Hyperfine Structure of the Ground and First Excited States in Light Hydrogen-Like Atoms and High-Precision Tests of QED

We consider hyperfine splitting of 1s and, in part, of 2s levels in light hydrogen-like atoms: hydrogen, deuterium, tritium, helium-3 ion, muonium and positronium. We discuss present status of precision theory and experiment for the hfs intervals. We pay a special attention to a specific difference, D21 = 8Ehfs(2s) − Ehfs(1s), which is known experimentally for hydrogen, deuterium and He ion. The difference is weakly affected by the effects of the nuclear structure and thus may be calculated with a high accuracy. We complete a calculation of the fourth order QED contributions to this difference and present here new results on corrections due to the nuclear effects. Our theoretical predictions appear to be in a fair agreement with available experimental data. Comparison of the experimental data with our examination of D21 allows to test the state-dependent sector of theory of the hfs separation of the 1s and 2s levels in the light hydrogen-like atoms up to 10. PACS. 12.20.Fv Quantum electrodynamics: Experimental tests – 21.45.+v Few-body systems – 31.30.Jv Relativistic and quantum electrodynamic effects in atoms and molecules – 32.10.Fn Fine and hyperfine structure