Simple analytical model for high-partial-wave ultracold molecular collisions

The investigation of ultracold atomic or molecular collision is important for us to understand the essence of a chemical reaction. We present a simple analytical model of arbitrary-order partial-wave scatterings for ultracold molecular collision in the threshold regime. The threshold formulas of the transmission and reflection coefficients are given. For high-partial-wave collision, shape resonance will take place because of the existence of a centrifugal barrier. We investigate the effect of shape resonance and short-range interaction on molecular collisions. Moreover, we find a method to fit the loss parameter from the experimental data of ultracold bosonic molecular collision. As an applied example, we calculate the thermally average loss rate for the ultracold ⁸⁷Rb¹³³Cs+⁸⁷Rb¹³³Cs collision, our results are consistent with the recent experimental and theoretical results of Gregory et al. [Nat. Commun. 10, 3104 (2019), 10.1038/s41467-019-11033-y].