Transport Cross Sections and Collisional Energy Relaxation of Superthermal O(3P) Atoms in N2 for Planetary Aeronomy

Abstract

Abstract Superthermal (“hot”) oxygen atoms deposit their energy in planetary upper atmospheres and in hypersonic shock layers through collisions with N2, but the rate at which they do so is set not by the magnitude of the collision cross section, which is dominated by forward diffraction, but by transport-weighted moments of the differential cross section (DCS). We derive momentum-transfer and viscosity cross sections, mean collisional deflections, and energy-relaxation rates for O(3P) + N2 from our previously reported quantum coupled-channel DCSs, for 16O, 17O, and 18O over collision energies 0.31–4.0 eV. The momentum-transfer cross section is well represented by σm = 9.90 × 10–16Ek–0.385 cm2 (Ek in eV), a factor of 28–32 below the collision cross section, with mean deflection ⟨1 – cos θ⟩ = 0.031–0.036. Rotationally inelastic channels supply 72–88% of it, so transport treatments built on elastic angular distributions underestimate the stopping power of N2 several-fold. The heavy-isotope enhancement of the integral elastic cross section (1–5%) does not survive transport weighting. σm is isotope-independent to within 0.4% above 0.6 eV, because the enhancement resides in the transport-inert forward cone, so isotopic effects in thermalization are kinematic (+2.9% recoil per collision for 18O relative to 16O). The mean energy loss per collision rises from 10 to 68 meV, and Monte Carlo slowing down gives ≈120 collisions and a stopping column of 3.7 × 1015 cm–2 to thermalize a nascent 3.48 eV atom in pure N2, some 20 times the isotropic hard-sphere estimate. A loss law that satisfies detailed balance in a 460 K bath raises the number of collisions by 6.5%. Comparing the isotopes at equal velocity instead of equal energy shifts σm by 1.5–2.8%, and this shift is purely kinematic.