either bosons or fermions, we obtain a special case of Eq. , given by $T_{{n{n^{\prime}}}}^{(\ell)}=|\delta_{nn^{\prime}}+f_{{n{n^{\prime}}}}^{(\ell)}|^2$, where the scattering amplitudes $f_{{n{n^{\prime}}}}^{(\ell)}$ are connected to the physical $K$ matrix, via $$\boldsymbol f^{(\ell)}=i\;{\mathbf{K}_{oo,\ell}^{1D,phys}} \left[\openone-i\;{\mathbf{K}_{oo,\ell}^{1D,phys}}\right]^{-1},
\label{eq:connection_f_kphys}$$ see also [@hess2014]. This relation in particular allows for a extension of previous studies on the CIRs in harmonic waveguides to distinguishable particles, as it is in detail discussed in Sec. \[sub:distinguishable\].

Results and Discussion {#sec:results_discussion}
======================

Universal Properties {#sub:universalities}
--------------------

We start our discussion of the universal properties for the (in)-elastic scattering in waveguides by considering the $\ell$-wave single partial wave approximation ([$\ell$-SPWA]{}). Since the main focus is the study of CIRs which typically occur in the vicinity of a free space resonance, the [$\ell$-SPWA]{} can safely be assumed to be accurate in the description of the scattering process. Recall that for the particular choice of a Lennard-Jones type 6-10 interatomic potential the background scattering length from higher lying partial waves ($\ell>1$) is negligible. The advantage of the [$\ell$-SPWA]{} is given by the fact, that (i) analytical results can be derived straightforwardly, see below and (ii) for certain energy regimes it serves as a good approximation for the coupled $\ell$-wave CIR [@giannakeas2012].

Employing thus the physical $K$ 