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Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei1–4. Here we focus on 9Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like 9Be3+. We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion— uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state 9Be+ (ref. 5), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations.A high-precision measurement of the shielding effects of multiple electrons on the nuclear magnetic moment is made possible by spectroscopy of hydrogen-like 9Be3+, which overcomes limitations from the nuclear structure. [ABSTRACT FROM AUTHOR]

A theoretical method to calculate Delbrück scattering amplitudes for photon energies above the electron‐positron (e+e−${e}^{+}{e}^{-}$) pair production threshold is presented. The method is based on the application of the relativistic Dirac–Coulomb Green function and describes the interaction of the virtual e+e−$e^+e^-$ pair with the Coulomb field of a target to all orders in the coupling strength parameter αZ$\alpha Z$. To illustrate the application of the developed approach, detailed calculations have been performed for the scattering of 2.754 MeV photons off bare ions with a wide range of nuclear charge numbers. Results of these calculations clearly indicate that the higher‐order terms beyond the Born approximation lead to a strong enhancement of the imaginary part of the Delbrück amplitude and have to be taken into account for the analysis and guidance of gamma‐ray scattering experiments. [ABSTRACT FROM AUTHOR]

We present a theoretical investigation of the elastic Rayleigh scattering of X-rays by atomic targets. Special attention is paid to the question of how the polarization of the scattered photons is affected if the incident light is itself polarized. In particular, we found that the circular polarization of the incoming X-rays may lead to a remarkable modification of the linear polarization of the scattered photons. Based on this 'circular-to-linear-polarization-transfer' and on the fact that the linear polarization of X-rays can be conveniently observed by solid-state Compton detectors, we argue that Rayleigh scattering may be used as a tool for circular polarimetry of hard X-rays. To illustrate our proposal, we performed detailed calculations of 145 and 500 keV circularly polarized photons scattered by lead atoms. Based on these calculations, we found that the photon scattering under large angles with respect to the incident beam direction is most favorable for the circular polarimetry of hard X-rays. In particular, for 500 keV photon energy and scattering angles around 70 deg we found a remarkable modification of the linear polarization of scattered light for the case when the incident radiation is circularly polarized. [ABSTRACT FROM AUTHOR]

Calculational results are presented for the fine structure splitting of the 23P state of helium and helium-like ions with nuclear charge Z up to 10. Theoretical predictions are in agreement with the latest experimental results for the helium fine structure intervals as well as with the most of the experimental data available for light helium-like ions. Comparing the theoretical value of the 23P0-23P1 interval in helium with experimental results (Zelevinsky et al. Phys. Rev. Lett. 95, 203001 (2005)), we determine the value of the fine structure constant a with an accuracy of 31 ppb. PACS Nos: 06.20.Jr, 31.30.jf, 12.20.Ds, 31.15.aj Nous presentons les resultats de calculs de la separation en structure fine de l'etat 23P de l'heelium et d'ions de type helium pour des charges Z allant jusqu'a 10. Les resultats theoriques sont en accord avec les plus recents resultats experimentaux pour la separation ultrafine dans l'helium, ainsi qu'avec la plupart des donneees experimentales disponibles pour les ions de type helium. En comparant la valeur theeorique dans l'heelium, de l'intervalle 23P0-23P1 avec les resultats expeerimentaux (Zelevinsky et al. Phys. Rev. Lett. 95, 203001 (2005)), nous determinons la valeur de la structure fine a avec une precision de 31 ppb. [Traduit par la Redaction], 1. Introduction The fine structure splitting of the [2.sup.3]P state in helium plays a special role in atomic spectroscopy, because it can be used for an accurate determination of the [...]

Abstract: We review the theoretical knowledge of anomalous magnetic moments of free electrons and muons, and of electrons bound in hydrogenlike ions. We discuss applications of these observations in the [...]

