arXiv subjects

V. A. Yerokhin

Publications and source records attributed to V. A. Yerokhin.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order corrections to the field shift in atomic systems

Differences in nuclear charge distributions between isotopes lead to small changes in atomic spectra known as the field shift. While largely proportional to the change in the mean-square nuclear radius, the field shift also contains higher-order contributions with different dependencies on nuclear moments. Their knowledge is required in searches for new physics using King plots, as they can induce deviations from King-plot linearity. We present a systematic expansion of the field-shift energies in terms of nuclear parameters and test its validity against direct numerical calculations for H-like ions. We also compute leading- and higher-order field-shift corrections for alkali-like systems from Li-like to Rb-like ions, and find that their ratio is nearly independent of the ionic charge state, agreeing with the corresponding hydrogenic $1s$ ratios on a sub-percent level. Motivated by this observation, we introduce an approximation in which these fractional contributions are assumed to be independent of the electronic configuration. We show that within this approximation, higher-order field-shift corrections do not contribute to King-plot nonlinearities.

physics.atom-ph↗

arXiv2026

Atomic parity violation in highly charged $^{40,48}$Ca and $^{208}$Pb ions

We calculate parity-violation-induced E1 amplitudes for the $1s\rightarrow 2s$ and $1s^2 2s\rightarrow 1s^2 3s$ transitions in H- and Li-like ions of $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb. In our analysis, we account for neutron skin effects and nuclear uncertainties for each nucleus. We consider the spin-independent weak-interaction contribution of the $Z^0$ boson described by standard model, as well as the effects of a hypothetical new $Z'$ boson of varying mass. We conclude that the neutron-skin corrections in the $^{40,48}$Ca isotope pair can mostly be neglected when considering $Z'$ boson effects, which is an advantage for the search for new parity-violating physics. On the other hand, both the neutron skin effect and the sensitivity to hypothetical $Z'$ interactions in $^{208}$Pb are shown to be significant.

physics.atom-ph↗

arXiv2026

Wichmann-Kroll Correction to the Interelectronic Interaction in He- and Li-Like Ions

We present a theoretical study of the higher-order QED contribution to the interelectronic interaction in He- and Li-like ions, where a virtual electron-positron loop is inserted into the photon line of the one-photon exchange diagram. Our approach is based on the Dirac-Coulomb Green's function and accounts for the interaction of the virtual $e^+e^-$ pair with the electric field of the nucleus to all orders in $αZ$, with $α$ being the fine-structure constant and $Z$ the atomic charge number. We show that the numerical convergence of the involved integrals can be significantly improved by explicitly subtracting the non-gauge-invariant spurious contributions from the integrands. We present improved numerical values for this contribution to the Lamb shift over a wide range of nuclear charge numbers $Z$. Our calculations agree well with previous results by Artemyev and co-workers [Phys. Rev. A 56, 3529 (1997); Phys. Rev. A 60, 45 (1999)] for He-like ions, but we find a discrepancy in the Li-like case. Moreover, we calculate the finite nuclear size correction to this diagram, which can reduce its size by more than 5% for heavy ions. The improved QED calculations not only decrease the uncertainty of theoretical predictions for the interelectronic interaction in few-electron ions but the methods could also be used in the future to improve calculations of closely related one-electron two-loop QED diagrams.

physics.atom-ph↗

arXiv2025

Model-independent determination of nuclear charge radii from Li-like ions

We demonstrate that recent advances in QED theory of Li-like ions [V. A. Yerokhin et al., Phys. Rev. A 112, 042801 (2025)] enable determinations of absolute nuclear charge radii for heavy elements. By incorporating constraints derived from electron-scattering data, we obtain radii that are independent of the assumed model of the nuclear charge distribution. Our approach is validated for $^{208}$Pb, a well-studied spherical nucleus, and is then applied to $^{209}$Bi, where low-lying nuclear excitations complicate the interpretation of muonic-atom data.

physics.atom-ph↗

arXiv2025

Two-loop vacuum polarization in a Coulomb field

The leading-order two-loop vacuum-polarization potential, linear in the Coulomb field of a nucleus, was first derived in the seminal 1955 work of Källén-Sabry. The higher-order two-loop vacuum-polarization corrections, however, have remained unknown until now. In this work, we compute Coulomb corrections to the Källén-Sabry potential, specifically those involving three, five, and seven Coulomb interactions inside the vacuum-polarization loop. The potentials are evaluated in momentum space and subsequently used to calculate one-electron energy shifts. Our results drastically reduce the theoretical uncertainty of the two-loop vacuum-polarization contribution to transition energies, which is required for next-generation tests of bound-state QED in heavy one and few-electron ions as well as for the determination of nuclear charge radii.

