Quantum Electrodynamic Corrections Research Articles

Relativistic calculations for total energies, ionization energies, and one-electron binding energies for Neodymium ions Nd I to Nd[formula omitted]

We present the results of calculations for the total energies, ionization energies, and one-electron binding energies for ground-state configurations of neodymium ions Nd I to Nd59+. These calculations are based on the Dirac–Fock approximation taking the Breit and quantum electrodynamics corrections into account. The configuration interaction method, taking into account all relativistic configurations corresponding to the non-relativistic one, is used to obtain total energies and wave functions in the intermediate coupling scheme. Comparison is given with other available data.

Nonlinear electrodynamics for the vacuum of Dirac materials: Photon magnetic properties and radiation pressures

We investigate the magnetic properties of photons propagating through Dirac materials in a magnetic field, considering both vacuum and medium contributions. Photon propagation properties are obtained through a second-order expansion of nonlinear Euler-Heisenberg electrodynamics at finite density and temperature considering Dirac material parameters (Dirac fine structure constant, band gap, and Fermi velocity). Total magnetization (including electron and photon contributions) and photon-effective magnetic moment are computed. Observables such as photon energy density, radiation pressure, and Poynting vector are obtained by an average of components of the energy-momentum tensor. All quantities are expressed in terms of Lagrangian derivatives. Those related to the vacuum are valid for any value of the external magnetic field, and both the weak- and strong-field limits are recovered. We discuss some ideas of experiments that may contribute to testing in Dirac materials the phenomenology of the strong magnetic field in the quantum electrodynamic (QED) vacuum and how nonlinear corrections on the magnetization, radiation pressure, and birefringence are amplified up to 103 times QED corrections. Published by the American Physical Society 2024

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

High-precision Transition Energy Measurements of Neon-like Fe xvii Ions

We improve by a factor of 4–20 the energy accuracy of the strongest soft X-ray transitions of Fe xvii ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10–15 meV, or velocity equivalent ±∼5 km s−1 in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than 4 million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and the development of optical clocks with highly charged ions.

One-Particle Operator Representation over Two-Particle Basis Sets for Relativistic QED Computations.

This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two-particle, "explicitly correlated" basis representation necessary for good numerical convergence of the interaction energy. It is demonstrated that a faithful representation of the one-particle operators, which appear in intermediate but essential computational steps, can be constructed over a many-particle basis set by accounting for the full Hilbert space beyond the physically relevant antisymmetric subspace. Applications of this development can be foreseen for the computation of quantum-electrodynamics corrections for a correlated relativistic reference state and high-precision relativistic computations of medium-to-high-Z helium-like systems, for which other two-particle projection techniques are unreliable.

Relativistic atomic structure calculations of Li-like ions used for plasma diagnostic studies

We have carried out atomic structure calculations using systematically enlarged multiconfiguration Dirac-Fock wavefunctions of Li-like ions of the most prominent plasma impurities (Ar, Ti, Fe, Ni, Kr and W) found in presently working tokamaks. Relativistic Breit interaction and quantum electrodynamic (QED) corrections such as vacuum polarization and self-energy corrections are also included in the calculations prior to the evaluation of low lying energy levels, transition probabilities, oscillator strengths and line strengths. Selective radiative data for electric dipole and magnetic quadrupole transitions are also reported. Special emphasis is given in the computations of fundamental quantities such as oscillator strengths as they are widely used in atomic data and analysis structure (ADAS) databases to evaluate quantities such as effective collision strengths. Present computed values are compared with existing available results on NIST database and few similar earlier computations and a good agreement has been found. We believe that the detailed atomic data with the relativistic and QED corrections will assist in spectroscopic studies such as accurate line identification and plasma modelling work in tokamak plasma, laser induced breakdown spectroscopy (LIBS), highly charged ions clocks and astrophysical observations.

