Vibrational relaxation cross sections for an atom-molecule collision a
re calculated by explicit numerical solution of the coupled equations
of scattering theory and shown to follow an inverse velocity dependenc
e at very low initial kinetic energies of the incident atom, in accord
ance with Wigner's threshold law. Rate constants for H + H-2 (upsilon,
j = 0) --> H + H-2(upsilon') < upsilon, j = 0) are calculated for all
the vibrational levels of H-2 and found to vary by seven orders of ma
gnitude between the deepest level upsilon = 0 and the vibrational leve
l upsilon = 12. (C) 1997 Elsevier Science B.V.