On the Atomic Photoeffect in Non-relativistic QED

TL;DR

This paper rigorously analyzes the photoelectric effect in non-relativistic QED, confirming the validity of perturbation theory and the dipole approximation for one-electron atoms.

Contribution

It provides a rigorous mathematical justification for the leading-order ionization probability and the accuracy of the dipole approximation in non-relativistic QED.

Findings

Ionization probability matches time-dependent perturbation theory at leading order

Dipole approximation introduces only sub-leading order errors

Results validate common approximations in quantum electrodynamics

Abstract

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, $\alpha$, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in $\alpha$. In this sense, the dipole approximation is rigorously justified.