Energy Interval 1S–2S in Muonic Hydrogen and Helium

The interval of a large structure of energy spectrum (1S–2S) in muonic helium and hydrogen is calculated using a quasi-potential method in quantum electrodynamics. Corrections of the order α⁴, α⁵, and α⁶ determined by relativistic effects, vacuum polarization effects, nuclear structure and recoil, as well as by combined corrections including those listed above, are taken into account. The nuclear structure effects are expressed in terms of the charge radius of nuclei in the case of the one-photon interaction and electromagnetic form factors of nuclei in the case of the two-photon interaction. Numerical values obtained for the (1S–2S) interval can be used for comparison with future experimental data and for more accurate determination of the charge radii of nuclei.