  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.
