Boundary-corrected four-body continuum-intermediate-state method: Single-electron capture from heliumlike atomic systems by fast nuclei

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).