Ultracold Collision Properties of Metastable Alkaline-Earth Atoms

Ultracold collisions of spin-polarized ${}^{24}\mathrm{M}\mathrm{g}$, ${}^{40}\mathrm{C}\mathrm{a}$, and ${}^{88}\mathrm{S}\mathrm{r}$ in the metastable ${}^{3}P_2$ excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.