1S-2S energy shift in muonic hydrogen

We calculate corrections of orders α 4 , α 5 , α 6 to the (1 S – 2 S ) fine structure interval in muonic hydrogen ( μp ), muonic tritium ( μt ) and muonic helium ion $$((\mu _2^3He) + )$$. They are determined by the effects of vacuum polarization, nuclear structure and recoil and relativistic corrections. The nuclear structure effects are taken into account in terms of the charge radii of the nuclei in one-photon interaction and in terms of electromagnetic form-factors in the case of two-photon interaction. The obtained results for the (1 S – 2 S ) splitting can be used for a comparison with future experimental data.