---
_id: '61353'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <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>\r\n
    \                 </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>"
article_number: '012001'
author:
- first_name: Katharina L.
  full_name: Franzke, Katharina L.
  last_name: Franzke
- first_name: Wolf Gero
  full_name: Schmidt, Wolf Gero
  id: '468'
  last_name: Schmidt
  orcid: 0000-0002-2717-5076
- first_name: Uwe
  full_name: Gerstmann, Uwe
  id: '171'
  last_name: Gerstmann
  orcid: 0000-0002-4476-223X
citation:
  ama: '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>'
  apa: '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>'
  bibtex: '@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} }'
  chicago: '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>.'
  ieee: '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>.'
  mla: '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>.'
  short: 'K.L. Franzke, W.G. Schmidt, U. Gerstmann, Journal of Physics: Conference
    Series 3027 (2025).'
date_created: 2025-09-18T11:17:05Z
date_updated: 2025-12-05T13:32:45Z
department:
- _id: '15'
- _id: '170'
- _id: '295'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '27'
- _id: '790'
doi: 10.1088/1742-6596/3027/1/012001
intvolume: '      3027'
issue: '1'
language:
- iso: eng
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '54'
  name: TRR 142 - Project Area A
- _id: '166'
  name: TRR 142 - Subproject A11
publication: 'Journal of Physics: Conference Series'
publication_identifier:
  issn:
  - 1742-6588
  - 1742-6596
publication_status: published
publisher: IOP Publishing
status: public
title: Finite-size and relativistic effects onto hyperfine interaction of muonic hydrogen
type: journal_article
user_id: '16199'
volume: 3027
year: '2025'
...