Comparative theoretical study of (e, 3e) on helium: Coulomb-waves versus close-coupling approach

Abstract

We discuss common features and differences in the fully differential cross sections (FDCS) for the electron-impact double ionization of He evaluated using the convergent close-coupling (CCC) method and various methods that utilize the three-body Coulomb wavefunctions (3C and C4FS). The calculations are restricted to the first Born approximation with respect to the interaction of the fast projectile with the target. In contrast to the similar (γ , 2e) reactions, where predictions of all the above theories qualitatively agree, there is a systematic difference between the FDCS calculated in the CCC and the 3C-type theories which is amplified as the momentum transfer from the projectile to the target increases. We argue that this fact is an indication that the P partial wave of a two-electron final state wavefunction is well described by the 3C model, but higher partial waves are poorly treated.

Second-order Born model for two-electron atomic ionization by fast charged-particle impact

“…In the CCC implementation of the first Born model, the binary peak is somewhat larger than the recoil one. It is just the reverse in the first Born model based on the asymptotically exact Coulomb wave functions [7].…”

“…This analysis is particularly transparent when the data are viewed as 2D density plots [7,16]. The two-peak cross-section pattern displayed in Figs.…”

“…However, there is a broad variation of the first and second Born results for the double ionization by electron impact. There is no agreement in the first Born model between the convergent close-coupling method and the calculations based on the asymptotically exact three-body Coulomb (3C) final state [7]. The latter method exhibits a very strong, sometime counterintuitive, dependence on the accuracy of the ground state, when an inferior ground state gives a better agreement with experiment on the absolute scale [8,9].…”

Double ionization of helium by proton impact: A generalized-Sturmian approach

“…They both present a smoother angular dependence but differ in key features such as the recoil-structure shape and the relative heights of each peak. We should add here that, in the case of electron impact, in contrast to the 3C counterpart, ab initio calculations such as the convergent close coupling (CCC) [27] showed a more prominent binary peak. In the present proton case, the comparison between our numerical results and those of the 3C variants reveals a similar feature.…”

“…The same authors further tackled the problem with an approach involving effective momenta [4]. In this second study, the obtained cross sections present structures that vary slowly with the ejection angles, a trend, to some degree, analogous to that observed for electron impact [16,18,27]. By providing FDCS with our GSF method, we wish to evaluate the success of these perturbative schemes.…”