  We show theoretically that ultracold hydrogen atoms have very favorable
properties for sympathetic cooling of molecules to microkelvin temperatures. We
calculate the potential energy surfaces for spin-polarized interactions of H
atoms with the prototype molecules NH(triplet-Sigma-) and OH(doublet-Pi) and
show that they are shallow (50 to 80 cm-1) and only weakly anisotropic. We
carry out quantum collision calculations on H+NH and H+OH and show that the
ratio of elastic to inelastic cross sections is high enough to allow
sympathetic cooling from temperatures well over 1 K for NH and around 250 mK
for OH.
