Multiple-Scattering Expansions for Nonrelativistic Three-Body Collision Problems. VI. Differential and Total Cross Section for Electron-Transfer Rearrangement Collisions

Abstract

Differential and total cross sections for electron-transfer rearrangement collisions are calculated in the first-order Faddeev-Watson multiple-scattering approximation for a number of three-body atomic systems. For the (${p}^{+}$, H) system, it is shown that the inclusion of the pure ${p}^{+}\ensuremath{-}{p}^{+}$ interaction to all orders (including the contributions coming from the on-shell Coulomb cuts) cancels only part of the effect given by the bare ${p}^{+}\ensuremath{-}{p}^{+}$ interaction so that the present electron-transfer cross section lies in between the Brinkman-Kramers and Jackson-Schiff cross sections and asymptotically approaches the Jackson-Schiff cross section from above in the high-energy limit (where the nonrelativistic approximation is no longer expected to be valid). The knock-out contributions to the electron-transfer amplitude at large angles are particularly important for the equal-mass resonant (${e}^{+}, {e}^{\ensuremath{-}}{e}^{+}$) electron-transfer collision. Owing to the ${e}^{+}\ensuremath{-}{e}^{+}$ knock-out contribution, the total (${e}^{+}, {e}^{\ensuremath{-}}{e}^{+}$) electron-transfer cross section exhibits an ${E}^{\ensuremath{-}3}$ energy dependence in the high-energy limit.