Dimer-atom scattering between two identical fermions and a third particle

TL;DR

This paper employs a diagrammatic T-matrix approach to analyze three-body scattering involving two identical fermions and a third particle, calculating dimer-atom scattering lengths across all mass ratios and exploring the effects of mass ratio variations.

Contribution

It provides exact dimer-atom scattering lengths for all mass ratios and reveals how the T-matrix behavior changes with increasing mass ratio, including sign changes and Efimov states.

Findings

Exact dimer-atom scattering lengths for all mass ratios.

T-matrix changes sign and becomes negative at large momenta for high mass ratios.

Multiple sign changes in T-matrix related to Efimov states.

Abstract

We use the diagrammatic $T$-matrix approach to analyze the three-body scattering problem between two identical fermions and a third particle (which could be a different species of fermion or a boson). We calculate the s-wave dimer-atom scattering length for all mass ratios, and our results exactly match the results of Petrov. In particular, we list the exact dimer-atom scattering lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In addition, unlike that of the equal-mass particles case where the three-body scattering $T$-matrix decays monotonically as a function of the outgoing momentum, we show that, after an initial rapid drop, this function changes sign and becomes negative at large momenta and then decays slowly to zero when the mass ratio of the fermions to the third particle is higher than a critical value (around 6.5). As the mass ratio gets higher, modulations of the $T$-matrix become more apparent with multiple sign changes, related to the "fall of a particle to the center" phenomenon and to the emergence of three-body Efimov bound states.