Sturmian basis set for the Dirac equation with finite nuclear size: Application to polarizability, Zeeman and hyperfine splitting, and vacuum polarization

2025/06/13 by V. K. Ivanov, Ivanov, V. K., D. A. Glazov +3 · 1 citation
Mathematics · Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.11988

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We investigate the application of the Sturmian basis set in relativistic atomic structure calculations. We propose a simple implementation of this approach and demonstrate its ability to provide various quantities for hydrogen-like ions, including binding energies, static dipole polarizability, g factor, hyperfine splitting, and nuclear magnetic shielding. Finally, we calculate the all-order (Wichmann-Kroll) vacuum polarization charge density, which was a challenge for the finite-basis-set approach until recently. Comparison of the obtained results with the previously published numerical and analytical calculations is presented. All calculations are performed with the finite size of the nucleus and can in principle be extended to arbitrary binding potentials.

Citations

• ²⁰⁸Pb nuclear charge radius revisited: closing the fine-structure-anomaly gap
• CODATA Recommended Values of the Fundamental Physical Constants: 2022
• Theory of the Lamb Shift in Hydrogen and Light Hydrogen‐Like Ions
• Hyperfine structure of hydrogen-like ions

Cited by

• Improved QED correction model for the GRASP2018 package
• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions

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