  We present an analytic description of ultracold collision between two
spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling of the Rashba
type. We show that regardless of how weak the spin-orbit coupling may be, the
ultracold collision at sufficiently low energies is significantly modified,
including the ubiquitous Wigner threshold behavior. We further show that the
particles are preferably scattered into the lower-energy helicity state due to
the break of parity conservation, thus establishing interaction with spin-orbit
coupling as one mechanism for the spontaneous emergence of handedness.