physics.atom-ph↗

arXiv2025

Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation

The two-loop electron self-energy correction is one of the most problematic QED effects and, for a long time, was the dominant source of uncertainty in the theoretical prediction of the bound-electron $g$ factor in hydrogen-like ions. A major breakthrough was recently achieved in [B. Sikora et al. Phys. Rev. Lett. 134, 123001 (2025)], where this effect was calculated without any expansion in the nuclear binding strength parameter $Zα$ (where $Z$ is the nuclear charge number and $α$ is the fine-structure constant). In this paper, we describe our calculations of one of the most difficult parts of the two-loop self-energy, represented by Feynman diagrams that are treated in the mixed momentum-coordinate representation.

physics.atom-ph↗

arXiv2025

QED calculations of the $2p$-$2s$ transition energies in Li-like ions

Systematic QED calculations of ionization energies of the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the $2p_{1/2}$--$2s$ and $2p_{3/2}$--$2p_{1/2}$ transition energies are performed for Li-like ions with the nuclear charge numbers $Z = 10$--$100$. The convergence of QED perturbative expansion is improved by using the extended Furry picture, which starts from the Dirac equation with a local screening potential. An ab initio treatment is accomplished for one- and two-photon electron-structure QED effects and the one-photon screening of the self-energy and vacuum-polarization corrections. This is complemented with an approximate treatment of the two-photon QED screening and higher-order (three or more photon) electron-structure effects. As a result, the obtained theoretical predictions improve upon the accuracy achieved in previous calculations. Comparison with available experimental data shows a good agreement between theory and experiment. In most cases, the theoretical values surpass the experimental results in precision, with only a few exceptions. In the case of uranium and bismuth, the comparison provides one of the most stringent tests of bound-state QED in the strong-field regime. Alternatively, the obtained results can be employed for high-precision determinations of nuclear charge radii.

physics.atom-ph↗

arXiv2025

$g$ Factor of Boron-like Tin

In the ALPHATRAP experiment, the $g$ factor of boron-like $^{118}\mathrm{Sn}^{45+}$ has been measured with a $0.5$ parts-per-billion uncertainty. This is the first high-precision measurement of a heavy boron-like $g$ factor. The measured value of $0.644\,703\,826\,5(4)$ is consistent with the presented \textit{ab initio} state-of-the-art theory calculations, which predict a value of $0.644\,702\,9(8)$. So far, the only boron-like $g$ factor measured with high precision has been $^{40}\mathrm{Ar}^{13+}$. The measurement presented here therefore tests quantum electrodynamics as well as many-electron interactions at much higher $Z$. Furthermore, we discuss the potential for an independent determination of the fine-structure constant $α$, which can be achieved with a specific difference of $g$ factors, combining the presented results with the recent electron $g$-factor measurement of hydrogen-like tin.

physics.atom-ph↗

arXiv2025

Two-loop electron self-energy with accelerated partial-wave expansion

Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Zα$ (where $Z$ is the nuclear charge number and $α$ is the fine structure constant). The presented approach features an accelerated convergence of the partial-wave expansion and allows calculations to be accomplished for nuclear charges lower than previously possible and with a higher numerical accuracy.

physics.atom-ph↗

arXiv2025

Self-energy correction to the E1 transition amplitudes in hydrogen-like ions

We present calculations of the self-energy correction to the $E1$ transition amplitudes in hydrogen-like ions, performed to all orders in the nuclear binding strength parameter. Our results for the $1s$-$2p_{1/2}$ transition for the hydrogen isoelectronic sequence show that the perturbed-orbital part of the self-energy correction provides the dominant contribution, accounting for approximately 99\% of the total correction for this transition. Detailed calculations were performed for $ns$-$n'p$ and $np$-$n'd$ transitions in H-like caesium. We conclude that the perturbed-orbital part remains dominant also for other $ns$-$n'p$ transitions, whereas for the $np$-$n'd$ matrix elements this dominance no longer holds. Consequently, the self-energy corrections for the $np$-$n'd$ one-electron matrix elements cannot be well reproduced by means of effective QED operators constructed for energy levels.

physics.atom-ph↗

arXiv2024

Nonlinear calcium King plot constrains new bosons and nuclear properties

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-Standard-Model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order Standard Model (SM) effects from BSM physics. We measure the IS of the transitions ${{}^{3}P_{0}~\rightarrow~{}^{3}P_{1}}$ in $\mathrm{Ca}^{14+}$ and ${{}^{2}S_{1/2} \rightarrow {}^{2}D_{5/2}}$ in $\mathrm{Ca}^{+}$ with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below $4\times10^{-11}$ for the five stable, even isotopes of calcium (${}^{40,42,44,46,48}\mathrm{Ca}$). Combined, these measurements yield a calcium KP nonlinearity with a significance of $\sim 900 σ$. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between $10~\mathrm{eV/c^2}$ and $10^7~\mathrm{eV/c^2}$.

