Capture of Electrons by Molecular Ions

The (unimolecular) capture of thermal electrons by diatomic molecular ions through excitation of rotation is considered. Using an approximate form of the Coulomb wave functions, first-order theory, and a point-quadrupole perturbation the cross section for capture of an electron with energy $\frac{{\hslash }^2{k}^2}{2m}$ into a bound state $n$ ($E_n=-\frac{R_y}{n^2}$) is found to be $\frac{2{\pi }^3{Q}^2{E}_n\delta \mathrm{}(E+|\mathrm{}{E}_n|+E_J-E_{J+2\mathrm{}})}{25{k,}^2}$ where $Q$ is the quadrupole moment in units of $e{a_0}^2$, and where $E_J$ and $E_{J+2\mathrm{}}$ are the initial and final rotational energies. The rate of capture of electrons in an ionized gas where $T_e=T_r=300\mathrm{}°$K is thus of the order ${10}^{-8\mathrm{}}$-${10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$/sec. These captures take place into states of very high $n$ which will come into equilibrium (through this and other processes) with the free electrons. It is not expected that these captures will make a significant contribution to the recombination rate but they may help to account for molecular spectra in recombining gases and enhanced rotational temperatures.