For diatomic ions with large room-temperature recombination rates $\alpha$, the simple temperature dependence

$\alpha =CT_{\mathrm{el}}^{}{}_{}{}^{-\frac{1}{2}}[1-\exp (-\frac{h\nu }{k{T}_{\mathrm{ion}}}\left)\right]$

is derived, which reproduces closely the precise experiments of Cunningham and Hobson, and others as well. The derivation uses the electronic threshold law plus a rapid fall off of the cross sections with vibrational state $v$.

• Received 23 December 1968

DOI:https://doi.org/10.1103/PhysRev.185.101