Dynamic electron correlation in interactions of light with matter formulated in b-space

TL;DR

This paper formulates light-matter scattering involving multiple electrons in the position space, deriving probability amplitudes that account for electron correlations and their dependence on the impact parameter, with applications to vortex photon beams.

Contribution

It introduces a position-space formulation of electron correlation effects in light-matter interactions, including explicit dependence on the impact parameter and applications to vortex beams.

Findings

Probability amplitude a(b) expressed in position space

Correlation effects reduce to product of single-electron amplitudes in independent approximation

Explicit impact parameter dependence demonstrated with vortex photon beams

Abstract

Scattering of beams of light and matter from multi-electron atomic targets is formulated in the position representation of quantum mechanics. This yields expressions for the probability amplitude, a(b), for a wide variety of processes. Here the spatial parameter b is the distance of closest approach of incoming particles traveling on a straight line with the center of the atomic target. The correlated probability amplitude, a(b), reduces to a relatively simple product of single electron probability amplitudes in the widely used independent electron approximation limit, where the correlation effects of the Coulomb interactions between the atomic electrons disappear. As an example in which a(b} has an explicit dependence on b}, we consider transversely finite vortex beams of twisted photons that lack the translational invariance of infinite plane-wave beams. Some experimental considerations and future applications are briefly considered.