The Gamma Factory initiative proposes to develop novel research tools at CERN by producing, accelerating, and storing highly relativistic, partially stripped ion beams in the SPS and LHC storage rings. By exciting the electronic degrees of freedom of the stored ions with lasers, high‐energy narrow‐band photon beams will be produced by properly collimating the secondary radiation that is peaked in the direction of ions' propagation. Their intensities, up to 1017 photons per second, will be several orders of magnitude higher than those of the presently operating light sources in the particularly interesting γ–ray energy domain reaching up to 400 MeV. This article reviews opportunities that may be afforded by utilizing the primary beams for spectroscopy of partially stripped ions circulating in the storage ring, as well as the atomic‐physics opportunities made possible by the use of the secondary high‐energy photon beams. The Gamma Factory will enable ground‐breaking experiments in spectroscopy and novel ways of testing fundamental symmetries of nature. [ABSTRACT FROM AUTHOR]

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r 1 , r 2 and r   =   | r → 1 − r → 2 | . The choice of the exponential basis functions of the form exp (− α r 1 − β r 2 − γ r) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α 5 m (where m is the electron mass) are complemented with the systematic treatment of higher-order α 6 m and α 7 m QED effects. [ABSTRACT FROM AUTHOR]

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects need to be performed without any expansion in the nuclear binding strength parameter Z α (where Z is the nuclear charge number and α is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades. [ABSTRACT FROM AUTHOR]

Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high‐precision determination of the proton charge radius drastically reduces the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two‐ and three‐loop QED effects, which calls for further advances in their calculations. The present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen‐like ions with the nuclear charge number up to Z=5 is reviewed. Theoretical errors due to various effects are critically examined and estimated. [ABSTRACT FROM AUTHOR]

We present a derivation of the electron’s mass from our experiment on the electronic g factor in 12C5+ and 16O7+ together with the most recent quantum electrodynamical predictions. The value obtained from 12C5+ is me=0.0005485799093(3) u, that from oxygen is me=0.0005485799092(5) u. Both values agree with the currently accepted one within 1.5 standard deviations but are four respectively two-and-a-half times more precise. The contributions to the uncertainties of our values and perspectives for the determination of the fine-structure constant α by an experiment on the bound-electron g factor are discussed. [Copyright &y& Elsevier]

We present a calculation of the hyperfine splitting of the 2^{3}S state in the ^{3}He atom with inclusion of all QED effects up to α^{3}E_{F}, where E_{F} is the Fermi splitting. Using the experimental value of the 1S hyperfine splitting in ^{3}He^{+}, we eliminate uncertainties from the nuclear structure and obtain the theoretical prediction for ^{3}He of ν_{hfs}=-6 739 701 181(41)  Hz, which is in perfect agreement with the experimental value -6 739 701 177(16)  Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A 1, 571 (1970)PLRAAN0556-279110.1103/PhysRevA.1.571]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a nonhydrogenic system.

We investigate the modification of the transverse electromagnetic interaction between two pointlike particles when one particle acquires a finite size. It is shown that the correct treatment of such interaction cannot be accomplished within the Breit approximation but should be addressed within the QED. The complete QED formula is derived for the finite-size nuclear recoil, exact in the coupling strength parameter Zα. Numerical calculations are carried out for a wide range of Z and verified against the (Zα)^{5} contribution. The comparison with the Zα expansion identifies the contribution of order (Zα)^{6}, which is linear in the nuclear radius and numerically dominates over the lower-order (Zα)^{5} term.

For more than 40 years, most astrophysical observations and laboratory studies of two key soft x-ray diagnostic 2p-3d transitions, 3C and 3D, in Fe XVII ions found oscillator strength ratios f(3C)/f(3D) disagreeing with theory, but uncertainties had precluded definitive statements on this much studied conundrum. Here, we resonantly excite these lines using synchrotron radiation at PETRA III, and reach, at a millionfold lower photon intensities, a 10 times higher spectral resolution, and 3 times smaller uncertainty than earlier work. Our final result of f(3C)/f(3D)=3.09(8)(6) supports many of the earlier clean astrophysical and laboratory observations, while departing by five sigmas from our own newest large-scale ab initio calculations, and excluding all proposed explanations, including those invoking nonlinear effects and population transfers.

We report a calculation of the fine-structure splitting in light heliumlike 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.

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known Zalpha-expansion coefficients is determined. For the 3He+ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order alpha(Z alpha)(4) to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha(2)(Z alpha)(4)ln([(Z alpha)(-2)] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.