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

TL;DR

This paper provides an analytical framework for understanding bosonic d-wave scattering in isotropic harmonic waveguides, comparing pseudopotential results with numerical simulations, and highlighting limitations under strong confinement.

Contribution

It introduces an analytical approach using a higher partial wave pseudopotential to study d-wave resonances in harmonic waveguides, and compares it with numerical methods.

Findings

Analytical results align qualitatively with numerical simulations under weak confinement.

Pseudopotential fails to capture interference effects under strong confinement.

Transmission resonance exhibits an asymmetric Fano profile in strong confinement regimes.

Abstract

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.