  We study collisions of para-H$_2$ with five rare gas atomic species (He, Ne,
Ar, Kr and Xe) over the range from 1 K to 1 $\mu$ K and evaluate the
feasibility of sympathetic cooling H$_2$ with ultracold ground state rare gas
atoms co-trapped within a deep optical trap. Collision cross-sections over this
large temperature range show that all of these species could be used to cool
H$_2$ to ultracold temperatures and that argon and helium are the most
promising species for future experiments.
