  We derive a pseudopotential in two dimensions (2D) with the presence of a 2D
Rashba spin-orbit-coupling (SOC), following the same spirit of frame
transformation in {[}Phys. Rev. A 95, 020702(R) (2017){]}. The frame
transformation correctly describes the non-trivial phase accumulation and
partial wave couplings due to the presence of SOC and gives rise to a different
pseudopotential than the free-space one, even when the length scale of SOC is
significantly larger than the two-body potential range. As an application, we
apply our pseudopotential with the Lippmann-Schwinger equation to obtain an
analytical scattering matrix. To demonstrate the validity, we compare our
results with a numerical scattering calculation of finite-range potential and
show perfect agreement over a wide range of scattering energy and SOC strength.
Our results also indicate that the differences between our pseudopotential and
the original free-space pseudopotential are essential to reproduce scattering
observables correctly.
