Quantum Electrodynamic Corrections Research Articles

Abinitio determination of the polarizability of neon

The static electric-dipole polarizability $\ensuremath{\alpha}$ of the neon atom was determined with a relative uncertainty of only about 0.003% using state-of-the-art ab initio approaches. The new value, $\ensuremath{\alpha}=2.661\phantom{\rule{0.16em}{0ex}}067(77)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, is almost five times more accurate than the previous ab initio estimate, $\ensuremath{\alpha}=2.660\phantom{\rule{0.16em}{0ex}}80(36)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)]. Similar to their work, we calculated $\ensuremath{\alpha}$ using ab initio methods up to full configuration interaction and added corrections for finite nuclear mass and size, relativistic, and quantum electrodynamics (QED) effects. The uncertainty reduction of this work was achieved in particular by employing extremely large basis sets, including newly developed ones of 11Z, 12Z, and 13Z quality. Moreover, the finite nuclear mass effects and most of the relativistic contributions were calculated at much higher levels of theory than in the work of Lesiuk et al. However, we adopted their values for the orbit-orbit part of the relativistic correction and for the Bethe logarithm needed to compute the QED correction. The uncertainty of our final value is still an order of magnitude larger than that of the experimental value recently measured by Gaiser and Fellmuth [Phys. Rev. Lett. 120, 123203 (2018)] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, ${\ensuremath{\alpha}}_{\mathrm{exp}}=2.661\phantom{\rule{0.16em}{0ex}}057(7)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, almost within the experimental uncertainty. This could indicate that the higher-order relativistic corrections and QED contributions, which dominate our uncertainty budget, are more accurate than expected considering the uncontrolled approximations involved in their calculation.

Quantum electrodynamic effects on counter-streaming instabilities in the whole k space.

In a recent work [Bret, EPL 135, 35001 (2021)10.1209/0295-5075/ac1e44], quantum electrodynamic (QED) effects were evaluated for the two-stream instability. It pertains to the growth of perturbations with a wave vector oriented along the flow in a collisionless counter-streaming system. Here, the analysis is extended to every possible orientation of the wave vector. The previous result for the two-stream instability is recovered, and it is proved that, even within the framework of a three-dimensional (3D) analysis, this instability remains fundamentally 1D even when accounting for QED effects. The filamentation instability, found for wave vectors normal to the flow, is weakly affected by QED corrections. As in the classical case, its growth rate saturates at large k_{⊥}. The saturation value is found independent of QED corrections. Also, the smallest unstable k_{⊥} is independent of QED corrections. Surprisingly, unstable modes found for oblique wave vectors do not follow the same pattern. For some, QED corrections do reduce the growth rate. But, for others, the same corrections increase the growth rate instead. The possibility for QED effects to play a role in unmagnetized systems is evaluated. Pair production resulting from γ emission by particles oscillating in the exponentially growing fields is not accounted for.

Calculations of relativistic, correlation, nuclear and quantum-electrodynamics corrections to the energies and ionization potentials of the ground state of lithium-like ions

This paper presents all the leading contributions to the relativistic binding energies and ionization potentials of the ground state of lithium-like ions with a nuclear charge in the range Z=3-20. Correlation, relativistic and quantum-electrodynamics corrections as well as the contributions due to the finite size of the nucleus (the field shift) and finite mass of the nucleus (the recoil effect) are evaluated. Relativistic calculations are performed by means of the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals using the Dirac-Coulomb-Breit Hamiltonian. Keywords: Li-like ions, ionization potential, relativistic calculations, configuration interaction, electron correlations, Breit interaction, field shift, nuclear recoil effect, QED corrections

Расчеты релятивистских, корреляционных, ядерных и квантово-электродинамических поправок к энергиям и потенциалам ионизации основного состояния литиеподобных ионов

This paper presents all the leading contributions to the relativistic total energies and ionization potentials of the ground state of lithium-like ions with a nuclear charge in the range Z = 3 − 20. Correlation, relativistic and quantum-electrodynamics corrections as well as contributions due to the finite size of the nucleus (field shift) and finite mass of the nucleus (recoil effect) are evaluated. Relativistic calculations are performed by means of the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals using the Dirac-Coulomb-Breit Hamiltonian.

QED Effect on the Nuclear Magnetic Shielding of ^{3}He.

