QED theory of the nuclear recoil effect in atoms

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in \alpha Z is formulated. The nuclear recoil corrections for atoms with one and two electrons over closed shells are considered in detail. The problem of the composite nuclear structure in the theory of the nuclear recoil effect is discussed.Comment: 20 pages, 6 figures, Late

Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ\alpha Z

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $\alpha Z$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(\alpha Z)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(\alpha Z)^4$ term, while for uranium it is above the leading $(\alpha Z)^2$ correction.Comment: 6 pages, 3 tables, 1 figur

Self-energy correction to the hyperfine structure splitting of the 1s and 2s states in hydrogenlike ions

The one-loop self-energy correction to the hyperfine structure splitting of the 1s and 2s states of hydrogenlike ions is calculated both for the point and finite nucleus. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike ^{209}Bi^{80+} and ^{165}Ho^{64+}.Comment: The table 2 is changed. 6 pages, 1 figure, Late

Mathematical Structure of Relativistic Coulomb Integrals

We show that the diagonal matrix elements $,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.Comment: 13 pages, no figure

g factor of Li-like ions with nonzero nuclear spin

The fully relativistic theory of the g factor of Li-like ions with nonzero nuclear spin is considered for the (1s)^2 2s state. The magnetic-dipole hyperfine-interaction correction to the atomic g factor is calculated including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. This correction is combined with the interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtain high-precision theoretical values for the g factor of Li-like ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from g factor experiments.Comment: 20 pages, 5 figure

Transition energy and lifetime for the ground state hyperfine splitting of high Z lithiumlike ions

The ground state hyperfine splitting values and the transition probabilities between the hyperfine structure components of high Z lithiumlike ions are calculated in the range $Z=49-83$. The relativistic, nuclear, QED and interelectronic interaction corrections are taken into account. It is found that the Bohr-Weisskopf effect can be eliminated in a combination of the hyperfine splitting values of the hydrogenlike and lithiumlike ions of an isotope. This gives a possibility for testing the QED effects in a combination of the strong electric and magnetic fields of the heavy nucleus. Using the experimental result for the $1s$ hyperfine splitting in ^{209}Bi^{82+}, the 2s hyperfine splitting in ^{209}Bi^{80+} is calculated to be \Delta E=0.7969(2) eV.Comment: The nuclear charge distribution correction \delta is corrected, 14 pages, Late

Non-perturbative calculation of the two-loop Lamb shift in Li-like ions

A calculation valid to all orders in the nuclear-strength parameter is presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, to the 2p-2s transition energies in heavy Li-like ions. The calculation removes the largest theoretical uncertainty for these transitions and yields the first experimental identification of two-loop QED effects in the region of the strong binding field

One-loop self-energy correction to the 1s and 2s hyperfine splitting in H-like systems

The one-loop self-energy correction to the hyperfine splitting of the 1s and 2s levels in H-like low-Z atoms is evaluated to all orders in Z\alpha. The results are compared to perturbative calculations. The residual higher-order contribution is evaluated. Implications to the specific difference of the hyperfine structure intervals 8\Delta \nu_2 - \Delta \nu_1 in He^+ are investigated.Comment: 17 pages, RevTeX, 3 figure

Relativistic Kramers-Pasternack Recurrence Relations

Recently we have evaluated the matrix elements $$,$where$O$$={1,\beta, i\mathbf{\alpha n}\beta} $are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions$_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here.Comment: 12 pages, no figures Will appear as it is in Journal of Physics B: Atomic, Molecular and Optical Physics, Special Issue on Hight Presicion Atomic Physic