Single-electron capture from heliumlike atomic systems by bare projectiles is investigated by means of the four-body boundary-corrected first Born approximation (CB1-4B). The effect of the dynamic electron correlation is explicitly taken into account through the complete perturbation potential. The quantum-mechanical post and prior transition amplitudes for single charge exchange encompassing symmetric and/or asymmetric collisions are derived in terms of two-dimensional real integrals in the case of the prior form and five-dimensional quadratures for the post form. An illustrative computation is performed for single-electron capture from helium by protons and α particles at intermediate and high impact energies. The role of dynamic correlations is examined as a function of increased projectile energy. The validity and utility of the proposed CB1-4B method is critically assessed in comparison with the existing experimental data for total cross sections, and excellent agreement is obtained.

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State-selective and total single-electron capture cross sections in fast collisions of a bare projectile with a heliumlike target are examined in the four-body formalism. A special emphasis is given to a proper inclusion of dynamic electron-electron correlation effects. For this purpose, the post form of the four-body boundary-corrected first Born approximation (CB1-4B) is utilized. With regard to our related previous study, where the prior version has been considered, in the present work an extensive analytical study of the post-transition amplitude for electron capture into the arbitrary final states n f l f m f of the projectile is carried out. The post-transition amplitude for single charge exchange encompassing symmetric and asymmetric collisions is derived in terms of five-dimensional integrals over real variables. The dielectronic interaction V 12 = 1/r 12 ≡ 1/| r 1 − r 2 | explicitly appears in the perturbation potential V f of the post-transition probability amplitude T + if , such that the CB1-4B method can provide information about the relative significance of the dynamic interelectron correlation in the collisions under study. An illustrative computation is performed involving state-selective and total single capture cross sections for the p-He collisions at intermediate and high impact energies. The so-called post-prior discrepancy, which plagues almost all the existing distorted wave approximations, is presently shown to be practically nonexistent in the CB1-4B method. The validity of our findings is critically assessed in comparisons with the available experimental data for both state-selective and total cross sections summed over all the discrete energy levels of the hydrogenlike atom formed with the projectile. Overall, excellent performance of the CB1-4B method is recorded, thus robustly establishing this formalism as the leading first-order description of high-energy single charge exchange, which is a collision of paramount theoretical and practical importance across interdisciplinary fields ranging from astrophysics to medicine.

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Single charge exchange in collisions between bare projectiles and heliumlike atomic systems at intermediate and high incident energies is examined by using the four-body formalism of the first-and second-order theories. The main purpose of the present study is to investigate the relative importance of the intermediate ionization continua of the captured electron compared to the usual direct path of the single electron transfer from a target to a projectile. In order to achieve this goal, comprehensive comparisons are made between the four-body boundary-corrected continuum-intermediate-states (BCIS-4B) method and the four-body boundary-corrected first Born (CB1-4B) method. The perturbation potential is the same in the CB1-4B and BCIS-4B methods. Both methods satisfy the correct boundary conditions in the entrance and exit channels. However, unlike the CB1-4B method, the second-order BCIS-4B method takes into account the electronic Coulomb continuum-intermediate states in either the entrance or the exit channel depending on whether the post or the prior version of the transition amplitude is used. Hence, by comparing the results from these two theories, the relative importance of the intermediate ionization electronic continua can be assessed within the four-body formalism of scattering theory. The BCIS-4B method predicts the usual second-order effect through double scattering of the captured electron on two nuclei as a quantum-mechanical counterpart of the Thomas classical two-step, billiard-type collision. The physical mechanism for this effect in the BCIS-4B method is also comprised of two steps such that ionization occurs first. This is followed by capture of the electron by the projectile with both processes taking place on the energy shell. Moreover, the role of the second, noncaptured electron in a heliumlike target is revisited. To this end, the BCIS-4B method describes the effect of capture of one electron by the interaction of the projectile nucleus with the other electron via the static electron-electron correlations in the target. This effect yields a novelty seen as the second Thomas peak. As an illustration, detailed computations were carried out involving both the differential and total cross sections for one-electron capture in the p − He collisions at intermediate and high impact energies. The results obtained in the BCIS-4B method are compared with those from the CB1-4B method and with the available experimental data. The overall usefulness of the BCIS-4B method is assessed in predicting experimental data for four-body single charge exchange both qualitatively (shapes of cross sections) and quantitatively (numerical values from measurements).