Atom-dimer and dimer-dimer scatterings in a spin-orbit-coupled Fermi gas

Using the diagrammatic approach, here we study how spin-orbit coupling (SOC) affects fermion-dimer and dimer-dimer scattering lengths in Born approximation, benchmark their accuracy with higher-order approximations. We consider both isotropic Rashba couplings three dimensions show that approximation gives accurate results $1/(m\ensuremath{\alpha}{a}_{s})\ensuremath{\ll}\ensuremath{-}1$ limit, where $m$ is mass of fermions, $\ensuremath{\alpha}$ strength SOC, ${a}_{s}$ $s$-wave length between fermions. This because higher-loop contributions form a perturbative series $1/(m\ensuremath{\alpha}{a}_{s})<0$ region controlled by smallness residue $Z$ dimer propagator. In sharp contrast, since grows square root binding energy $1/(m\ensuremath{\alpha}{a}_{s})>0$ region, all are similar order.