Dissociation of Hydrogen Molecules by Vibrational Excitation and Three-Body Recombination Coefficient

The recombination of two atoms in the presence of a third body is of importance in gas kinetics. The evaluation of its probability coefficient can be reduced to that of the reverse process, the dissociation of a molecule by collision, by means of the principle of detailed balance. Various mechanisms for dissociation are briefly discussed, and an attempt is made to estimate the general order of magnitude of the cross section for the excitation of a molecule into the vibrational continuum of its electronic ground state by carrying through a calculation for the dissociation of a hydrogen molecule by collision with an electron, proton, and hydrogen atom. The Born approximation is not satisfactory for the heavy particles at low energies, and a tentative method of correcting the cross section by means of the exact one-dimensional problem is given. The resulting value of the cross section for dissociation of a hydrogen molecule by a hydrogen atom is of the order ${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$ at low energies; the three-body recombination coefficient for the reverse process, namely, the recombination of two hydrogen atoms in the presence of a third, is ∼${10}^{-43\mathrm{}}$ ${\mathrm{cm}}^6$/sec, which is very much smaller than the experimental value.