Relativistic configuration-interaction calculations on K α X-ray satellites of medium-charge Be-like ions

This study puts forward a calculation of the transitions of 1s2s22p 1P1−1s22s2 1S0 and 1s2s22p 3P1−1s22s2 1S0 for Be-like ions (Z = 6–30) using the multiconfiguration Dirac-Hartree–Fock (MCDHF) and relativistic configuration interaction methods. The computational results include transition wavelengths, transition probabilities, line strengths, and weighted oscillator strengths. The calculations also consider the contributions of the Breit interaction and quantum electrodynamics corrections (QED) to these levels. The results show that the contribution of the Breit interaction, self-energy, and vacuum polarization increase rapidly with increasing nuclear charge for certain configurations. The present calculated values are in good agreement with previous theoretical and experimental results, with errors better than 0.3%. A V/A L comparisons demonstrate the reliability of the data.

Theoretical investigation of magnetic-field and hyperfine-induced transition parameters for magnesium-like and chlorine-like ions

In this paper, we report an extensive theoretical study of the magnetic-field and hyperfine-induced transition parameters for magnesium-like ions from Cr XIII to Zn XIX and chlorine-like ions from Mn IX to Co XI. These ions have a high abundance in the astrophysical plasma. Zeeman splitting level energies, hyperfine- and/or magnetic-field dependent wavelengths, and transition rates of the 3s3p 3P2,1,0→3s21S0 (for magnesium-like ions) and the 3p43d 4D7/2→ 3p52P3/2 line (for chlorine-like ions), are computed using the multiconfiguration Dirac–Fock method. Some higher-order effects, such as the Breit interaction and quantum electrodynamics corrections, are included in the relativistic configuration interaction method, as this makes the results more accurate. A comparison between the our predictions and other theoretical and experimental values is made. A satisfactory agreement is achieved. Besides providing valuable information for spectral line analysis, the present work will have a variety of implications for fusion and astrophysical plasma sources, for example, in the determination of magnetic fields in solar coronas and other stars.

Wavelengths and E1, E2, M1, and M2 line strengths in Nb XXX

The calculations are performed to calculate the excitation energies, wavelengths, line strengths, transition probabilities, and weighted oscillator strengths for the electric-dipole (E1), electric-quadrupole (E2), magnetic-dipole (M1), and magnetic-quadrupole (M2) transitions between the lowest 301 fine-structure levels of the 3snl (n = 3 − 6, l = 0 − 5), 3pnl (n = 3 − 5, l = 0 − 4), and 3dnl (n = 3 − 5, l = 0 − 4) configurations in Mg-like niobium, Nb XXX. In addition, the level designations in the LS- and jj-coupling schemes and lifetimes are presented. The calculations are carried out using the GRASP2018 atomic structure package which is based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, with the contributions of the Breit interaction and quantum electrodynamics (QED) corrections included. The accuracy of the present energies, lifetimes, and transition data is calculated utilizing a comparison of the results from the present MCDHF largest layers from two different approaches, as well as the comparison with theoretical and experimental data that are currently accessible.

Fitting for the energy levels of hydrogen

Atomic hydrogen energy levels calculated to high precision are required to assist experimental researchers working on spectroscopy in the pursuit of testing quantum electrodynamics (QEDs) and probing for physics beyond the Standard Model. There are two important parts to the problem of computing these levels: an accurate evaluation of contributions from QED and using an accurate value for the proton charge radius as an input. Recent progress on QED corrections to the fine structure, as well as increasing evidence that a proton charge radius in the range of 0.84 fm is favored over the previously adopted larger value in the 0.88 fm range, has advanced the field, yet several state-of-the-art measurements remain in contradiction with this smaller value. Motivated by on-going and future work in this area, we present here a simple parameterization for the energy levels of hydrogen at the level of hyperfine structure using the so-called relativistic Ritz approach. The fitting of a finite sample of QED-generated levels at low to intermediate principal quantum number, n, gives a generally applicable formula for all values of n for each distinct angular momentum channel, given in this work up to orbital angular momentum number . We also provide a simple linear parameterization for the shift in hydrogen energy levels as a function of the proton radius, providing a useful cross check for extant and future measured energy intervals.