The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of ^{1}H, ^{3}He^{+}, and ^{3}He are calculated to be 17.735 436(3)×10^{-6}, 35.507 434(9)×10^{-6}, and 59.967 029(23)×10^{-6}, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of ^{3}He^{+} and planned ^{3}He^{2+}, they open the window for high-precision absolute magnetometry using ^{3}He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.

Energy levels and transition data of 3p63d8 and 3p53d9 configurations in Fe-like ions (Z = 57,60,62,64,65)

Atomic data of highly charged ions (HCIs) offer an attractive means for plasma diagnostic and stars identification, and the investigations on atomic data are highly desirable. Herein, based on the fully relativistic multi-configuration Dirac–Hartree–Fock (MCDHF) method, we have performed calculations of the fine-structure energy levels, wavelengths, transition rates, oscillator strengths, and line strengths for the lowest 21 states of 3p63d8–3p53d9 electric dipole (E1) transitions configurations in Fe-like ions (Z = 57, 60, 62, 64, 65). The correlation effects of valence–valence (VV) and core–valence (CV) electrons were systematically considered. In addition, we have taken into account transverse-photon (Breit) interaction and quantum electrodynamics (QED) corrections to treat accurately the atomic state wave functions in the final relativistic configuration interaction (RCI) calculations. Our calculated energy levels and transition wavelengths are in excellent agreement with the available experimental and theoretical results. Most importantly, we predicted some new transition parameters that have not yet been reported. These data would further provide critical insights into better analyzing the physical processes of various astrophysical plasmas.

Relativistic coupled-cluster calculation of hyperfine-structure constants of Th3+229 and evaluation of the electromagnetic nuclear moments of Th229

$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations are included in coupled-cluster calculation. With the measured value of the hyperfine-structure constants [Phys. Rev. Lett. 106. 223001(2011)], we get the magnetic dipole moment, $\mu=0.359(9)$, and the electric quadrupole moment, $Q=2.95(7)$, of the $^{229}$Th nucleus. Our magnetic dipole moment is perfectly consistent with the recommended values, $\mu=0.360(7)$, from the all-order calculation by Safronova \textit{et. al.}[Phys.Rev.A 88, 060501 (2013)], but our electric quadrupole moment is smaller than their recommended value, $Q=3.11(6)$, about 5\%. Our results show that the non-linear terms of single and double excitations, which were not included in the all-order calculation by Safronova \textit{et. al.}, are very crucial to produce a precise $Q$ value of $^{229}$Th. Additionally, we also present magnetic octupole hyperfine-structure constants and some important non-diagonal hyperfine transition matrix elements, which are required for further extracting the magnetic octupole moment $\Omega$ of $^{229}$Th nucleus.

Benchmark Calculations of the Energy Spectra and Oscillator Strengths of the Beryllium Atom

In this work, we present a series of benchmark variational calculations for the ground and 19 lowest bound excited singlet S and P states of the beryllium atom. The nonrelativistic wave functions of the states that represent the motion of the nucleus and the four electrons around the center of mass of the atom are expanded in terms of up to 17 000 all-particle explicitly correlated Gaussians. The Gaussians are optimized independently for each state. The leading relativistic corrections to the energy levels are computed in the framework of the perturbation theory and they explicitly include the nuclear recoil effects. We also calculate the leading quantum electrodynamics (QED) corrections for each considered state. Using the obtained energy levels and the corresponding wave functions, we compute the transition frequencies, transition dipole moments, and oscillator strengths. A comparison with the available experimental data shows very good agreement. The results of this most comprehensive set of calculations of spectroscopic accuracy for Be to date may open up new applications pertinent to the precision tests of QED, determination of the nuclear charge radius, and modeling matter-radiation equilibria of the beryllium gas that has relevance to the physics of interstellar media.

Shape Resonances in H_{2} as Photolysis Reaction Intermediates.

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30MHz (1.4mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Radiative and photon-exchange corrections to new-physics contributions to energy levels in few-electron ions

The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The $1s$, $2s$ and $2p_{1/2}$ ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It is shown that, for light Li-like and B-like ions, photon-exchange corrections are comparable to or even larger, by up to several orders of magnitude, than the leading one-electron contribution from the new interaction, when the latter is mediated by heavy bosons.

