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Motivated by the recent progress in cooling and trapping polar molecules, wepresent a simplified version of the rigorous contact pseudopotential foranisotropically-interacting polarized particles [A. Derevianko, Phys. Rev. A67, 033607 (2003); Phys. Rev. A 72, 039901(E) (2005)]. The simplifications arecarried out for a practically important case of harmonically confined particlesdescribed by sufficiently smooth wavefunctions. The resulting contactpseudo-potential depends on the K-matrix of the underlying scattering processand is represented as a sum over pairs of partial waves coupled by thecollision. 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 inthe derivatives reflects the anisotropy of the original interaction potential:there is a preferential appearance of the derivatives along the polarizingfield.

Simplified contact pseudopotential for anisotropic interactions of polarized particles under harmonic confinement