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

Pseudopotentials for Two-dimentional Ultracold Scattering in the Presence of Synthetic Spin-orbit-coupling