S2 Rydberg spectrum of the boron atom

Benchmark variational calculations of the lowest ten Rydberg $^{2}S$ states of two stable isotopes of the boron atom $(^{10}\mathrm{B} \mathrm{and} ^{11}\mathrm{B})$ are reported. The nonrelativistic wave functions of this five-electron system are expanded in terms of 16 000 all-particle explicitly correlated Gaussians (ECGs). The ECG nonlinear exponential parameters are extensively optimized using a procedure that employs the analytic gradient of the energy with respect to these parameters. A finite nuclear mass value is used in the calculations and the motion of the nucleus is explicitly represented in the nonrelativistic Hamiltonian. The leading relativistic corrections to the energy levels are computed in the framework of the perturbation theory. The lowest-order quantum electrodynamics corrections are also estimated. The results obtained for the energy levels enable determination of interstate transition frequencies with accuracy that approaches the available experimental spectroscopic data.

Relativistic Calculations of the Chemical Properties of the Superheavy Element with Z = 119 and Its Homologues

Relativistic calculations of the electronic structure of the superheavy element of the eighth period $-$ eka-francium ($Z=119$) and its homologues, which form the group of alkali metals, are performed in the framework of the configuration-interaction method and many-body perturbation theory using the basis of the Dirac-Fock-Sturm orbitals (DFS). The obtained values of the ionization potentials, electron affinities, and root-mean-square radii are compared with the corresponding values calculated within the non-relativistic approximation. A comparison with the available experimental data and the results of previous theoretical calculations is given as well. The analysis of the obtained results indicates a significant influence of the relativistic effects for the francium and eka-francium atoms, which leads to a violation of the monotonic behaviour of the listed above chemical properties as a function of the alkaline-element atomic number. In addition, the quantum electrodynamics corrections to the ionization potentials are evaluated by employing the model Lamb-shift operator (QEDMOD).

Fine structure calculations of excitation energies, lifetimes and radiative properties of S-like Kr XXI

Extensive and systematic calculations for energy levels and lifetimes are carried out for the lowest 145 levels arising from the 3s23p4, 3s3p5, 3s23p33d, 3p6, 3s3p43d and 3s23p23 d2 configurations in S-like Kr XXI ion using the multiconfiguration Dirac-Fock (MCDF) method. Additionally, radiative data such as transition wavelengths, absorption oscillator strengths, line strengths and radiative decay rates have also been computed for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground state. The importance of Breit interaction (BI) and quantum electrodynamics (QED) corrections on the energy levels has also been estimated. To assess the credibility and integrity of our MCDF energies, independent calculations using the relativistic configuration interaction (RCI) approach have also been performed. Detailed comparisons are made between our two sets of results, as well as with other existing experimental and theoretical values, and a good agreement is achieved. The present results will be helpful for the modeling and diagnostics of fusion plasmas.

Quantum electrodynamic effects on the two-stream instability

We consider the quantum electrodynamic corrections to the two-stream instability. We find these corrections vanish at first order unless a guiding magnetic field is considered. With respect to the classical version of the instability, quantum electrodynamic effects reduce the most unstable wave vector and its growth rate by a factor , with , where α is the fine-structure constant and B cr the Schwinger critical magnetic field. Although derived for a cold system, these results are valid for the kinetic case. The results are valid in the range and, actually, up to linear corrections in ξ.

Electron affinity of oganesson

The electron affinity (EA) of superheavy element Og is calculated by the use of the relativistic Fock-space coupled cluster (FSCC) and configuration interaction methods. The FSCC cluster operator expansion included single, double, and triple excitations treated in a non-perturbative manner. The Gaunt and retardation electron-electron interactions are taken into account. Both methods yield the results that are in agreement with each other. The quantum electrodynamics correction to EA is evaluated using the model Lamb-shift operator approach. The electron affinity of Og is obtained to be 0.076(4) eV.

