article published Katharina L. Franzke author Wolf Gero Schmidt author 4680000-0002-2717-5076 Uwe Gerstmann author 1710000-0002-4476-223X 15 department 170 department 295 department 35 department 230 department 429 department 27 department 790 department Computing Resources Provided by the Paderborn Center for Parallel Computing project TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen project TRR 142 - Project Area A project TRR 142 - Subproject A11 project <jats:title>Abstract</jats:title> <jats:p>Muonic hydrogen is an exotic atom where a muon instead of an electron is bound to a proton. The comparably high mass of the muon (≈ 207 · <jats:italic>m<jats:sub>e</jats:sub> </jats:italic>) has two important effects, (i) the reduced mass of the system becomes more important, and (ii) the muon is localized much closer to the nucleus. Thus, muonic hydrogen is not only excellently suitable for evaluating highly precise quantum electrodynamic (QED) calculations, but may also be used for assessing new approaches including finite nuclear size (FNS) effects to evaluate the proton structure and improve calculation schemes for the hyperfine splittings of many-particle systems, as e.g. to be implemented in density functional theory (DFT) software packages. Here, starting from Dirac’s equation we calculate the relativistic hyperfine splitting of the ground state and several excited states of muonic hydrogen analytically for different charge and magnetization models. The FNS related hyperfine shifts are compared with the differences between QED calculations and experimental measurements. This comparison also allows to unravel the role of the reduced mass, which is on one hand crucial in case of muonic atoms, but on the other hand is by no means well defined in relativistic quantum mechanics.</jats:p> IOP Publishing2025 eng 1742-6588 1742-659610.1088/1742-6596/3027/1/012001 30271 Franzke, Katharina L., et al. “Finite-Size and Relativistic Effects onto Hyperfine Interaction of Muonic Hydrogen.” <i>Journal of Physics: Conference Series</i>, vol. 3027, no. 1, 012001, IOP Publishing, 2025, doi:<a href="https://doi.org/10.1088/1742-6596/3027/1/012001">10.1088/1742-6596/3027/1/012001</a>. Franzke KL, Schmidt WG, Gerstmann U. Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen. <i>Journal of Physics: Conference Series</i>. 2025;3027(1). doi:<a href="https://doi.org/10.1088/1742-6596/3027/1/012001">10.1088/1742-6596/3027/1/012001</a> @article{Franzke_Schmidt_Gerstmann_2025, title={Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen}, volume={3027}, DOI={<a href="https://doi.org/10.1088/1742-6596/3027/1/012001">10.1088/1742-6596/3027/1/012001</a>}, number={1012001}, journal={Journal of Physics: Conference Series}, publisher={IOP Publishing}, author={Franzke, Katharina L. and Schmidt, Wolf Gero and Gerstmann, Uwe}, year={2025} } Franzke, K. L., Schmidt, W. G., &#38; Gerstmann, U. (2025). Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen. <i>Journal of Physics: Conference Series</i>, <i>3027</i>(1), Article 012001. <a href="https://doi.org/10.1088/1742-6596/3027/1/012001">https://doi.org/10.1088/1742-6596/3027/1/012001</a> K. L. Franzke, W. G. Schmidt, and U. Gerstmann, “Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen,” <i>Journal of Physics: Conference Series</i>, vol. 3027, no. 1, Art. no. 012001, 2025, doi: <a href="https://doi.org/10.1088/1742-6596/3027/1/012001">10.1088/1742-6596/3027/1/012001</a>. Franzke, Katharina L., Wolf Gero Schmidt, and Uwe Gerstmann. “Finite-Size and Relativistic Effects onto Hyperfine Interaction of Muonic Hydrogen.” <i>Journal of Physics: Conference Series</i> 3027, no. 1 (2025). <a href="https://doi.org/10.1088/1742-6596/3027/1/012001">https://doi.org/10.1088/1742-6596/3027/1/012001</a>. K.L. Franzke, W.G. Schmidt, U. Gerstmann, Journal of Physics: Conference Series 3027 (2025). 613532025-09-18T11:17:05Z2025-12-05T13:32:45Z