arXiv subjects

Vladimir A. Yerokhin

Publications and source records attributed to Vladimir A. Yerokhin.

52 records · Page 3Linked to original sources

arXiv2018

Theory of the Lamb shift in hydrogen and light hydrogen-like ions

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 reduced 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. We review the present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge number up to $Z = 5$. Theoretical errors due to various effects are critically examined and estimated.

physics.atom-ph↗

arXiv2018

Three-photon exchange nuclear structure correction in hydrogenic systems

The complete relativistic $O(α^2)$ nuclear structure correction to the energy levels of ordinary (electronic) and muonic hydrogen-like atoms is investigated. The elastic part of the nuclear structure correction is derived analytically. The resulting formula is valid for an arbitrary hydrogenic system and is much simpler than analogous expressions previously reported in the literature. The analytical result is verified by high-precision numerical calculations. The inelastic $O(α^2)$ nuclear structure correction is derived for the electronic and muonic deuterium atoms. The correction comes from a three-photon exchange between the nucleus and the bound lepton and has not been considered in the literature so far. We demonstrate that in the case of deuterium, the inelastic three-photon exchange contribution is of a similar size and of the opposite sign to the corresponding elastic part and, moreover, cancels exactly the model dependence of the elastic part. The obtained results affect the determination of nuclear charge radii from the Lamb shift in ordinary and muonic atoms.

physics.atom-ph↗

arXiv2015

Theory of the helium isotope shift

Theory of the isotope shift of the centroid energies of light few-electron atoms is reviewed. Numerical results are presented for the isotope shift of the $2^3P$-$2^3S$ and $2^1S$-$2^3S$ transition energies of $^3$He and $^4$He. By comparing theoretical predictions for the isotope shift with the experimental results, the difference of the squares of the nuclear charge radii of $^3$He and $^4$He, $δR^2$, is determined with high accuracy.

physics.atom-ph↗

arXiv2010

Helium fine structure theory for determination of α

We present recent progress in the calculation of the helium fine-structure splitting of the 2^3P_J states, based on the quantum electrodynamic theory. Apart from the complete evaluation of mα^7 and m^2/Mα^6 corrections, we have performed extensive tests by comparison with all experimental results for light helium-like ions and with the known large nuclear charge asymptotics of individual corrections. Our theoretical predictions are still limited by the unknown mα^8 term, which is conservatively estimated to be 1.7 kHz. However, comparison with the latest experimental result for the 2^3P_0 - 2^3P_2 transition [M. Smiciklas and T. Shiner, Phys. Rev. Lett. 105, 123001 (2010)] suggests that the higher-order contribution is in fact much smaller than the theoretical estimate. This means that the spectroscopic determination of αcan be significantly improved if another measurement of the 2^3P_0 - 2^3P_2 transition in helium-like Li^+ or Be^{2+} ion is performed.

physics.atom-ph↗

arXiv2010

Fine structure of helium and light helium-like ions

Calculational results are presented for the fine-structure splitting of the 2^3P state of helium and helium-like ions with the 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 2^3P_0-2^3P_1 interval in helium with the experimental result [T. Zelevinsky et al. Phys. Rev. Lett. 95, 203001 (2005)], we determine the value of the fine-structure constant αwith an accuracy of 31 parts per billion.

physics.atom-ph↗

arXiv2010

Nuclear size correction to the Lamb shift of one-electron atoms

The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p_{1/2}, and 2p_{3/2} states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Zα. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Zα. Extrapolation of the all-order numerical results obtained towards Z=1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.

physics.atom-ph↗

arXiv2010

Electron-atom bremsstrahlung: double differential cross section and polarization correlations

The leading-order electron-atom bremsstrahlung is investigated within the rigorous relativistic approach based on the partial-wave representation of the Dirac wave functions in the external atomic field. Approximating the atomic target by an effective local potential, we calculate the double-differential cross section and the polarization correlations in a wide range of the impact energies. Connection between the bremsstrahlung at the hard-photon end point of the spectrum and the continuum-threshold limit of the radiative recombination is studied. A detailed analysis of the screening effect and the energy dependence of the polarization correlations is presented, with the main focus on the high impact energy region.

physics.atom-ph↗

arXiv2010

The off-resonant dielectronic recombination in a collision of an electron with a heavy hydrogen-like ion

The recombination of an electron with an (initially) hydrogen-like ion is investigated. The effect of the electron-electron interaction is treated rigorously to the first order in the parameter 1/Z and within the screening-potential approximation to higher orders in 1/Z, with Z being the nuclear charge number. The two-electron correction contains the dielectronic-recombination part, which contributes to the process not only under the resonance condition for the projectile energy but also in the regions far from resonances. The mechanism of the off-resonant dielectronic recombination is studied in detail.

physics.atom-ph↗

arXiv2010

Theoretical energies of low-lying states of light helium-like ions

Rigorous quantum electrodynamical calculation is presented for energy levels of the 1^1S, 2^1S, 2^3S, 2^1P_1, and 2^3P_{0,1,2} states of helium-like ions with the nuclear charge Z=3...12. The calculational approach accounts for all relativistic, quantum electrodynamical, and recoil effects up to orders mα^6 and m^2/Mα^5, thus advancing the previously reported theory of light helium-like ions by one order in α.

physics.atom-ph↗

arXiv2010

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 α^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.

physics.atom-ph↗

arXiv2010

The two-loop self-energy: diagrams in the coordinate-momentum representation

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Zα) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.

physics.atom-ph↗

arXiv2009

Self-energy correction to the hyperfine splitting and the electron g factor in hydrogen-like ions

The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Accurate numerical values for the remainder functions are provided for 2P states and for nS states with n=1,2,3.

physics.atom-ph↗

arXiv2006

Quantum electrodynamic corrections to the hyperfine structure of excited S states

State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of nS states for arbitrary principal quantum number n. The calculations comprise both the self-energy and the vacuum-polarization correction of order alpha(Z alpha)^2 E_F and the recoil correction of order (Z alpha)^2 (m/M) E_F. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of nS states with n=2,...,8 are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions involving highly excited S states.

physics.atom-ph↗

arXiv2005

Complete two-loop correction to the bound-electron g factor

Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(α/π)^2 (Z α)^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.

physics.atom-ph↗

arXiv2005

One-loop self-energy correction in a strong binding field

A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z αis presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a partial-wave expansion that converges more rapidly than in the other methods reported in the literature.

physics.atom-ph↗

arXiv2000

Leading logarithmic contribution to the second-order Lamb shift induced by the loop-after-loop diagram

Contribution of order α^2 (Z α)^6 \ln^3(Z α)^{-2} to the ground-state Lamb shift in hydrogen induced by the loop-after-loop diagram is evaluated analytically. An additional contribution of this order is found compared to the previous calculation by Karshenboim [JETP 76, 541 (1993)]. As a result, an agreement is achieved for this correction between different numerical and analytical methods.

hep-ph↗