Time correlation in two-electron transitions produced in fast collisions of atoms with matter and light

Abstract

Time connection between electrons in dynamic atomic systems is considered. We describe time correlation in terms of the Dyson time ordering operator T. In this paper we decompose T into an uncorrelated term T unc , plus a correlated term T cor ϭTϪT unc , which interconnects the time-dependent external interactions. We show that time correlation between electrons requires both T cor and spatial electron-electron correlation. Two examples are analyzed. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of T cor in amplitudes for coherently interfering pathways changes resonance intensities and profiles.Understanding time correlation between electrons requires connecting the concept of spatial correlation with time. Spatial correlation arises from the Coulomb interactions between electrons ͓1-3͔. Without this correlation the electrons are independent in both space and time, i.e., they do not mix with one another in space and they evolve independently in time ͓3͔. In this paper we address time correlation between electrons, namely, how electrons communicate about time. We show that both temporal correlation of external interactions and spatial correlation between electrons are required for time correlation between electrons.Cross sections of multielectron atoms dynamically interacting with both matter and light have been widely studied for many years ͓4-6͔. In the last decade studies of multiple electron transitions have lead to more detailed understanding of correlated dynamic reaction mechanisms ͓3,7-10͔. Now, new experimental techniques ͓10-12͔ are providing data in unprecedented detail, which can be used to test in greater depth new descriptions of collision dynamics. Thus, both a conceptual and an observational basis is now available for more explicit studies of how time works in quantum multiparticle dynamics. In this paper we analyze two atomic processes in which time correlation between electrons affects reaction cross sections. The first case is a kinematic peak in a reaction in which electron transfer and ionization both occur. In this case time correlated and time uncorrelated amplitudes add incoherently. The second case is double electron excitation where coherent reaction pathways interfere. In the second case time correlation between electrons produces a large effect on both the shape and intensity of a double excitation resonance.Time dependence is imposed on a quantum system ͓13-16͔ by an external time-dependent interaction V I (t). The general expression for the probability amplitude, a f i (t) ϭ͗ f ͉U I (t,t i )͉i͘, for scattering of one or more electrons from ͉i͘ at time t i to ͉ f ͘ at time t may be described most conveniently in the interaction representation ͓3,5͔ using the evolution operator U I (t,tЈ), which satisfies i ‫ץ‬U I ͑ t,tЈ͒/‫ץ‬tϭV I ͑ t ͒U I ͑ t,tЈ͒, ͑1͒with the initial condition lim t→Ϫϱ U I (t,Ϫϱ)ϭÎ. The formal solution for the evolution operator may be expressed as a time orde...

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