Intermediate ionization continua for double charge exchange at high impact energies

We investigate the problem of two-electron capture from heliumlike atomic systems by bare nuclei ZP+(ZT;e1,e2)i→(ZP;e1,e2)f+ZT at high incident energies, using the four-body formalism of the first- and second-order theories. Our goal is to establish the relative importance of the intermediate ionization continua of the two electrons in comparison with the usual direct path of the double electron transfer. For this purpose we presently introduce the boundary-corrected continuum-intermediate-state (BCIS) approximation, which preserves all the features of two-electron capture as a genuine four-body problem. The proposed second-order theory provides a fully adequate description of the fact that, in an intermediate stage of collision, both electrons move in the field of the two Coulomb centers. The previously devised boundary-corrected first Born (CB1) approximation can be obtained as a further simplification of the BCIS model if the invoked two-electron Coulomb waves are replaced by their long-range logarithmic phase factors defined in terms of the corresponding interaggregate separation R. The BCIS method is implemented on the symmetric resonant double charge exchange in collisions between α particles and He(1s2) at impact energies E≥900 keV. The obtained results for the differential and total cross sections are compared with the available experimental data and satisfactory agreement is recorded. As the incident energy increases, a dramatic improvement is obtained in going from the CB1 to the BCIS approximation, since the latter closely follows the measurement, whereas the former overestimates the observed total cross sections by two orders of magnitude