Scattering and effective interactions of ultracold atoms with spin-orbit coupling

We derive an analytical expression for the scattering amplitude of two ultracold atoms of arbitrary spin and with general spin-orbit (SO) coupling, on the basis of our recent work (Phys. Rev. A \textbf{86}, 053608 (2012)). As an application, we demonstrate that SO coupling can induce scattering resonance in the case with finite scattering length. The same approach can be applied to calculate the two-body bound state of SO-coupled ultracold atoms. For the ultracold spin-1/2 fermi gases in three- or two- dimensional systems with SO coupling, we also obtain the renormalization relation of effective contact interaction with momentum cutoff, as well as the applicability of Huang-Yang pseudo-potential.