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

Relativistic recoil, electron-correlation, and QED effects on the 2p_j-2s transition energies in Li-like ions

The relativistic nuclear recoil, higher-order interelectronic-interaction, and screened QED corrections to the transition energies in Li-like ions are evaluated. The calculation of the relativistic recoil effect is performed to all orders in 1/Z. The interelectronic-interaction correction to the transition energies beyond the two-photon exchange level is evaluated to all orders in 1/Z within the Breit approximation. The evaluation is carried out employing the large-scale configuration-interaction Dirac-Fock-Sturm method. The rigorous calculation of the complete gauge invariant sets of the screened self-energy and vacuum-polarization diagrams is performed utilizing a local screening potential as the zeroth-order approximation. The theoretical predictions for the 2p_j-2s transition energies are compiled and compared with available experimental data in the range of the nuclear charge number Z=10-60.Comment: 39 pages, 3 figures, 11 table

Zeeman effect of the hyperfine structure levels in hydrogenlike ions

The fully relativistic theory of the Zeeman splitting of the $1s$ hyperfine structure levels in hydrogenlike ions is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit -- Rabi formula are calculated and discussed. The results can be used for a precise determination of nuclear magnetic moments from $g$ factor experiments.Comment: 13 page

QED theory of the nuclear recoil effect on the atomic g factor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in \alpha Z and to first order in m/M is formulated. The complete \alpha Z-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (\alpha Z)^2 m/M for an arbitrary state of a hydrogenlike atom.Comment: 17 page

Negative-continuum dielectronic recombination into excited states of highly-charged ions

The recombination of a free electron into a bound state of bare, heavy nucleus under simultaneous production of bound-electron--free-positron pair is studied within the framework of relativistic first--order perturbation theory. This process, denoted as "negative-continuum dielectronic recombination" leads to a formation of not only the ground but also the singly- and doubly-excited states of the residual helium-like ion. The contributions from such an excited--state capture to the total as well as angle-differential cross-sections are studied in detail. Calculations are performed for the recombination of (initially) bare uranium U$^{92+}$ ions and for a wide range of collision energies. From these calculations, we find almost 75 % enhancement of the total recombination probability if the excited ionic states are taken into account.Comment: 8 pages, 4 figures, accepted to PR

QED calculation of the 2p1/2-2s and 2p3/2-2s transition energies and the ground-state hyperfine splitting in lithiumlike scandium

We present the most accurate up-to-date theoretical values of the {2p_{1/2}}-{2s} and {2p_{3/2}}-{2s} transition energies and the ground-state hyperfine splitting in ${\rm Sc}^{18+}$. All two- and three-electron contributions to the energy values up to the two-photon level are treated in the framework of bound-state QED without \aZ-expansion. The interelectronic interaction beyond the two-photon level is taken into account by means of the large-scale configuration-interaction Dirac-Fock-Sturm (CI-DFS) method. The relativistic recoil correction is calculated with many-electron wave functions in order to take into account the electron-correlation effect. The accuracy of the transition energy values is improved by a factor of five compared to the previous calculations. The CI-DFS calculation of interelectronic-interaction effects and the evaluation of the QED correction in an effective screening potential provide significant improvement for the $2s$ hyperfine splitting. The results obtained are in a good agreement with recently published experimental data.Comment: 10 pages, 2 table

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

Self-energy correction to the bound-electron g factor in H-like ions

The one-loop self-energy correction to the 1s electron g factor is evaluated to all orders in Z\alpha with an accuracy, which is essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [Beier et al. Phys. Rev. Lett. 88, 011603 (2002)]. The new value of the electron mass is found to be m_e = 0.000 548 579 909 3(3) u

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

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