  Annihilation cross-section of ultra low-energy atomic antihydrogen ($%
E\le10^{-5}$ a.u.) on atomic hydrogen are calculated within a quantum
mechanical coupled channels approach. The results differ from the
extrapolations of semiclassical models to low energies. The main features of
the observables are found to be determined by a family of $H\bar{H}$
nearthreshold states.
