Low-energy scatterings and pseudopotential of polarized quadrupoles

We investigate the low-energy scattering properties of two identical particles interacting via the polarized quadrupolar interaction. It is shown that a series of $s$- and $p$-wave resonances appear for identical bosons and fermions, respectively, as the strength of the quadrupolar interaction increases. Interestingly, scattering resonances also appear on the generalized scattering length corresponding to the coupling between the $s$ and $d$ waves. This observation inspires us to propose a new pseudopotential for the quadupolar interaction. We also explore the bound-state properties of two particles in both free space and harmonic traps.