Comprehensive study of 3-body and 4-body models of single ionization of helium

Abstract

The frozen core approximation has been successfully used for many years to model 4-body collisions as 3-body collisions. We present a comprehensive comparison of 3-body and 4-body models for the process of single ionization of helium by electron impact using our 4-body distorted wave model. Differences between the two models are observed in both magnitude and peak locations. We identify four possible sources for the discrepancies between the models, and isolate the specific physical causes of the discrepancies.

Frozen Core Approximation and Nuclear Screening Effects in Single Electron Capture Collisions

“…Thus, we conclude that the change of state of the inactive electron is not the primary cause of the discrepancies between the 3-Body and 4-Body FDCS. This is consistent with our previous work for the single ionization process, in which the change of state of the inactive electron had a negligible effect on the FDCS [25,26].…”

“…We can then conclude that the concept of the frozen core approximation, in which the inactive electron does not change state, is valid for single electron capture, but that care must be used in modeling the projectile-target interaction. These results are consistent with our past studies of the frozen core approximation and nuclear screening [25][26][27]. In summary, we used the first Born approximation in 3-Body and 4-Body models of single electron capture to explore the effects of the frozen core approximation.…”

“…Previously, we have examined the frozen core approximation in electron and heavy ion impact single ionization of helium [25,26], as well as the 5-body process of He + + He electron capture [27]. In our study of single ionization, we found that the initial state projectile-target interaction and the final state ionic potential were most influential on the magnitude and shape of the fully differential cross sections (FDCS).…”

“…In particular, the 4-Body perturbation contains a sum of three terms, while the 3-Body perturbation is only two terms. Past work on the analysis of 3-Body and 4-Body models for single ionization has shown that the perturbation potential alters the shape of the FDCS [25,26]. Additionally, FBA models are known to predict a deep minimum in the FDCS caused by a cancellation of terms in the perturbation [7,[30][31][32].…”

Quantum mechanical potentials and inactive electron effects in charge exchange collisions

“…In electron capture collisions, it is common to neglect inactive electrons in what is known as the frozen core approximation. Some of our previous work has focused on the validity of the frozen core approximation in electron and heavy ion ionization collisions [15,16]. Here, we extend this work to electron capture differential cross sections with dressed projectiles.…”