Quantum scattering cross sections of O($^3P$) + N$_2$ collisions for planetary aeronomy

Abstract: "Hot atoms", which are atoms in their excited states, transfer their energy to the surrounding atmosphere through collisions. This process of energy transfer is known as thermalization, and it plays a crucial role in various astrophysical and atmospheric processes. Thermalization of hot atoms is mainly governed by the amount of species present in the surrounding atmosphere and the collision cross-section between the hot atoms and surrounding species. In this work, we investigated the elastic and inelastic collisions between hot oxygen atoms and neutral N$_2$ molecules, relevant to oxygen gas escape from the martian atmosphere and for characterizing the chemical reactions in hypersonic flows. We conducted a series of quantum scattering calculations between various isotopes of O($^3P$) atoms and N$_2$ molecules across a range of collision energies (0.3 to 4 eV), and computed both their differential and collision cross-sections using quantum time$-$independent coupled-channel approach. Our differential cross-section results indicate a strong preference for forward scattering over sideways or backward scattering, and this anisotropy in scattering is further pronounced at higher collision energies. By comparing the cross-sections of three oxygen isotopes, we find that the heavier isotopes consistently have larger collision cross-sections than the lighter isotopes over the entire collision energy range examined. However, for all the isotopes, the variation of collision cross-section with respect to collision energy is the same. As a whole, the present study contributes to a better understanding of the energy distribution and thermalization processes of hot atoms within atmospheric environments. Specifically, the cross$-$sectional data presented in this work is directly useful in improving the accuracy of energy relaxation modeling of O and N$_2$ collisions over Mars and Venus atmospheres.