RELAXATION DYNAMICS OF HOT PROTONS IN A THERMAL BATH OF ATOMIC-HYDROGEN

We present a rigorous kinetic theory formulation of the relaxation of hot protons (H+) in a bath of thermal atomic hydrogen (H). We apply th e (well-known) quantum-mechanical scattering theory to (H+,H) collisio ns and calculate the differential elastic cross section as a function of collision energy and scattering angle. This calculation includes th e effects Of both direct and charge-exchange scattering. We then solve the time-dependent Boltzmann equation numerically for the H+ distribu tion function with an initial delta-function distribution. We also con sider two approximate models for the collision dynamics, each based on the assumption that charge exchange dominates the relaxation and that no momentum is transferred in a collision (the linear-trajectory appr oximation). The first model uses the Rapp-Francis [J. Chem. Phys. 37, 2631 (1962)] energy-dependent cross section in the exact kernel which defines the Boltzmann collision operator. The second model uses a hard -sphere cross section in an approximate collision kernel. We compare t he relaxation behavior calculated with the approximate formulations wi th the exact solution. We also calculate the mobility of H+ in H and c ompare the exact and-approximate; formulations. This study has applica tions to processes in astrophysics and aeronomy such as the non-therma l escape of H from planetary atmospheres.