Cooling–heating phase transition of the Euler–Heisenberg-AdS black hole

We investigate the cooling–heating phase transition of the Euler–Heisenberg-AdS black hole. First, the black hole thermodynamic quantities and the state equation are reviewed. Then, we research cooling–heating phase transition and further plot the inversion and isenthalpic curves in the T–P plane. Meanwhile, we find that the inversion temperature gradually decreases with the increase of Euler–Heisenberg parameter a for the inversion curves, while this parameter has no effect in the cooling region, and the isenthalpic curves gradually move to the positive direction of X-axis with the increase of Euler–Heisenberg parameter a in the heating region. In particular, the inversion temperature and pressure of this black hole are negative, we deem that this case is caused by the vacuum polarization and the quantum electrodynamics corrections, which makes the electromagnetic energy (repulsion force) produced by the black hole shield the gravity produced by the black hole mass. In addition, this explanation has been mentioned in previous studies [M. Daniela and B. Nora, Phys. Rev. D 102, 084011 (2020); R. Ruffini, Y. B. Wu and S. S. Xue, Phys. Rev. D 88, 085004 (2013)].

Forbidden transitions between the 2p3/2 and 2p1/2 states of ground B-like ions with 14 ≤ Z ≤ 92

The magnetic-dipole M1 and electric quadrupole E2 transition energies and rates between the two fine structure states of 1s22s22p configuration for B-like ions with 14 92 have been calculated using the multi-configuration Dirac-Fock (MCDF) method. The interactions with atomic core have been considered and the core-valence correlation contributions to the level energies are evaluated in the active space approximation. The finite nuclear size, the frequency dependent and independent Breit interaction and quantum electrodynamics (QED) corrections have been included in the calculations. To improve the accuracy of the present data on the forbidden line energies and rates, the QED corrections to the transition energies have been adjusted using QEDMOD code with MCDF wavefunctions. The sensitivity of the transition parameters on the nature of the spin orbitals has been probed by considering two sets of calculations, one with fully relaxed and the other with a common set of radial functions. The present line energies and lifetime of the 2s22p 2 p 3/2 state are found to be in excellent agreement with available experimental and theoretical data.

Relativistic coupled-cluster calculation of the electric dipole polarizability and correlation energy of Cn, Nh+ , and Og: Correlation effects from lighter to superheavy elements

We employ a fully relativistic coupled-cluster theory to calculate the ground-state electric dipole polarizability and electron correlation energy of superheavy elements Cn, Nh$^+$ and Og. To assess the trend of electron correlation as function of $Z$, we also calculate the correlation energies for three lighter homologs--Zn, Cd and Hg; Ga$^+$, In$^+$ and Tl$^+$; Kr, Xe and Rn--for each superheavy elements. The relativistic effects and quantum electrodynamical corrections are included using the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the theory. Furthermore, large bases are used to test the convergence of results. Our recommended values of polarizability are in good agreement with previous theoretical results for all SHEs. From our calculations we find that the dominant contribution to polarizability is from the valence electrons in all superheavy elements. Except for Cn and Og, we observe a decreasing contribution from lighter to superheavy elements from the Breit interaction. For the corrections from the vacuum polarization and self-energy, we observe a trend of increasing contributions with $Z$. From energy calculations, we find that the second-order many-body perturbation theory overestimates the electron correlation energy for all the elements considered in this work.

On the Biot–Savart law of electromagnetism applied to the atomic circulation current *

The law of Biot and Savart, derived by observation of the magnetic field produced by electric current flowing in a macroscopic conductor, is shown to yield the correct expression for the nuclear hyperfine interaction, when applied to the electron circulation current derived for hydrogenic atoms from the theories of Pauli and Dirac, as further developed independently by Darwin, Gordon and Hartree. The law thus applies also on the microscopic scale to the magnetic field generated by the electron probability flux of the various atomic eigenstates, and may clearly be generalised formally for application to many-electron atoms, as outlined by Hartree. The present, fully relativistic, treatment is advantageous in avoiding the usual artificial splitting of the hyperfine interaction into a magnetic dipole–dipole contribution and a separate contribution arising from electron orbital motion. The formula obtained forms the basis for the inclusion of higher order (quantum electrodynamic and nuclear recoil) corrections. Interest in this subject is enhanced by observations of ‘strongly forbidden’ (magnetic dipole) atomic transitions arising from the nuclear magnetic interaction, notably the 21 cm line of hydrogen, which has played an important role in astrophysics, in both measurements of galactic rotation and studies of the early Universe.

Benchmarking calculations with spectroscopic accuracy of level energies and wavelengths in W LVII–W LXII tungsten ions

Atomic properties of n=3 states of the W56+ - W61+ ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈0.01%. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W56+ - W61+ ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.