Time ordering in atomic collisions

TLDR

The study develops a general framework for incorporating time ordering into many‑electron processes induced by charged‑particle impact. The authors perform a second‑order calculation of helium double ionization, treating electron–electron interaction solely through a shake‑off term. They find that time ordering is required to generate odd‑power Z terms in the cross section, enabling distinct values for positively and negatively charged projectiles, while interference between shake‑off and second‑order terms only partially accounts for the charge‑sign dependence.

Abstract

We present a general treatment for the effect of time ordering in the many-electron processes induced by charged-particle impact. We show that time ordering is essential in order to obtain odd power Z terms in the cross section which is necessary to get different values for positively and negatively charged projectiles. A second-order calculation is performed for the double ionization of helium. The electron - electron interaction is taken into account only by the shake-off term. The interference between the shake-off and second-order term is responsible only for a part of the dependence of the cross sections on the sign of the charge of the projectile.