Accounting the effects of electron re-scattering in the single-electron charge-exchange reaction


Purpose. In our work, the three-body Dodd-Greider integral equations have been reviewed by focusing on the correct Coulomb asymptotic forms of the wave functions for the problem of rearrangement scattering. On the basis of the Dodd-Greider integral equations with Coulomb interactions, the theory of one-electron capture in collisions of hydrogen-like atoms and positively charged ions with taken to account for electron rescattering effects are reviewed. Specifically, distorted wave theories for one-electron capture reactions in energetic collisions of hydrogen-like atoms with positive ions are recapitulated.
Methods. In particular, the reaction amplitude is highlighted as a first iteration term of the solution of the Dodd-Greider equations for the three-body scattering operator. It is emphasized that to reproduce the Thomas peak in the angular distribution of the reaction products, it is necessary to account for the effects of Coulomb re-scattering of the captured electron. In approximation of the “single-step” collision, this method reduces to the version of the well-known boundary-corrected first Born approximation, where the asymptotic behavior of the particles in the entrance and exit reaction channels is described by two-body Coulomb wave functions. The short-range interaction due to incomplete screening of the nucleus by atomic electrons is taken into account in the perturbing potential.
Results. This theory was applied to study the influence of Coulomb interactions in the final state on angular and energy distributions of the products of the charge-transfer reactions at intermediate collision energies. Due to the sufficiently complete allowance for the interaction after the collision and the fast convergence of the Dodd-Greider perturbation theory series, the proposed method provides good consistency with the experimental data.
Conclusions. An important feature of this method is a consistent preservation of the proper asymptotic limits of the wave functions of a colliding system in the entrance and exit reaction channels that takes into account the long-range nature of the Coulomb interactions

Keywords: eikonal approximation, Green's function, single-electron charge exchange, atom, ion