We analytically derive the general pseudo-potential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems, using the frame work developed by Huang and Yang for 3D scattering. We also analytically derive the low energy dependence of the scattering phase-shift for an arbitrary interaction with a power-law decaying tail, V_ 2D(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

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... t dependence of the pseudo-potential 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.