  Motivated by the recent progress in cooling and trapping polar molecules, we
present a simplified version of the rigorous contact pseudopotential for
anisotropically-interacting polarized particles [A. Derevianko, Phys. Rev. A
67, 033607 (2003); Phys. Rev. A 72, 039901(E) (2005)]. The simplifications are
carried out for a practically important case of harmonically confined particles
described by sufficiently smooth wavefunctions. The resulting contact
pseudo-potential depends on the K-matrix of the underlying scattering process
and is represented as a sum over pairs of partial waves coupled by the
collision. The contribution of each pair of the coupled waves (l and l')
involves a tensor product of derivatives of orders l and l'. The asymmetry in
the derivatives reflects the anisotropy of the original interaction potential:
there is a preferential appearance of the derivatives along the polarizing
field.
