Electron collisional excitation of interstellar molecular ions

Electron collisions may be significant in causing rotational transitions $$(J\rightarrow J\pm 1)$$ in interstellar molecular ions. Of the three approximations which have been used to calculate the corresponding cross-sections (Coulomb–Born, time-dependent perturbation theory, Glauber), the Glauber is shown to be unsatisfactory in the relevant energy range. A semi-empirical general formula is presented which enables the cross-sections to be evaluated simply and which has the correct threshold and high-energy forms. The resulting expression for the rate coefficient is considered to be sufficiently accurate for current astrophysical applications. Results are presented for the 0–1 transition in CH⁺, CO⁺, HCO⁺ and N₂ H⁺ ions.