arXiv subjects

V. A. Yerokhin

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

At least 55 records · Page 3Linked to original sources

arXiv2018

Energy levels of core-excited $1s2l2l'$ states in lithium-like ions: argon to uranium

Energy levels and fine-structure intervals of the $1s2l2l'$ core-excited states are calculated for ions along the Li isoelectronic sequence from argon to uranium. The calculation is performed by the relativistic configuration-interaction method adapted for treatment of autoionizing core-excited states. The calculational approach includes the relativistic treatment of the nuclear recoil effect, the leading QED shifts as delivered by the model QED operator, and the frequency dependence of the Breit interaction. The $1s2l2l'-1s^22l$ transition energies are obtained by combining the present results for the $1s2l2l'$ states with energies of the $1s^22l$ states compiled from previous calculations. All theoretical energies are supplied with uncertainty estimates. Our theoretical predictions for the $1s2l2l'-1s^22l$ transitions are significantly more accurate than the best experimental results available today and can be used for calibrating experimental X-ray spectra.

physics.atom-ph↗

arXiv2018

Theory of the two-loop self-energy correction to the $\boldsymbol g$ factor in non-perturbative Coulomb fields

Two-loop self-energy corrections to the bound-electron $g$ factor are investigated theoretically to all orders in the nuclear binding strength parameter $Zα$. The separation of divergences is performed by dimensional regularization, and the contributing diagrams are regrouped into specific categories to yield finite results. We evaluate numerically the loop-after-loop terms, and the remaining diagrams by treating the Coulomb interaction in the electron propagators up to first order. The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the $g$ factor.

physics.atom-ph↗

arXiv2018

Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions

The two-loop self-energy correction to the Lamb shift of hydrogen-like ions is calculated for the $1s$, $2s$, and $2p_{1/2}$ states and nuclear charge numbers $Z = 30$-$100$. The calculation is performed to all orders in the nuclear binding strength parameter $Zα$. As compared to previous calculations of this correction, numerical accuracy is improved by an order of magnitude and the region of the nuclear charges is extended. An analysis of the $Z$-dependence of the obtained results demonstrates their consistency with the known $Zα$-expansion coefficients.

physics.atom-ph↗

arXiv2018

Access to improve the muon mass and magnetic moment anomaly via the bound-muon $g$ factor

A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude.

hep-ph↗

arXiv2017

Relativistic configuration-interaction calculations of energy levels of the $1s^22l$ and $1s2l2l'$ states in lithium-like ions: carbon through chlorine

We present systematic calculations of energy levels of the $1s^22l$ and $1s2l2l'$ states of ions along the lithium isoelectronic sequence from carbon till chlorine. The calculations are performed by using the relativistic-configuration-interaction method adapted to the treatment of autoionizing core-excited states. The relativistic energies are supplemented with the QED energy shifts calculated within the model QED operator approach. A systematic estimation of the theoretical uncertainties is performed for every electronic state and every nuclear charge. The results are in agreement with existing high-precision theoretical and experimental data for the ground and first excited states. For the core-excited states, our theory is much more accurate than the presently available measurements.

physics.atom-ph↗

arXiv2017

One-loop electron self-energy for the bound-electron $g$ factor

We report calculations of the one-loop self-energy correction to the bound-electron $g$ factor of the $1s$ and $2s$ states of light hydrogen-like ions with the nuclear charge number $Z \le 20$. The calculation is carried out to all orders in the binding nuclear strength. We find good agreement with previous calculations and improve their accuracy by about two orders of magnitude.

physics.atom-ph↗

arXiv2017

Electron-correlation effects in the $g$-factor of light Li-like ions

We investigate electron-correlation effects in the $g$-factor of the ground state of Li-like ions. Our calculations are performed within the nonrelativistic quantum electrodynamics (NRQED) expansion up to two leading orders in the fine-structure constant $α$, $α^2$ and $α^3$. The dependence of the NRQED results on the nuclear charge number $Z$ is studied and the individual $1/Z$-expansion contributions are identified. Combining the obtained data with the results of the all-order (in $Zα$) calculations performed within the $1/Z$ expansion, we derive the unified theoretical predictions for the $g$-factor of light Li-like ions.

