arXiv subjects

Vladimir A. Yerokhin

Publications and source records attributed to Vladimir A. Yerokhin.

At least 37 records · Page 2Linked to original sources

arXiv2023

QED theory of the nuclear recoil with finite size

We investigate the modification of the transverse electromagnetic interaction between two point-like 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 $Z\,α$. Numerical calculations are carried out for a wide range of $Z$ and verified against the $(Z\,α)^5$ contribution. The comparison with the $Z\,α$ expansion identifies the contribution of order $(Z\,α)^6$, which is linear in the nuclear radius and numerically dominates over the lower-order $(Z\,α)^5$ term.

physics.atom-ph↗

arXiv2022

QED $mα^7$ effects for triplet states of helium-like ions

We perform ab initio calculations of the QED effects of order $mα^7$ for the $2^3S$ and $2^3P$ states of He-like ions. The computed effects are combined with previously calculated energies from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], thus improving the theoretical accuracy by an order of magnitude. The obtained theoretical values for the $2^3S$-$2^3P_{0,2}$ transition energies are in good agreement with available experimental results and with previous calculations performed to all orders in the nuclear binding strength parameter $Zα$. For the ionization energies, however, we find some inconsistency between the $Zα$-expansion and all-order calculations, which might be related to a similar discrepancy between the theoretical and experimental results for the ionization energies of helium [V. Patkóš et al., Phys. Rev. A 103, 042809 (2021)].

physics.atom-ph↗

arXiv2022

Relativistic Bethe logarithm for triplet states of helium-like ions

We report a calculation of relativistic corrections of order $mα^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the $mα^7$ effects in helium performed in [V. Patkóš, V. A. Yerokhin, K. Pachucki, Phys. Rev. A 103, 042809 (2021)], where a significant discrepancy with experimental results was found. The large-$Z$ limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results obtained from the hydrogen theory.

physics.atom-ph↗

arXiv2022

QED calculations of energy levels of helium-like ions with $5 \leq Z \leq 30$

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Zα$ is presented for the ground and $n = 2$ excited states of helium-like ions. After subtracting the first terms of the $Zα$ expansion from the all-order results, we identify the higher-order QED effects of order $mα^7$ and higher. Combining the higher-order remainder with the results complete through order $mα^6$ from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and non-mixing $n=2$ states of helium-like ions with $Z = 5-30$. For the mixing $2^1 P_1$ and $2^3 P_1$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z > 10$.

physics.atom-ph↗

arXiv2021

Nonlinearities of King's plot and their dependence on nuclear radii

Investigations of isotope shifts of atomic spectral lines provide insights into nuclear properties. Deviations from the linear dependence of the isotope shifts of two atomic transitions on nuclear parameters, leading to a nonlinearity of the so-called King plot, are actively studied as a possible way of searching for the new physics. In the present work we calculate the King-plot nonlinearities originating from the Standard-Model atomic theory. The calculation is performed both analytically, for a model example applicable for an arbitrary atom, and numerically, for one-electron ions. It is demonstrated that the Standard-Model predictions of the King-plot nonlinearities are hypersensitive to experimental errors of nuclear charge radii. This effect significantly complicates identifications of possible King-plot nonlinearities originating from the new physics.

physics.atom-ph↗

arXiv2021

Atomic structure calculations of helium with correlated exponential functions

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 $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ 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 $α^5m$ (where $m$ is the electron mass) are complemented with the systematic treatment of higher-order $α^6m$ and $α^7m$ QED effects.

physics.atom-ph↗

arXiv2021

Complete $α^7\,m$ Lamb shift of helium triplet states

We have derived the complete formula for the $α^7\,m$ contribution to energy levels of an arbitrary triplet state of the helium atom, performed numerical calculations for the $2^3S$ and $2^3P$ states, and thus improved the theoretical accuracy of ionization energies of these states by more than an order of magnitude. Using the nuclear charge radius extracted from the muonic helium Lamb shift, we obtain the theoretical prediction in excellent agreement with the measured $2^3S - 2^3P$ transition energy [X.~Zheng et al., Phys. Rev. Lett. {\bf 199}, 263002 (2017)]. At the same time we observe significant discrepancies with experiments for the $2^3S- 3^3D$ and $2^3P - 3^3D$ transitions.

