Electron-impact excitation of molecular ions

A simple expression is derived that relates the rate coefficient for dipole-allowed electron-impact excitation of a molecular ion in the Coulomb-Born approximation to the Einstein A coefficient for the corresponding radiative decay. Results are given for several molecular ions of astrophysical interest. A general analytic expression is obtained for the equilibrium rotational level populations in the ground vibrational state of any molecular ion excited by collisions with electrons. The expression depends only upon the electron temperature, the electron density, and the rotational constant of the molecular ion. A similar expression is obtained for neutral polar molecules.