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V. M. Shabaev

Publications and source records attributed to V. M. Shabaev.

At least 181 records · Page 10Linked to original sources
arXiv2004

Relativistic and QED corrections to the g factor of Li-like ions

Calculations of various corrections to the g factor of Li-like ions are presented, which result in a significant improvement of the theoretical accuracy in the region Z = 6-92. The configuration-interaction Dirac-Fock method is employed for the evaluation of the interelectronic-interaction correction of order 1/Z^2 and higher. This correction is combined with the 1/Z interelectronic-interaction term derived within a rigorous QED approach. The one-electron QED corrections of first in αare calculated to all orders in the parameter αZ. The screening of QED corrections is taken into account to the leading orders in αZ and 1/Z.

physics.atom-ph↗
arXiv2003

Dual kinetic balance approach to basis set expansions for the Dirac equation

A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.

physics.atom-ph↗
arXiv2003

Relativistic calculations of isotope shifts in highly charged ions

The isotope shifts of forbidden transitions in Be- and B-like argon ions are calculated. It is shown that only using the relativistic recoil operator can provide a proper evaluation of the mass isotope shift, which strongly dominates over the field isotope shift for the ions under consideration. Comparing the isotope shifts calculated with the current experimental uncertainties indicates very good perspectives for a first test of the relativistic theory of the recoil effect in middle-Z ions.

physics.atom-ph↗
arXiv2002

Virial relations for the Dirac equation and their applications to calculations of H-like atoms

Virial relations for the Dirac equation in a central field and their applications to calculations of H-like atoms are considered. It is demonstrated that using these relations allows one to evaluate various average values for a hydrogenlike atom. The corresponding relations for non-diagonal matrix elements provide an effective method for analytical evaluations of infinite sums that occur in calculations based on using the reduced Coulomb-Green function. In particular, this method can be used for calculations of higher-order corrections to the hyperfine splitting and to the g factor in hydrogenlike atoms.

physics.atom-ph↗
arXiv2002

Self-energy correction to the bound-electron g factor in H-like ions

The one-loop self-energy correction to the 1s electron g factor is evaluated to all orders in Zαwith an accuracy, which is essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [Beier et al. Phys. Rev. Lett. 88, 011603 (2002)]. The new value of the electron mass is found to be m_e = 0.000 548 579 909 3(3) u.

hep-ph↗
arXiv2001

Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.

physics.atom-ph↗
arXiv2001

Recoil correction to the bound-electron g factor in H-like atoms to all orders in $αZ$

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $αZ$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(αZ)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(αZ)^4$ term, while for uranium it is above the leading $(αZ)^2$ correction.

physics.atom-ph↗
arXiv2001

Finite nuclear size correction to the bound-electron g factor in a hydrogenlike atom

The finite nuclear size correction to the bound-electron g factor in hydrogenlike atoms is investigated in the range Z=1-20. An analytical formula for this correction which includes the non-relativistic and dominant relativistic contributions is derived. In the case of the 1s state, the results obtained by this formula are compared with previous non-relativistic analytical and relativistic numerical calculations.

physics.atom-ph↗
arXiv2001

Two-loop self-energy correction in H-like ions

A part of the two-loop self-energy correction, the so-called P term, is evaluated numerically for the 1s state to all orders in Zα. Our calculation, combined with the previous investigation [S. Mallampalli and J. Sapirstein, Phys. Rev. A 57, 1548 (1998)], yields the total answer for the two-loop self-energy correction in H-like uranium and bismuth. As a result, the major uncertainty is eliminated from the theoretical prediction for the Lamb shift in these systems. The total value of the ground-state Lamb shift in H-like uranium is found to be 463.93(50) eV.

physics.atom-ph↗
arXiv2001

QED theory of the nuclear recoil effect on the atomic g factor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in αZ and to first order in m/M is formulated. The complete αZ-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (αZ)^2 m/M for an arbitrary state of a hydrogenlike atom.

physics.atom-ph↗
arXiv2001

One-loop self-energy correction to the 1s and 2s hyperfine splitting in H-like systems

The one-loop self-energy correction to the hyperfine splitting of the 1s and 2s levels in H-like low-Z atoms is evaluated to all orders in Zα. The results are compared to perturbative calculations. The residual higher-order contribution is evaluated. Implications to the specific difference of the hyperfine structure intervals 8Δν_2 - Δν_1 in He^+ are investigated.

hep-ph↗
arXiv2000

The two-time Green's Function and screened Self-Energy for two-electron quasi-degenerate States

Precise predictions of atomic energy levels require the use of QED, especially in highly-charged ions, where the inner electrons have relativistic velocities. We present an overview of the two-time Green's function method; this method allows one to calculate level shifts in two-electron highly-charged ions by including in principle all QED effects, for any set of states (degenerate, quasi-degenerate or isolated).

physics.atom-ph↗
arXiv2000

Relativistic recoil corrections to the atomic energy levels

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in αZ and to first order in m/M is considered. The complete αZ - dependence formulas for the relativistic recoil corrections to the atomic energy levels are derived in a simple way. The results of numerical calculations of the recoil effect to all orders in αZ are presented for hydrogenlike and lithiumlike atoms. These results are compared with analytical results obtained to lowest orders in αZ. It is shown that even for hydrogen the numerical calculations to all orders in αZ provide most precise theoretical predictions for the relativistic recoil correction of first order in m/M.

physics.atom-ph↗
arXiv1998

Transition energy and lifetime for the ground state hyperfine splitting of high Z lithiumlike ions

The ground state hyperfine splitting values and the transition probabilities between the hyperfine structure components of high Z lithiumlike ions are calculated in the range $Z=49-83$. The relativistic, nuclear, QED and interelectronic interaction corrections are taken into account. It is found that the Bohr-Weisskopf effect can be eliminated in a combination of the hyperfine splitting values of the hydrogenlike and lithiumlike ions of an isotope. This gives a possibility for testing the QED effects in a combination of the strong electric and magnetic fields of the heavy nucleus. Using the experimental result for the $1s$ hyperfine splitting in ^{209}Bi^{82+}, the 2s hyperfine splitting in ^{209}Bi^{80+} is calculated to be ΔE=0.7969(2) eV.

physics.atom-ph↗
arXiv1997

Recoil correction to the ground state energy of hydrogenlike atoms

The recoil correction to the ground state energy of hydrogenlike atoms is calculated to all orders in αZ in the range Z = 1-110. The nuclear size corrections to the recoil effect are partially taken into account. In the case of hydrogen, the relativistic recoil correction beyond the Salpeter contribution and the nonrelativistic nuclear size correction to the recoil effect, amounts to -7.2(2) kHz. The total recoil correction to the ground state energy in hydrogenlike uranium (^{238}U^{91+}) constitutes 0.46 eV.

physics.atom-ph↗