Green's functions method  in the reactions of a single-electron charge-exchange


Purpose. Currently there is no unified theory of electron capture, describing all the variety of the single-electron capture processes. Our work is devoted to the theoretical study of the single-electron charge exchange process during collisions of multiply charged ions with atoms or molecules of the target.
Methods. To describe the single-electron charge exchange process we use semiclassical eikonal approximation, which takes into account the screening of the core of the incident multi-charged ion. Potential of the field affecting the transiting electron by the nucleus and the core of the incident multiply charged ion is selected as shielded Coulomb potential. The analytical expressions for the probability and electron capture cross sections from K-shell of a hydrogen atom in an arbitrary n'-shell of the bare and screened incident ion were obtained. The summation of the spectrum of degenerate finite states is carried out using the technique of the Coulomb Green's function.
Results. We explored the influence of the shielding effects of the incident ion by its own electrons on the cross section of single-electron capture in fast ion-atomic colli-sions. The effects of shielding of the incident ion affect both the value of cross-sections, and the nature of their dependence on the collision energy. Systematic calculations of the charge exchange cross sections for hydrogen atoms on Cq+, Nq+, Oq+ ions (q=1, 2, 3) have been performed, and their comparison with experimental data has been carried out.
Conclusions. We note that the method of summation of probabilities and charge-exchange cross-section presented here is transferable directly, or simply be generalizable to other first order approximations of perturbation theory. The results obtained here can serve as a starting point in this case. This circumstance opens the possibility for the formulation of a wide range of models, underlying the practical calculations of charge-exchange cross-section in high-energy ion-atomic collisions

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