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, D ₂₁ = 8E _hfs(2s) - E _hfs(1s), which is known experimentally for hydrogen, deuterium and ³ 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^-8. Received 22 September 2001