefficients for the scattering amplitude at a 