Complex scattering length trends for rotationally-excited molecules in ultracold collisions with He

The study of atom-molecule collisions in the ultracold regime has attracted substantial attention in recent years with an interdisciplinary impact on physics, chemistry, and quantum computation. These two-body collisions are governed by $s$-wave scattering with inelastic quenching processes becoming important for high internal excitation. In this work, quantum close-coupling scattering calculations are performed for rotationally-excited linear molecules (H$_2$, HD, CO, O$_2$, and CO$_2$) and non-linear molecules (H$_2$O, NH$_3$, and CH$_4$) due to collisions with He. The results are given in terms of the ratio of the imaginary part of the scattering length $\beta$ to the real part $\alpha$ which give measures of inelastic and elastic probabilities, respectively. For linear molecules, the ratio $\beta / \alpha$ generally increases with decreasing rotational constant. Conversely, $\beta /\alpha \sim 0.1$ for all of the considered non-linear molecules, nearly independent of rotational excitation. Such a large ratio, indicating significant quenching, suggests that these non-linear molecules would not be good candidates for cooling and trapping experiments.