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