Interelectronic-interaction Corrections Research Articles

Relativistic Calculation of the Nuclear Recoil Effect on the g Factor of the 2P3/2 State in Highly Charged B-like Ions

The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.

Релятивистский расчёт эффекта отдачи ядра для g-фактора состояния ^2P-=SUB=-3/2-=/SUB=- многозарядных бороподобных ионов

The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.

QED theory of the specific mass shift in few-electron atoms

The quantum electrodynamics formalism to treat the interelectronic-interaction correction of first order in $1/Z$ to the two-electron part of the nuclear recoil effect on binding energies in atoms and ions is developed. The nonperturbative in $\alpha Z$ calculations of the corresponding contribution to the energies of the $1s^2$ state in He-like and the $1s^2 2s$ and $1s^2 2p_{1/2}$ states in Li-like ions are performed in the range $Z=5-100$. The behavior of the two-electron part of the nuclear recoil effect beyond the lowest-order relativistic approximation as $Z$ grows is studied.

Relativistic nuclear-recoil effect on the g factor of highly charged boronlike ions

The nuclear recoil effect on the $g$ factor of the ground state of highly charged B-like ions is studied to first order in the electron-to-nucleus mass ratio $m/M$. The leading one-electron and two-electron recoil contributions are calculated nonperturbatively in the parameter $\alpha Z$ within the rigorous QED formalism. The interelectronic-interaction correction to the nuclear recoil effect is evaluated in the Breit approximation by means of perturbation theory to the first order in $1/Z$. The higher-order interelectronic-interaction corrections are taken into account partially by performing the calculations with the effective screening potential. The results obtained represent the most accurate up-to-date treatment of the nuclear recoil effect on the $g$ factor of highly charged B-like ions in the range $Z = 20$--$92$.

Interelectronic-interaction contribution to the nonlinear Zeeman effect in boronlike ions

Relativistic calculations of the second- and third-order contributions in magnetic field to the Zeeman splitting in boronlike ions are presented for the wide range of nuclear charge numbers $Z=6$--$92$. The interelectronic-interaction correction of the first order in $1/Z$ is evaluated to all orders in $\alpha Z$. The higher-order corrections in $1/Z$ are taken into account approximately by means of effective screening potentials. The obtained results are important for interpretation of experimental data on the Zeeman splitting in boronlike ions, in particular, for the ARTEMIS experiment presently implemented at GSI.

Theory of Bound-Electron g Factor in Highly Charged Ions

The paper presents the current status of the theory of bound-electron g factor in highly charged ions. The calculations of the relativistic, quantum electrodynamics (QED), nuclear recoil, nuclear structure, and interelectronic-interaction corrections to the g factor are reviewed. Special attention is paid to tests of QED effects at strong coupling regime and determinations of the fundamental constants.

Observation of the hyperfine transition in lithium-like bismuthBi20980+: Towards a test of QED in strong magnetic fields

We performed a laser spectroscopic determination of the $2s$ hyperfine splitting (HFS) of Li-like $^{209}\text{Bi}^{80+}$ and repeated the measurement of the $1s$ HFS of H-like $^{209}\text{Bi}^{82+}$. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum f\"ur Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of $\approx 0.71\,c$. Pulsed laser excitation of the $M1$ hyperfine-transition was performed in anticollinear and collinear geometry for $\text{Bi}^{82+}$ and $\text{Bi}^{80+}$, respectively, and observed by fluorescence detection. We obtain $\Delta E^{(1s)}= 5086.3(11)\,\textrm{meV}$ for $\text{Bi}^{82+}$, different from the literature value, and $\Delta E^{(2s)}= 797.50(18)\,\textrm{meV}$ for $\text{Bi}^{80+}$. These values provide experimental evidence that a specific difference between the two splitting energies can be used to test QED calculations in the strongest static magnetic fields available in the laboratory independent of nuclear structure effects. The experimental result is in excellent agreement with the theoretical prediction and confirms the sum of the Dirac term and the relativistic interelectronic-interaction correction at a level of 0.5% confirming the importance of accounting for the Breit interaction.

Interelectronic-interaction effects on the two-photon decay rates of heavy He-like ions

Based on a rigorous quantum electrodynamics (QED) approach, a theoretical analysis is performed for the two-photon transitions in heavy He-like ions. Special attention is paid to the interelectronic-interaction corrections to the decay rates that are taken into account within the two-time Green-function method. Detailed calculations are carried out for the two-photon transitions $2 {}^{1}{S}_{0}\ensuremath{\rightarrow}1 {}^{1}{S}_{0}$ and $2 {}^{3}{S}_{1}\ensuremath{\rightarrow}1 {}^{1}{S}_{0}$ in He-like ions within the range of nuclear numbers $Z=28$--92. The total decay rates together with the spectral distributions are given. The obtained results are compared with experimental values and previous calculations.

Relativistic recoil, electron-correlation, and QED effects on the2pj-2stransition energies in Li-like ions

The relativistic nuclear recoil, higher-order interelectronic-interaction, and screened QED corrections to the transition energies in Li-like ions are evaluated. The calculation of the relativistic recoil effect is performed to all orders in $1/Z$. The interelectronic-interaction correction to the transition energies beyond the two-photon-exchange level is evaluated to all orders in $1/Z$ within the Breit approximation. The evaluation is carried out employing the large-scale configuration-interaction Dirac-Fock-Sturm method. The rigorous calculation of the complete gauge invariant sets of the screened self-energy and vacuum-polarization diagrams is performed utilizing a local screening potential as the zeroth-order approximation. The theoretical predictions for the $2{p}_{j}$-$2s$ transition energies are compiled and compared with available experimental data in the range of the nuclear charge number $Z=10$--60.

