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QED theory of the hyperfine splitting of the $1s$ and $2s$ state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_{HFS}(2s)-E_{HFS}(1s). We take into account fourth order corrections and nuclear structure effects. The theoretical prediction is now of a higher accuracy than the experiment is. The study of the difference provides the most accurate test (on a level of a part in 10^8) of the QED theory of $1s$ HFS up to date. The theory agrees with most of the experimental data.Comment: 4 page

The relativistic recoil contributions to the Uehling corrections are revisited. We consider a controversy in recent calculations, which are based on different approaches including Breit-type and Grotch-type calculations.We have found that calculations of those authors were in fact done in different gauges and in some of those gauges contributions to retardation and two-photon-exchange effects were missed. We have evaluated such effects and obtained a consistent result.We present a correct expression for the Grotch-type approach which produces a correct gaugeinvariant result.We also consider a finite-nuclear-size correction for the Uehling term.The results are presented for muonic hydrogen and deuterium atoms and for muonic helium-3 and helium-4 ions.

Abstract:Energy levels of a two-body atomic system in an external homogeneous magnetic field can be presented in terms of magnetic moments of their components, however, those magnetic moments being related to bound particles differ from their free values. Study of bound g factors in simple atomic systems are now of interest because of a recent progress in experiments on medium Z ions and of a new generation of muonium experiments possible with upcoming intensive muon sources. We consider bound corrections to the g factors in several atomic systems, experimental data for which are available in literature: hydrogen, helium-3 ion, muonium, hydrogen-like ions with spinless nuclei with medium Z.