Theory of the Lamb shift and Fine Structure in muonic $\mathrm{^4He}$ ions and the muonic $\mathrm{^3He-^4He}$ Isotope Shift

Understand

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 $(\mathrm{\mu^4He})^+$.

• 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.