Hydrogen effective magnetic moments

The magnetic effect due to the adsorption of oxygen is more difficult to explain. Per atom adsorbed this is within the limits of the accuracy equal to the effect of hydrogen. Now for the oxygen adsorption bond no connection with the d-character of the metal is generally assumed. At least in NiO the bond formation is considered as due to s-electrons. The magnetic moment per nickel atom in this antiferromagnetic compound is equal to that of the isolated nickel atom and corresponds to two unpaired d-elec-... 

The hyperfine structure interval in hydrogen is known experimentally on a level of accuracy of one part in 1012, while the theory is of only the 10 ppm level [9]. In contrast to this, the muonium hfs interval [12] is measured and calculated for the ground state with about the same precision and the crucial comparison between theory and experiment is on a level of accuracy of few parts in 107. Recoil effects are more important in muonium (the electron to nucleus mass ratio m/M is about 1/200 in muonium, while it is 1/2000 in hydrogen) and they are clearly seen experimentally. A crucial experimental problem is an accurate determination of the muon mass (magnetic moment) [12], while the theoretical problem is a calculation of fourth order corrections (a(Za)2m/M and (Za)3m/M) [11]. 

Precise measurements on g factors of electrons bound in atomic Hydrogen and the Helium ion 4He+ were carried out by Robinson and coworkers. The accuracies of 3 x 10-8 for the Hydrogen atom [5] and of 6 x 10-7 for the Helium ion [6] were sensitive to relativistic effects. Other measurements of the magnetic moment of the electron in Hydrogen-like ions were performed at GSI by Seelig et al. for Lead (207Pb81+) [7] and by Winter et al. for Bismuth (209Bi82+) [8] with precisions of about 10-3 via lifetime measurements of hyperfine transitions. These measurements were also only sensitive to the relativistic contributions. 

In the case of the recent experiment with hydrogen-like carbon the nontrivial QED effects contribute an observable amount (see Table 1). We need to mention that, due to some delay of the final publications of the experimental result [1] and theoretical calculations [10], no actual theoretical predictions have been published. Most of the presentations (conference and seminar talks and posters) dealt with unaccurate theoretical predictions because it was believed that nothing had been known on the two-loop corrections. However, that was not the case, because from the beginning of the theoretical calculations up to recent re-calculations it was clearly stated ed [6] that the (Za)2 term in Eq. (4) is of pure kinematic origin and so the result is valid in any order of the expansion in a for the anomalous magnetic moment of a free electron, and in particular... 

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