V. G. Ivanov

Hyperfine structure in hydrogen and helium ion

Abstract QED theory of the hyperfine splitting of the 1 s and 2 s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8 E HFS (2 s )− E HFS (1 s ). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α ( Zα ) 3 E F and examined the recoil contribution in order ( Zα ) 3 m / M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 10 8 ) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.

The g factor of the proton

We consider higher order corrections to the g factor of a bound proton in hydrogen atom and their consequences for a magnetic moment of free and bound proton and deuteron as well as some other objects.

Nonrelativistic contributions of order α5mμc2 to the Lamb shift in muonic hydrogen and deuterium, and in the muonic helium ion

Contributions to the energy levels in light muonic atoms and, in particular, to the Lamb shift fall into a few well-distinguished classes. The related diagrams are calculated using different approaches. In particular, there is a specific kind of non-relativistic contributions. Here we consider such corrections to the Lamb shift in order

Hyperfine structure of the ground and first excited states in light hydrogen-like atoms and high-precision tests of QED

alpha^5m_mu

Second-order corrections to the wave function at the origin in muonic hydrogen and pionium

. These contributions are due to free vacuum polarization loops as well as to various effects of light-by-light scattering. The closed loop in the related diagrams is an electronic one, which allows a non-relativistic consideration of the muon. Both kinds of contributions have been known for a while, however, the results obtained up to date are only partial ones. We complete a calculation of the

Recoil correction to the proton finite-size contribution to the Lamb shift in muonic hydrogen

alpha^5m_mu

Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

contributions for muonic hydrogen. The results are also adjusted for muonic deuterium and muonic helium ion.

BOUND MU +MU - SYSTEM

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 3He+ 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 Is and 2s levels in the light hydrogen-like atoms up to 10−8.

RADIATIVE CORRECTIONS TO DIPOLE MATRIX ELEMENTS IN HYDROGEN-LIKE ATOMS

Nonrelativistic second-order corrections to the wave function at the origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at the origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects, and the hyperfine splitting. The results are obtained for the 1s and 2s states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of {pi}{sup +} and {pi}{sup -}. Applications to the hyperfine structure and the Lamb shift in muonic hydrogen are also considered.

Electron shielding of the nuclear magnetic moment in a hydrogenlike atom

The Lamb shift in muonic hydrogen was measured some time ago to a high accuracy. The theoretical prediction of this value is very sensitive to the proton finite-size effects. The proton radius extracted from muonic hydrogen is in contradiction with the results extracted from elastic electron-proton scattering. That creates a certain problem for the interpretation of the results from the muonic hydrogen Lamb shift. For the latter we need also to take into account the two-photon-exchange contribution with the proton finite size involved. The only way to describe it relies on the data from the scattering, which may produce an internal inconsistency of theory. Recently the leading proton-finite-size contribution to the two-photon exchange was found within the external field approximation. The recoil part of the two-photon-exchange has not been considered. Here we revisit calculation of the external-field part and take the recoil correction to the finite-size effects into account.