physics.atom-ph↗

arXiv2021

Nonradiative $α^7m$ QED effects in Lamb shift of helium triplet states

Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $α^7m$, where $α$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons, and the nucleus. The complete calculation of the $α^7m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and muonic helium atoms and thus provide a stringent test of the Standard Model of fundamental interactions.

hep-ph↗

arXiv2021

Relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states of He

With this work we start a project of calculating the QED contribution of order $α^7m$ to the $2^3P$-$2^3S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states, which is the most numerically demanding part of the project.

physics.atom-ph↗

arXiv2021

Radiative $\bm{α^7m}$ QED contribution to the helium Lamb shift

We present a derivation of the last unknown part of the $α^7m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S = 1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the $α^7m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.

physics.atom-ph↗

arXiv2020

QED calculation of the $\bf{2p}$ fine structure in Li-like ions

Large-scale {\em ab initio} QED calculations are performed for the $2p_{3/2}$--$2p_{1/2}$ fine-structure interval of Li-like ions with nuclear charges $Z = 5\,$--$\,92$. Improved theoretical predictions are obtained by combining together two complementary theoretical methods, namely, the approach that accounts for all orders in the binding nuclear strength and the nonrelativistic QED approach that accounts for all orders in the nonrelativistic electron-electron interaction. The resulting unified approach provides theoretical predictions which are more accurate than the available experimental results across the interval of the nuclear charges considered.

physics.atom-ph↗

arXiv2020

QED calculation of ionization energies of $1snd$ states in helium

Quantum electrodynamical (QED) calculations of ionization energies of the $1snd\,D$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $mα^5$ and extend the theory by calculating the complete $mα^6$ correction. The total contribution of the $mα^6$ effects is shown to be much smaller than previously estimated, due to a large cancelation between the radiative and non-radiative parts of this correction. As a result of our calculations, we confirm the previously reported deviations between measured transition energies and theoretical predictions for the $nD$--$2S$ and $nD$--$2P$ transitions. Possible reasons for this discrepancy are analyzed.

physics.atom-ph↗

arXiv2020

High Resolution Photoexcitation Measurements Exacerbate the Long-Standing Fe XVII Oscillator Strength Problem

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.

physics.atom-ph↗

arXiv2020

Calculations of QED effects with the Dirac Green function

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 has to be performed without any expansion in the nuclear binding strength parameter $Zα$ (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.

physics.atom-ph↗

arXiv2020

Atomic physics studies at the Gamma Factory at CERN

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 $10^{17}$ 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 afforded 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.

physics.atom-ph↗

arXiv2019

Equation of motion for a bound system of charged particles

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.

physics.atom-ph↗

arXiv2019

Quantum electrodynamic corrections to the $1s3d$ states of the helium atom

We perform quantum electrodynamic calculations of the ionization energy of the $1s3d$ states of the $^4$He atom, including a complete evaluation of the $mα^6$ correction. We find a large contribution from the nonradiative part of this correction, which has not been accounted for in previous investigations. The additional contribution shifts theoretical predictions for ionization energies by about 10$\,σ$. Despite this shift, we confirm the previously reported systematic deviations between measured experimental results and theoretical predictions for transitions involving $3D$ states. The reason for these deviations remains unknown.

physics.atom-ph↗

arXiv2018

Nuclear-structure corrections to the hyperfine splitting in muonic deuterium

Nuclear structure corrections of orders $Zα\, E_F$ and $(Zα)^2 E_F$ are calculated for the hyperfine splitting of the muonic deuterium. The obtained results disagree with previous calculations and lead to a $5\,σ$ disagreement with the current experimental value of the $2S$ hyperfine splitting in $μ$D.

physics.atom-ph↗