Exceptional points in the spectra of atoms in external fields

TL;DR

This paper explores the existence and properties of exceptional points in the spectra of hydrogen atoms subjected to external electric and magnetic fields, revealing their impact on atomic resonance behaviors and photoionization.

Contribution

It introduces a systematic method to identify exceptional points in atomic spectra and analyzes their effects using effective models and spectral data.

Findings

Existence of exceptional points in hydrogen atom spectra confirmed.

Relation between exceptional points and avoided level crossings analyzed.

Impact on dipole matrix elements and photoionization cross section studied.

Abstract

We investigate exceptional points, which are branch point singularities of two resonance eigenstates, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedure to systematically search for exceptional points is presented, and their existence is proven. The properties of the branch point singularities are discussed with effective low-dimensional matrix models, their relation with avoided level crossings is analyzed, and their influence on dipole matrix elements and the photoionization cross section is investigated. Furthermore, the rare case of a connection between three resonances almost forming a triple-degeneracy in the form of a cubic root branch point is discussed.