The recombination of two hydrogen atoms in the presence of a third in a thermal collision is considered, the principle of detailed balance being used to obtain the three-body coefficient $C_3$ from the cross section ${\sigma }_2$ of the reverse, dissociation process. This cross section is calculated by a method developed previously which depends on correcting the Born approximation by means of the exact one-dimensional problem. We consider the case when the molecule is formed in a highly excited vibrational state of the electronic ground state and the excess energy of several $\mathrm{kT}$ goes into translational energy of the third atom. The three-body coefficient in this case is of order 3×${10}^{-36\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$, which is still much smaller than the empirical values. Some estimate is made of the validity of the correction method.

The excitation and de-excitation of the first vibrational state of hydrogen by collisions with protons is investigated, and it is found that an excited molecule requires ${10}^3$ to ${10}^4$ thermal collisions to lose its excitation; this is roughly of the correct order of magnitude for such processes.

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