Analytical treatment of bosonic d-wave scattering in isotropic harmonic waveguides

We analyze d-wave resonances in atom-atom scattering in the presence of harmonic confinement by employing a higher partial wave pseudopotential. Analytical results for the scattering amplitude and transmission are obtained and compared to corresponding numerical ones, which employ the Lennard-Jones potential. Qualitative agreement is observed for weak confinement. For strong confinement the pseudopotential does not capture the s- and d-wave interference phenomena yielding an asymmetric Fano profile for the transmission resonance.