Abstract
We analytically derive the general pseudopotential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems using the frame work developed by Huang and Yang for three-dimensional scattering. We also analytically derive the low-energy dependence of the scattering phase shift for an arbitrary interaction with a power-law decaying tail, V2D (ρ) ρ-α (for α>2). We apply our results to the 2D dipolar gases (α=3) as an example, calculating the momentum and dipole moment dependences of the pseudopotential for both s - and p -wave scattering channels if the two scattering particles are in the same 2D layer. Results for the s -wave scattering between particles in two different (parallel) layers are also investigated. Our results can be directly applied to the systems of dipolar atoms and/or polar molecules in a general 2D geometry. © 2009 The American Physical Society.