Taking the Coulomb effects into account in the reactions of one-electron charge exchange

Abstract

Within the framework of a single mathematical approach based on the first iteration of the Dodd–Greider equations, direct and two-step mechanisms of electron capture have been described, and their correlation with angular distributions of reaction products has been ascertained. The purpose of this modification of the Dodd–Greider integral equations for the quantum mechanical operator of three-particle scattering with rearrangement is to take into account the Coulomb asymptotic behavior of wave functions in the problem of inelastic scattering with redistribution. On this basis, the theory of the reaction of single-electron charge exchange was constructed when a collision of the hydrogen-like atom with a positively charged ion is performed, taking into account the effects of the multiple Coulomb scattering of the electron by the ion target residue. In particular, the amplitude of the reaction is distinguished as the first iterative term for solving the Dodd–Greider equations for the operator of three bodies, and the short-acting interaction that causes the electron transitions is taken into account in the distorting potential. It has been shown that in the one-fold scattering approximation, this method leads to the so-called first Coulomb–Born approximation, where the asymptotic behavior of particles in the input and output channels of the reaction is described by two-particle Coulomb wave functions. A more detailed study of the reaction of the resonance charge transfer between a proton and a hydrogen atom showed that without a correct inclusion of the Coulomb interaction into the wave function of the final state, recreating Thomas’ peak in the angular distributions of the products of this reaction cannot be. The proposed method provides a good agreement with the experimental data of both complete and differential cross-sections due to the advantages of this method, in particular, the full consideration of the interaction after the collision and rapid convergence of the series of the Dodd–Greider perturbation theory.