  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, $V_{\rm
2D}(\rho)\propto \rho^{-\alpha}$ (for $\alpha>2$). We apply our results to the
2D dipolar gases ($\alpha=3$) as an example, calculating the momentum and
dipole moment 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.