physics.atom-ph↗

arXiv2017

Higher-order recoil corrections for singlet states of the helium atom

We investigate the finite nuclear mass corrections in the helium atom in order to resolve a significant disagreement between the $2^3S - 2^3P$ and $2^3S - 2^1S$ transition isotope shifts. These two transitions lead to discrepant results for the nuclear charge radii difference between $^4$He and $^3$He. The accurate treatment of the finite nuclear mass effects is quite complicated and requires the use of the quantum field theoretical approach. We derive $α^6 m^2/M$ correction with the help of nonrelativistic QED and dimensional regularization of the three body Coulombic system, and present accurate numerical results for low lying states. The previously reported $4 σ$ discrepancy in the nuclear charge radius difference between $^3$He and $^4$He from two different atomic isotope shift transitions is confirmed, which calls for verification of experimental transition frequencies.

physics.atom-ph↗

arXiv2016

Higher-order recoil corrections for triplet states of the helium atom

Nuclear recoil corrections of order $α^6\,m^2/M$ are calculated for the lowest-lying triplet states of the helium atom. It improves the theoretical prediction for the isotope shift of the $2^3S-2^3P$ transition energy and influences the determination of the ${}^3\textrm{He}-{}^4\textrm{He}$ nuclear charge radii difference. This calculation is a step forward on the way towards the direct determination of the charge radius of the helium nucleus from spectroscopic measurements.

physics.atm-clus↗

arXiv2016

Muonic vacuum polarization correction to the bound-electron $g$-factor

The muonic vacuum polarization contribution to the $g$-factor of the electron bound in a nuclear potential is investigated theoretically. The electric as well as the magnetic loop contributions are evaluated. We found these muonic effects to be observable in planned trapped-ion experiments with light and medium-heavy highly charged ions. The enhancement due to the strong Coulomb field boosts these contributions much above the corresponding terms in the free-electron $g$-factor. Due to their magnitude, muonic vacuum polarization terms are also significant in planned determinations of the fine-structure constant from the bound-electron $g$-factor.

physics.atom-ph↗

arXiv2016

Unexpectedly large difference of the electron density at the nucleus in the 4p $^2$P$_{1/2,3/2}$ fine-structure doublet of Ca$^+$

We measured the isotope shift in the $^2$S$_{1/2}$-$^2$P$_{3/2}$ (D2) transition in singly-ionized calcium ions using photon recoil spectroscopy. The high accuracy of the technique enables us to resolve the difference between the isotope shifts of this transition to the previously measured isotopic shifts of the $^2$S$_{1/2}$-$^2$P$_{1/2}$ (D1) line. This so-called splitting isotope shift is extracted and exhibits a clear signature of field shift contributions. From the data we were able to extract the small difference of the field shift coefficient and mass shifts between the two transitions with high accuracy. This J-dependence is of relativistic origin and can be used to benchmark atomic structure calculations. As a first step, we use several ab initio atomic structure calculation methods to provide more accurate values for the field shift constants and their ratio. Remarkably, the high-accuracy value for the ratio of the field shift constants extracted from the experimental data is larger than all available theoretical predictions.

physics.atom-ph↗

arXiv2016

Electric dipole polarizabilities of Rydberg states of alkali atoms

Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali atoms, Rb and Cs, for the $nS$, $nP_{1/2, 3/2}$, and $nD_{3/2, 5/2}$ states with large principal quantum numbers up to $n = 50$. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semi-empirical core-polarization potential. The obtained results are compared with those from a simpler semi-empirical approach and with available experimental data.

