Vacuum polarization and Wichmann-Kroll correction in the finite basis set approximation

• URL: http://arxiv.org/abs/2406.06758v1
• Date: Mon, 10 Jun 2024 19:36:11 GMT
• Title: Vacuum polarization and Wichmann-Kroll correction in the finite basis set approximation
• Authors: V. K. Ivanov, S. S. Baturin, D. A. Glazov, A. V. Volotka,
• Abstract summary: We study the convergence of the finite basis set method with different types and sizes of basis sets. We consider several heavy hydrogen-like ions and evaluate the vacuum polarization correction for $S$ and $P$ electron orbitals.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The finite basis set method is commonly used to calculate atomic spectra, including QED contributions such as bound-electron self-energy. Still, it remains problematic and underexplored for vacuum-polarization calculations. We fill this gap by trying this approach in its application to the calculation of the vacuum-polarization charge density and the Wichmann-Kroll correction to the electron binding energy in a hydrogen-like ion. We study the convergence of the method with different types and sizes of basis sets. We cross-check our results for the Wichmann-Kroll correction by direct integration of the Green's function. As a relevant example, we consider several heavy hydrogen-like ions and evaluate the vacuum polarization correction for $S$ and $P$ electron orbitals.

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