Fine structure of helium-like ions and determination of the fine structure constant

We report a calculation of the fine structure splitting in light helium-like atoms, which accounts for all quantum electrodynamical effects up to order \alpha^5 Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.Comment: 4 pages, 3 tables, with a typo in Eq. (9) correcte

Finite nuclear mass corrections to electric and magnetic interactions in diatomic molecules

In order to interpret precise measurements of molecular properties the finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is shown that they can be obtained systematically in the perturbative approach. The formulae for the leading corrections to the relativistic contribution to energy, the transition electric dipole moment, the electric polarizability, and the magnetic shielding constant are presented.Comment: 24 pages, submitted to Phys. Rev.

Accurate Born-Oppenheimer potential for HeH+

We demonstrate high accuracy calculations for the HeH$^+$ molecule using newly developed analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic $^1\Sigma^+$ state is obtained in the range of 0.1 -- 60 au with precision of about $10^{-12}$ au. As an example at the equilibrium distance $r=1.463\,283$ au the Born-Oppenheimer potential amounts to $-2.978\,708\,310\,771(1)$. Obtained results lay the ground for theoretical predictions in HeH$^+$ with spectroscopic precision.Comment: 7 page

Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of $2^3P_J$ levels in helium are obtained by the calculation of contributions of order $\alpha^5 Ry$. New results for transition frequencies, $\nu_{01} = 29 616 943.01(17)$ kHz and $\nu_{12} = 2 291 161.13(30)$ kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.Comment: 4 page

Precision study of positronium and precision tests of the bound state QED

Despite its very short lifetime positronium provides us with a number of accurate tests of the bound state QED. In this note a brief overview of QED theory and precision experiments on the spectrum and annihilation decay of the positronium atom is presented. Special attention is paid to the accuracy of theoretical predictions.Comment: A talk presented at 9th International Workshop on Slow Positron Beam Techniques for Solids and Surfaces (SLOPOS), Dresden, 200

Extrapolation of the Zalpha-Expansion and Two--Loop Bound--State Energy Shifts

Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zalpha and ln[(Zalpha)^{-2}], where Z is the nuclear charge number and alpha is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zalpha expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zalpha-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic nonlogarithmic coefficient B_60.Comment: 10 pages, LaTeX, Phys. Lett. B, in pres