QED calculation of interelectron interaction corrections for transition probabilities in two-electron ions

Accurate QED calculations of the transition probabilities between the quasidegen-erate two-electron configurations (1s2p)1P1,3P1 and the ground state (1s1s) 1 S0 (E1 transitions) are presented for highly charged ions with nuclear charge numbers Z = 10- 92. A special technique has been developed to master the bad convergence of the perturbation expansion for the interelectron interaction in the low Z region.

Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions

The ground-state hyperfine splitting values of high- Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1 / Z perturbation theory and the large-scale configuration–interaction Dirac–Fock–Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: 45Sc 16+, 57Fe 21+, 207Pb 77+, and 209Bi 78+. For lead and bismuth the experimental values of the 1 s hyperfine splitting are employed to improve significantly the theoretical results by reducing the uncertainty due to the nuclear effects.

Magnetic-dipole transition probabilities in B-like and Be-like ions

The magnetic-dipole transition probabilities between the fine-structure levels (1s^2 2s^2 2p) ^2P_1/2 - ^2P_3/2 for B-like ions and (1s^2 2s 2p) ^3P_1 - ^3P_2 for Be-like ions are calculated. The configuration-interaction method in the Dirac-Fock-Sturm basis is employed for the evaluation of the interelectronic-interaction correction with negative-continuum spectrum being taken into account. The 1/Z interelectronic-interaction contribution is derived within a rigorous QED approach employing the two-time Green function method. The one-electron QED correction is evaluated within framework of the anomalous magnetic-moment approximation. A comparison with the theoretical results of other authors and with available experimental data is presented.

Evaluation of quasidegenerate energy levels of two-electron configurations for multicharged ions

We present an accurate QED calculation of the interelectron interaction corrections to the energy of the (1s2p)1P1 and (1s2p)3P1 two-electron configurations for ions with nuclear charge 10⩽Z⩽92. When the fully relativistic treatment based on j–j coupling scheme is employed, the corresponding energy levels become quasidegenerate in the region Z⩽40. To evaluate the energies of these configurations within the framework of QED we utilize the line profile approach. The numerical results we have obtained are compared with available experimental data and with different calculations.

G factor of lithiumlike ions

The g factor of Li-like ions in the range Z=6–92 is evaluated. The interelectronic-interaction corrections of order 1/Z2 and higher are taken into account by the configuration-interaction Dirac–Fock method. This result is combined with the 1/Z term derived within a rigorous QED approach. The one-electron QED correction of first order in α is obtained by employing our recent results for the self-energy term and by evaluating the vacuum-polarization term. The screening of the QED effects is calculated to the leading orders in αZ and 1/Z. A significant improvement of the theoretical accuracy of the g-factor values is achieved.

Hyperfine Splitting of Low-Lying Levels in Heavy Li-Like Ions

The magnetic dipole and the electric quadrupole hyperfine splitting in heavy Lilike ions is calculated for the (1s)22p1/2 and (1s)22p3/2 states. The numerical results include the one-electron contributions as well as the interelectronic-interaction correction of order 1/Z, calculated within a rigorous QED approach. Total hyperfine splitting energies are presented for heavy Li-like ions in the range Z = 49–83.

Relativistic and QED corrections to thegfactor 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 correction of first order in $\ensuremath{\alpha}$ is obtained by employing our recent results for the self-energy term and by evaluating the vacuum-polarization contribution. The screening of QED corrections is taken into account to the leading orders in $\ensuremath{\alpha}Z$ and $1∕Z$.

Interelectronic-interaction effect on the transition probability in high-ZHe-like ions

The interelectronic-interaction effect on the transition probabilities in high-$Z$ He-like ions is investigated within a systematic quantum electrodynamic approach. The calculation formulas for the interelectronic-interaction corrections of first order in $1∕Z$ are derived using the two-time Green-function method. These formulas are employed for numerical evaluations of the magnetic transition probabilities in heliumlike ions. The results of the calculations are compared with experimental values and previous calculations.

Calculation of quasidegenerate energy levels of two-electron ions

Accurate QED calculations of the interelectron interaction corrections for the $(1s2p){2}^{1}{P}_{1}$ and $(1s2p){2}^{3}{P}_{1}$ two-electron configurations for ions with nuclear charge numbers $10\ensuremath{\leqslant}Z\ensuremath{\leqslant}92$ are performed within the line profile approach. Total energies of these configurations are evaluated. Employing the fully relativistic treatment based on the $j\ensuremath{-}j$ coupling scheme these energy levels become quasidegenerate in the region $Z\ensuremath{\leqslant}40$. To treat such states within the framework of QED we utilize the line profile approach. The calculations are performed within the Coulomb gauge.

The interelectron interaction corrections to the hyperfine structure of the 2p3/2 state in Li-like, B-like and N-like 20983Bi ions

The lowest-order interelectron interaction corrections to the hyperfine structure intervals for the 2p3/2 state in Li-like, B-like and N-like 20983Bi ions are calculated. The contributions of the magnetic dipole, electric quadrupole and magnetic octupole moments are included. The ‘dynamical’ model of hyperfine interaction is employed, where the electron is assumed to interact with the valence proton in the 20983Bi nucleus via the exchange of a virtual photon. Within this model the magnetic and electric moment distributions inside the nucleus are taken into account simultaneously.

QED Theory of Transition Probabilities and Line Profiles in Highly Charged Ions

A rigorous QED theory of the spectral line profiles is applied to transition probabilities in few-electron highly charged ions. Interelectron interaction corrections are included as well as radiative corrections. Parity nonconserving (PNC) amplitudes with effective weak interactions between the electrons and nucleus are also considered. QED and interelectron interaction corrections to the PNC amplitudes are derived.