physics.atom-ph↗

arXiv2024

One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge

Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly hydrogen, these computations are complicated by large numerical cancellations and the slow convergence of the partial-wave expansion. Methods with accelerated convergence of the partial-wave expansion have been recently put forward [V. A. Yerokhin, K. Pachucki, V. M. Shabaev, Phys. Rev. A 72, 042502 (2005); J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023)]. In our work we extend the accelerated-convergence methods to the previously hardly accessible region of nuclear charges $Z < 5$ and higher excited states.

physics.atom-ph↗

arXiv2024

Two-loop electron self-energy for low nuclear charges

Calculations of the two-loop electron self-energy for the $1S$ Lamb shift are reported, performed to all orders in the nuclear binding strength parameter $Zα$ (where $Z$ is the nuclear charge number and $α$ is the fine structure constant). Our approach allows calculations to be extended to nuclear charges lower than previously possible and improves the numerical accuracy by more than an order of magnitude. Extrapolation of our all-order results to hydrogen yields a result twice as precise as the previously accepted value [E. Tiesinga et al. Rev. Mod. Phys. 93, 025010 (2021)], differing from it by 2.8 standard deviations. The resulting shift in the theoretical prediction for the $1S$-$2S$ transition frequency in hydrogen decreases the value of the Rydberg constant by one standard deviation.

physics.atom-ph↗

arXiv2024

QED calculations of the E1 transition amplitude in neon-like iron and nickel

We calculated QED corrections to the $E1$ transition amplitudes in Ne-like iron and nickel. For the $2p \to 3d$ transitions the dominant effect came from the many-electron mixing, or electronic correlations. For the $2p \to 3s$ transitions the correlation and one-electron effects were comparable and tended to compensate each other. Our ab initio calculations showed that vertex corrections were negligible for both types of transitions. Other QED corrections were accurately reproduced by including effective QEDMOD operator in the many-electron relativistic configuration interaction calculation.

physics.atom-ph↗

arXiv2024

QED Corrections in Unstable Vacuum

Self-energy and vacuum polarization effects in quantum electrodynamics (QED) are calculated for the supercritical Coulomb field, where Dirac energy levels become embedded in the negative-energy continuum. In this regime, the quantum vacuum becomes unstable, resulting in spontaneous electron-positron pair creation. By calculating the imaginary part of the QED correction, we gain access to an unexplored channel of vacuum instability: radiative spontaneous pair creation. Our results show that this radiative channel is greatly enhanced in the vicinity of the threshold of the supercritical regime, providing evidence for nonperturbative effects with respect to the fine-structure constant $α$. We therefore conjecture that the total probability of spontaneous pair creation could differ significantly from the predictions of Dirac theory, especially near the supercritical threshold.

physics.atom-ph↗

arXiv2023

Delbrück scattering above the pair production threshold: Going beyond the Born approximation

We present a theoretical method to calculate Delbrück scattering amplitudes for photon energies above the electron-positron pair production threshold. The method is based on the application of the relativistic Dirac-Coulomb Green function and describes the interaction of the virtual $e^+e^-$ pair with the Coulomb field of a target to all orders in the coupling strength parameter $αZ$. 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.

physics.atom-ph↗

arXiv2023

Low-energy tests of Delbrück scattering

We present a theoretical study of elastic photon scattering by atomic targets. This process is of special interest since various channels from atomic and nuclear physics as well as quantum elctrodynamics (QED) contribute to it. In this work, we focus on Delbrück scattering which proceeds via production of virtual $e^+e^-$ pairs. In particular, we explore whether and how the Delbrück channel can be "seen" in present synchrotron experiments which employ strongly linearly polarized light in the energy range of a few hundred keV. In order to answer this question, detailed calculations have been performed for the scattering of 300 keV and 889.2 keV photons off helium-like tin ions. Based on these calculations, we argue that the Delbrück scattering for the energies below the threshold for $e^+e^-$ pair creation leads to a shift in the angular distribution and the polarization of the scattered photons which can be observed by state-of-the-art solid-state detectors.

physics.atom-ph↗

arXiv2023

Stringent test of QED with hydrogenlike tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond $10^{15}\,\text{V}/\text{cm}$ for the innermost electrons. Especially in few-electron highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the last decades. Another approach is the measurement of $g$ factors in highly charged ions. However, so far, either experimental accuracy or small field strength in low-$Z$ ions limited the stringency of these QED tests. Here, we report on our high-precision, high-field test of QED in hydrogenlike $^{118}$Sn$^{49+}$. The highly charged ions were produced with the Heidelberg-EBIT (electron beam ion trap) and injected into the ALPHATRAP Penning-trap setup, where the bound-electron $g$ factor was measured with a precision of 0.5 parts-per-billion. For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about $0.012\,\%$, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests via the Lamb shift and, with anticipated advances in the $g$-factor theory, surpass them by more than an order of magnitude.

physics.atom-ph↗