Theory of the Lamb shift and Fine Structure in muonic ions and the muonic Isotope Shift
Marc Diepold (1) · Beatrice Franke (1 and 2) · Julian J. Krauth (1 and 3) · Aldo Antognini (4 and 5) · Franz Kottmann (4) · Randolf Pohl (3 and 1) ((1) Max Planck Institute of Quantum Optics, 85748 Garching, Germany, (2) TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada, (3) Johannes Gutenberg-Universität Mainz, QUANTUM, Institut für Physik & Exzellenzcluster PRISMA, 55099 Mainz, (4) Institute for Particle Physics and Astrophysics, ETH Zurich, 8093 Zurich, Switzerland, (5) Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland)
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 . 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 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 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.