Kinetic rate coefficients for electron-driven collisions with CH$^+$: dissociative recombination and rovibronic excitation

TL;DR

This work delivers state-resolved rate coefficients for CH+ electron collisions covering dissociative recombination and rovibronic excitation, derived with a unified quantum-mechanical framework that fuses R-matrix electron scattering, rovibrational frame transformation, and MQDT. The approach extends prior DR methodology to excitation processes, including a Hermitian vibrational Hamiltonian and a Coulomb-Born correction scheme to handle long-range dipole coupling, enabling accurate cross sections and Maxwellian-averaged rate coefficients from 1 K to 10,000 K. Comparisons with Cryogenic Storage Ring data and prior theory show improved agreement for DR, VE within the ground electronic state, and RE, with some discrepancies in vibronic transitions to excited electronic states attributed to channel treatment. The results furnish reliable collision data for astrophysical interpretation and plasma modeling of hydrocarbons, and they provide a benchmark for theoretical methods on complex molecular ions like CH+.

Abstract

Cross sections and rate coefficients for rovibronic excitation of the CH$^+$ ion by electron impact and dissociative recombination of CH$^+$ with electrons are evaluated using a theoretical approach combining an R-matrix method and molecular quantum defect theory. The method has been developed and tested, comparing the theoretical results with the data from the recent Cryogenic Storage Ring experiment. The obtained cross sections and rate coefficients evaluated for temperatures from 1~K to 10,000~K could be used for plasma modeling in interpretation of astrophysical observations and also in technological applications where molecular hydrocarbon plasma is present.

Figures (7)

• Figure 1: State-selected DR cross sections from the ground vibronic state of CH+. The solid line was obtained with (\ref{['eqn:kinetic_rate_select']}) using the theoretical DR cross sections obtained with the current method forer2023unified. The dashed line with an error-curve represents recent experimental data paul2022experimental. The dot-dashed line represents previous calculations mezei2019dissociative.
• Figure 2: State-selected kinetic VE rate coefficients within the ground electronic state of CH+. Solid lines represent rate coefficients from the present calculations, dashed lines are taken from a previous calculation jiang2019cross. The cross sections are obtained according to (\ref{['eqn:XS_norot']}) and the kinetic rates are obtained according to (\ref{['eqn:kinetic_rate_select']}).
• Figure 3: State-selected kinetic VE rate coefficients from the ground electronic state of CH+ to the first excited state of CH+. Solid lines represent rate coefficients from the present calculations, dashed lines are taken from a previous calculation jiang2019cross. The cross sections are obtained according to (\ref{['eqn:XS_norot']}) and the kinetic rates are obtained according to (\ref{['eqn:kinetic_rate_select']}).
• Figure 4: Rotational excitation cross sections within the ground vibronic state of CH+. The cross sections are obtained according to (\ref{['eqn:XS_rot']}), and convolved with a Gaussian as per (\ref{['eqn:convolution_gauss_numerical']}) with $\gamma=1$ meV (thin lines) and $\gamma=5$meV (thick lines).
• Figure 5: Comparison of cross sections for rotational excitation $j=0 \to j'=1$ obtained using the R-matrix approach with $s$, $p$, and $d$ partial waves ($\sigma^\text{R-mat}$) and the closed-form total Coulomb-Born approximation ($\sigma^{TCB}$). The figure shows also the partial Coulomb-Born cross section obtained with $s$, $p$, and $d$ partial waves ($\sigma^\text{PCB}$) and the cross section where the R matrix data is combined with the total Coulomb-Born cross section accounting for partial wave with $l>2$ ($\sigma^\text{RVE}$).