New Fit for the O+-O Collision Frequency Including Fine Structure Effects

A new fit is presented for the oxygen ion-neutral collision frequency ${\nu }_{\text{in}}$. The fit explicitly depends on the neutral temperature $T_n$, which characterizes the thermal distribution of fine structure levels of O(³$P_J,J=0$,1,2), and the reduced temperature $T_r=\frac{1}{2}\left(T_n+T_i\right)$, where $T_i$ is the ion temperature. A physically realistic fitting function adapted from the exact solution of a two-state system is constrained to approach plausible analytic models in the limits that $T_r$ is high (Dalgarno's model, $T_r\gtrsim 500K$) or $T_r$ is low (Langevin's model, $T_r\lesssim 20$–50 K). The target data for the fit are determined from the cross sections calculated by Hickman et al. (1997, https://doi.org/10.1103/PhysRevA.56.4633) and their extrapolations to lower and higher energies using the Langevin and Dalgarno models. The fit reproduces the target data within 1% for any $T_n$ and for any $T_r$ in the range $40K\lesssim T_r\lesssim 10000K$. The values of the fitting parameters suggest that the fine structure effect is more important than the effect of the long range ion-quadrupole and polarization potentials for $T_r\lesssim 500$ K. A relationship is derived between the parameters of the Dalgarno model and the exponent $\lambda$ of the power law dependence (${\nu }_{\text{in}}\propto T_r^{\lambda }$) at high $T_r$.