Collisions with charged particles, namely with electrons and heavier ions are not considered in the radiative-transfer calculations presented in this paper, but may play an important role in the excitation of the CH Λ-doublet, particularlyin regions with high electron fractions, 

$x_{\textrm{e}} = n_{\textrm{e}}/(n_{\textrm{H}}  2n_{\textrm{H}_{2}}) >10^{-5}$xe=ne/(nH+2nH2)>10−5
–10−4. Such high electron fractions are ubiquitous in the diffuse molecular clouds present along the lines of sight studied here and may even be prevalent in the clouds surrounding the observed HII regions themselves, making electrons an important collision partner at low gas temperatures T ≤ 100 K. Bouloy & Omont (1977, 1979) studied the impact of collisional excitation by electrons on Λ-doublet transitions with particular emphasis on the ground-state Λ-doublet transitions of OH. These authors compute the collisional rate coefficients for collisions with electrons, either using perturbation methods such as those used by Goss & Field (1968) or using the Born approximation, both of which yield comparable results. These authors concluded that collisions with electrons, while incapable of inducing level inversion in the ground-state lines of OH at 18 cm, are responsible for thermalising them. Bouloy et al. (1984) further studied the excitation conditions of the ground-state lines of CH, and model the excitation by considering the radiative and collisional (de-) excitation of CH with H, H2, and electrons. Their results once again point to the role played by the collisions with electrons in thermalising the CH lines rather than inverting them. However, the excitation temperature of OH is found to be a 1–2 K above TCMB as derived from the resolved optical spectra of the OH A − X band transitions (Felenbok & Roueff 1996) or when measured by comparing the emission and absorption profiles of the radio L-band transitions of OH (Liszt & Lucas 1996, and references therein). This implies that densities much higher than the critical density are needed for thermalisation, which might also be the case for CH. More recently, Goldsmith & Kauffmann (2017) examined the impact of electron excitation on high-dipole-moment molecules like HCN, HCO+, CS, and CN in various interstellar environments. As long-range forces dominate the collisional cross-sections for electron excitation, the cross-sections and, in turn, the collisional rate coefficients scale with the square of the electric dipole moment, μe. Hence, the electron collisional rate coefficients for CH with μe = 1.46 D (Phelps & Dalby 1966) are ≃ 25 % of those of HCN with μe = 2.985 D (Ebenstein & Muenter 1984). Scaling the value of the HCN–e− collisional rate coefficient at T ≤ 100 K from Faure et al. (2007), we find the CH–e− collisional rates to be of the order of ~ 2 × 10−5 cm3 s−1. From this we can compute the critical electron fractional abundance, x* (e−), which defines the fractional abundance of electrons required for the collisional rate coefficients with electrons to be the same as that with H2 such that x* (e−) = ncrit(e−)∕ncrit(H2). Under the validity of these assumptions, x*(e−) for CH is ~10−6, making CH likely to be affected by electron excitation. Therefore, a complete treatment of the radiative–collisional (de-)excitation of the CH ground state would still require the availability of accurate collisional rate coefficients for collisional excitation by electrons. However, to our knowledge, these are currently not available.
Citation: Goss & Field (1968)
Citation function: Uses