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  • Open Access

Relativistic effects on photoabsorption cross sections of highly charged ions

Anvar Khujakulov*

Caterina Cocchi

  • Institut für Festkörpertheorie und Optik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany and Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, 07745 Jena, Germany

  • *Contact author: anvar.khujakulov@uni-jena.de
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Phys. Rev. A 114, 023109 – Published 26 August, 2026

DOI: https://doi.org/10.1103/hq5k-bwzj

Abstract

The study of highly charged ions offers a unique platform for probing the breakdown of nonrelativistic theory under the influence of extreme electromagnetic environments. Here we investigate the photoabsorption of highly charged ions within the dipole approximation using both the time-dependent Schrödinger equation (TDSE) and the time-dependent Dirac equation (TDDE), modeling the external field as an instantaneous broadband excitation. Nonrelativistic scaling relations with respect to the nuclear charge are utilized as a diagnostic tool to systematically identify and quantify relativistic contributions. Within the purely nonrelativistic TDSE framework, these scaling relations hold exactly, allowing the absorption spectra of arbitrary highly charged ions to be inferred directly from a neutral hydrogenic reference. However, as the nuclear charge increases, relativistic effects become dominant through a sizable blueshift in the absorption cross section, due to the relativistic enhancement of the binding energy. We further evaluate semirelativistic TDSE approximations by direct comparison with full TDDE simulations, assessing their predictive power and establishing the regimes where a full Dirac treatment is indispensable for quantitative accuracy. These results establish a baseline for subattosecond relativistic quantum coherence and transient polarization, providing the theoretical groundwork for impulse spectroscopy at next-generation x-ray free-electron laser facilities.

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Phys. Rev. A 114, 023109– Published 26 August, 2026
  • Received 31 March 2026
  • Accepted 31 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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