Unified treatment of resonant and non-resonant mechanisms in dissociative recombination: benchmark study of CH$^+$

TL;DR

This work introduces a unified MQDT-based framework for dissociative recombination that treats direct and indirect mechanisms on equal footing by performing fixed-$R$ electron-scattering calculations and then applying rovibronic frame transformations to obtain a fully rovibronic S-matrix. It avoids the need to compute bound dissociative states of the neutral molecule, instead generating vibrational continua with a complex absorbing potential and mapping to the CH$^+$ rovibronic channel space, including rotational structure. The CH$^+$ DR cross section calculated with this approach agrees with state-resolved CSR measurements, reproducing both the magnitude and resonance structure, and demonstrates the method's applicability to open-shell diatomic ions. The study highlights practical improvements over previous methods and outlines paths to further enhance accuracy, such as incorporating energy-dependent scattering matrices and long-range coupling effects, with broad significance for plasma modelling and astrochemistry.

Abstract

The theoretical approach developed here treats uniformly the direct and indirect mechanisms of dissociative recombination (DR) in a diatomic ion. The present theory is based on electron scattering calculations performed at several internuclear distances in the molecule. It is easy to implement becaus there is no need to separately evaluate couplings and the bound dissociative states of the neutral molecule. The theory can be applied to molecular ions with or without electronic resonances at low energies. The approach is applied to compute the DR cross section in electron-CH$^+$ collisions. The computed cross section agrees generally well with recent state-resolved data from a cryogenic storage-ring experiment, which validates the approach.

Figures (4)

• Figure 1: Lowest potential energy curves of the CH$^+$ ion. The dashed line shows the wave function of one of the dissociative vibrational states, obtained with the CAP.
• Figure 2: Elements of the K-matrix and scattering-phase matrix as functions of the internuclear distance. The notation for each coupling's partial waves is of the form $l'\lambda'\sim l\lambda$. The plotted matrix elements labeled in (b) describe couplings between channels in the same electronic target state in the C$_{\infty v}$ point group.
• Figure 3: Comparison of the DR cross section obtained in the present study with the recent CSR experiment data paul_CHp. Three thin solid lines of different color represent cross sections for the CH$^+$ being in the ground vibronic state X$^1\Sigma^+$($v=0$) in three different rotational states $j=0,1,2$. The thick solid line represents the $j=0$ theoretical cross section, accounting for uncertainties in collision energy distribution in the experiment. The experimental cross section, obtained for $v=0,j=0$, is shown with circles.
• Figure 4: "Reduced" cross section, $E_\text{el}\sigma(E_\text{el})$. The present theoretical data are shown with the solid (black) line. The experimental data are shown with circles paul_CHp, triangles amitay1996dissociative, squares mul1981. The previous theoretical data are shown by dashed (magenta) chakrabarti2018dissociative, dot-dashed (green) carata2000core, double-dot-dashed (red) takagi1991dissociative, and dot-double-dashed (indigo) mezei2019dissociative lines.