Quantum scattering of hot H/D on CO$_2$: Cross sections and rate coefficients for planetary atmospheres and their evolution

TL;DR

This study provides precise quantum mechanical calculations of H/D--CO$_2$ collision cross sections and rate coefficients, revealing significant deviations from previous assumptions, which impact models of planetary atmospheres and their evolution.

Contribution

It offers the first detailed quantum scattering data for H/D--CO$_2$ collisions, improving accuracy over empirical and scaled estimates used in atmospheric modeling.

Findings

Scattering is strongly forward-peaked, reducing momentum transfer cross sections.

Mass-scaling overestimates cross sections by factors of 30--45.

Isotopic differences up to 35\% affect D/H fractionation models.

Abstract

Collisions between hot hydrogen atoms and CO$_2$ play a central role in energy transfer and atmospheric escape in CO$_2$-rich planetary atmospheres. We present quantum mechanical $j_z$-conserving coupled-states calculations of state-resolved cross sections for H/D--CO$_2$ collisions at energies up to 5~eV, benchmarked to within 7\% of close-coupling results. Scattering is strongly forward-peaked, yielding momentum-transfer cross sections substantially smaller than commonly assumed: mass-scaling from O/C--CO$_2$ systems overestimates H--CO$_2$ total cross sections by factors of 30--45, while existing empirical fits underestimate the low-energy regime by up to $\sim$45\%. Isotopic substitution (H/D) produces energy-dependent differences of up to 35\% at $E<0.1$~eV, invalidating uniform scaling approaches for D/H fractionation. Maxwellian-averaged rate coefficients derived from our cross sections are significantly smaller than mass-scaled values, implying reduced H--CO$_2$ energy transfer efficiency. In atmospheric escape modelling, these revisions can shift Martian exobase altitudes by 10--20~km, leading to order-unity changes in thermal escape rates, and have implications for hydrogen loss in early CO$_2$-dominated planetary atmospheres. Our results provide essential quantum-mechanical inputs for revisiting atmospheric evolution scenarios on Mars, early Earth, and CO$_2$-rich exoplanets.