High-energy behaviour of the transition probabilities and total cross sections for charge exchange

Abstract

A second-order method for charge exchange is introduced. Using the impact-parameter method, a transition amplitude for the ground-state capture from atomic hydrogen by fast protons is obtained in closed analytical form. At vanishingly small impact parameters rho , the Brinkman-Kramers (BK) transition probability (behaving as nu -10 with increasing incident velocity nu ) is found, but reduced by the factor 0.2857. At large impact parameters, the dominant contribution arises from the second-order effects in the second-order in the electron-proton interaction. Total cross sections for the capture into 2s and 3s states of atomic hydrogen in H + +H(1s) collisions as well as for the capture summed over all final discrete states of H are in excellent agreement with experimental data.