physics.atom-ph↗

arXiv2016

Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogen-like ions

Accurate calculations of the nuclear recoil effect to the Lamb shift of hydrogen-like atoms are presented. Numerical results are reported for the $ns$ states with $n \leq 5$ and for the $2p_{1/2}$ and $2p_{3/2}$ states. The calculations are performed to the first order in the electron-nucleus mass ratio and 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 obtained results provide accurate predictions for the higher-order remainder beyond the known $Zα$-expansion terms. In the case of hydrogen, the remainder was found to be much larger than anticipated. This result resolves the previously reported disagreement between the numerical all-order and the analytical $Zα$-expansion approaches for the nuclear recoil effect in the hydrogen Lamb shift.

physics.atom-ph↗

arXiv2016

Weighted difference of g-factors of light Li-like and H-like ions for an improved determination of the fine-structure constant

A weighted difference of the $g$-factors of the Li- and H-like ion of the same element is studied and optimized in order to maximize the cancellation of nuclear effects. To this end, a detailed theoretical investigation is performed for the finite nuclear size correction to the one-electron $g$-factor, the one- and two-photon exchange effects, and the QED effects. The coefficients of the $Zα$ expansion of these corrections are determined, which allows us to set up the optimal definition of the weighted difference. It is demonstrated that, for moderately light elements, such weighted difference is nearly free from uncertainties associated with nuclear effects and can be utilized to extract the fine-structure constant from bound-electron $g$-factor experiments with an accuracy competitive with or better than its current literature value.

physics.atom-ph↗

arXiv2016

The $g$-factor of light ions for an improved determination of the fine-structure constant

A weighted difference of the $g$-factors of the H- and Li-like ions of the same element is theoretically studied and optimized in order to maximize the cancelation of nuclear effects between the two charge states. We show that this weighted difference and its combination for two different elements can be used to extract a value for the fine-structure constant from near-future bound-electron $g$-factor experiments with an accuracy competitive with or better than the present literature value.

physics.atom-ph↗

arXiv2016

Many-electron effects on the x-ray Rayleigh scattering by highly charged He-like ions

The Rayleigh scattering of x-rays by many-electron highly charged ions is studied theoretically. The many-electron perturbation theory, based on a rigorous quantum electrodynamics approach, is developed and implemented for the case of the elastic scattering of (high-energetic) photons by helium-like ion. Using this elaborate approach, we here investigate the many-electron effects beyond the independent-particle approximation (IPA) as conventionally employed for describing the Rayleigh scattering. The total and angle-differential cross sections are evaluated for the x-ray scattering by helium-like Ni$^{26+}$, Xe$^{52+}$, and Au$^{77+}$ ions in their ground state. The obtained results show that, for high-energetic photons, the effects beyond the IPA do not exceed 2% for the scattering by a closed $K$-shell.

physics.atom-ph↗

arXiv2015

Nuclear recoil effect in the Lamb shift of light hydrogen-like atoms

We report high-precision calculations of the nuclear recoil effect to the Lamb shift of hydrogen-like atoms to the first order in the electron-nucleus mass ratio and to all orders in the nuclear binding strength parameter $Zα$. The results are in excellent agreement with the known terms of the $Zα$ expansion and allow an accurate identification of the nonperturbative higher-order remainder. For hydrogen, the higher-order remainder was found to be much larger than anticipated. This result resolves the long-standing disagreement between the numerical all-order and the analytical $Zα$-expansion approaches to the recoil effect and completely removes the second-largest theoretical uncertainty in the hydrogen Lamb shift of the $1S$ and $2S$ states.

physics.atom-ph↗

arXiv2015

Target effects in negative-continuum assisted dielectronic recombination

The process of recombination of a quasi-free electron into a bound state of an initially bare nucleus with the simultaneous creation of a bound-electron--free-positron pair is investigated. This process is called the negative-continuum assisted dielectronic recombination (NCDR). In a typical experimental setup, the initial electron is not free but bound in a light atomic target. In the present work, we study the effects of the atomic target on the single and double-differential cross sections of the positron production in the NCDR process. The calculations are performed within the relativistic framework based on QED theory, with accounting for the electron-electron interaction to first order in perturbation theory. We demonstrate how the momentum distribution of the target electrons removes the non-physical singularity of the differential cross section which occurs for the initially free and monochromatic electrons.

physics.atom-ph↗