Collisional Excitation Transfer ofS−PType Between Identical Atoms

Abstract

The electronic excitation transfer cross section between identical atoms in $S$ and $P$ states in the gas phase was investigated theoretically in the low-incident-energy range by means of the impact-parameter method. With respect to the $P$ states of an atom, all three degenerate $P$ states of mutually orthogonal polarizations were taken into account. The direction of $P$ polarization was taken into account using two different methods. These methods were the "fixed-atom approximation" and the "rotating-atom approximation," respectively. The difference between the solution from coupled equations with respect to the direction of $P$-state polarization and those from the respective approximations mentioned above was studied. The fixed-atom approximation was found to be better than the rotating-atom approximation for the computation of the over-all cross section of $S-P$-type excitation transfer. The cross section obtained from the coupled equations was nearly one-half of that from the rotating-atom approximation and nearly 1.5 times as much as that from the fixed-atom approximation. It is shown that the total cross section can be written as $\sigma =\frac{3.36\pi e^2{\mu }^2}{\hslash v}$, where $v$ represents the relative velocity of an incident atom, $e$ the electronic charge, and $\mu$ the transition dipole matrix element between the $S$ and $P$ states under consideration.