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A general treatment of ultracold two-body scattering in the presence ofisotropic spin-orbit coupling (SOC) is presented. Owing to the mixing ofdifferent partial wave channels, scattering with SOC is in general a coupledmultichannel problem. A systematic method is introduced to analytically solve aclass of coupled differential equations by recasting the coupled channelproblem as a simple eigenvalue problem. The exact Green's matrix in thepresence of SOC is found, which readily gives the scattering solutions for anytwo identical particles in any total angular momentum subspace havingnegligible center of mass momentum. Application of this formalism to two spin-1bosons shows the ubiquitous low energy threshold behavior for systems withisotropic SOC. A modified threshold behavior shows up, which does not occur forthe spin-orbit coupled spin-1/2 system. We also confirm the parity-breakingmechanism for the spontaneous emergency of handedness, that has been proposedby Duan et. al. [1]. Additionally, a two-body bound state is found for anyarbitrarily small and negative scattering length. Our study sheds light on thefew-body side of SOC physics and provides one step towards understandingultracold scattering in a non-Abelian gauge field.

General ultracold scattering formalism with isotropic spin orbit coupling