Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

Marc Diepold, Beatrice Franke, Julian J. Krauth*, Aldo Antognini, Franz Kottmann, Randolf Pohl

*Corresponding author for this work

Research output: Contribution to JournalReview articleAcademicpeer-review


We provide an up to date summary of the theory contributions to the 2S → 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (μ4He)+. This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the 3He–4He isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n=2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.

Original languageEnglish
Pages (from-to)220-244
Number of pages25
JournalAnnals of Physics
Publication statusPublished - 1 Sept 2018


  • Fine structure
  • Helium
  • Isotope shift
  • Lamb shift
  • Muonic atoms/ions
  • Nuclear structure


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