Hyperfine structure of the metastable level in hydrogen-like atoms

Precision methods for measuring the hyperfine splitting E_HFS(2S) of the metastable level in light hydrogen-like systems such as hydrogen, deuterium, and the ³He⁺ ion are considered. These measurements open up a new possibility for precise testing of quantum electrodynamics (QED) of bound states in hadronic systems. While the direct calculation of the energy levels in such systems runs into the problem of the uncertainty of the nuclear charge radius, the contribution of energy corrections appearing in the calculation of the parameter D₂₁ = 8E_HFS(2S) - E_HFS(1S) taking the finite size of the nucleus into account becomes smaller. The results of calculations of D₂₁ are presented and compared with experimental values. The approach considered in the paper allows the testing of some bound-state QED corrections to the hyperfine splitting energy at a level of 10^-7, which is comparable with the results of precision QED tests based on the study of the hyperfine splitting in leptonic systems.