Thermodynamics and microstructures of Euler–Heisenberg black hole in a cavity

Euler–Heisenberg black holes with quantum electrodynamics (QED) correction are embraced by a cavity in this paper, which serves as a boundary of the black hole spacetime and contributes to the equilibrium of the system. We explore the thermodynamic properties of the black hole, including the phase transitions and phase structures. The small/large black hole phase transition occurs for a negative QED parameter, while the reentrant phase transition can be observed for a small positive QED parameter. Then the thermodynamic geometry is investigated to diagnose microscopic interactions of black hole thermodynamic systems. For the reentrant phase transition, the small black holes are dominated by repulsion for the first-order coexistence curve, while the interaction between the small black hole molecules could be attractive or repulsive for the small/large black hole phase transition.

Quantum electrodynamic corrections to cyclotron states in a Penning trap

Quantum electrodynamic corrections to cyclotron states in a Penning trap

Calculations of energy levels, radiative transition parameters, hyperfine structure constants [formula omitted] - [formula omitted], Landé [formula omitted] factors and isotope shifts for Sc XX using the MCDF-RCI method

Large scale calculations for the energy levels, transition rates, oscillator strengths, lifetimes, hyperfine interaction constants, Landé gJ factors, and isotope shift factors have been performed for 1s2 and 1snl(n=2−8andl≤n−1) levels of He-like Sc XX ion. The general-purpose relativistic atomic structure package (GRASP2018) based on the fully relativistic multiconfiguration Dirac–Fock (MCDF) method is used to carry out the calculations. The leading quantum electrodynamic corrections, Breit interaction and nuclear recoil effects are also included in the succeeding relativistic configuration interaction (RCI) calculations. The relativistic isotope shift (RIS4) programme is used to determine the mass and field shifts factors. Furthermore, the percentage uncertainty in the transition parameters and lifetimes is estimated. A detailed comparison of the present results with the corresponding values from the NIST database and other theoretical and experimental works, wherever available, has been done, and an excellent agreement is achieved. A large section of the results is reported for the first time in the present work.

Energy levels, lifetimes, and transition probabilities for Sr XXXII

The fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approach was used to calculate the excitation energies and lifetimes for the lowest 272 levels that belonging to the 2{s}^{2}2{p}^{3}, 2s2{p}^{4}, 2{p}^{5}, 2{s}^{2}2{p}^{2}3l, 2s2{p}^{3}3l, and 2{p}^{4}3l (l=s, p, d) configurations for N-like strontium, Sr XXXII, as well as the wavelengths, weighted oscillator strengths, transition probabilities, and line strengths for the electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among these levels. The Breit-interaction (BI), and quantum electrodynamics (QED) corrections have been incorporated into the computations. In order to assess the uncertainties of the current calculations, comparisons with available data, and the results from the largest MCDHF layers have all performed.

Pre-Born–Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen

For rovibronic states corresponding to the B and electronic states of the hydrogen molecule, the pre-Born–Oppenheimer (four-particle) non-relativistic energy is converged to a 1–3 parts-per-billion relative precision. The four-particle non-relativistic energy is appended with leading-order relativistic, leading- and estimated higher-order quantum-electrodynamics corrections. The resulting term values referenced to the rovibronic ground state are obtained in an excellent agreement with the experimental results. Further results are reported and discussed for other rovibronic states assignable to the and the and electronic states.

Evaluation of the Bethe Logarithm: From Atom to Chemical Reaction

A general computational scheme for the (nonrelativistic) Bethe logarithm is developed, opening the route to "routine" evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small polyatomic and polyelectronic molecular systems. The implementation relies on the Schwartz method and minimization of a Hylleraas functional. In relation with electronically excited states, a projection technique is considered, which ensures positive definiteness of the functional over the entire parameter (photon momentum) range. Using this implementation, the Bethe logarithm is converged to a relative precision better than 1:103 for selected electronic states of the two-electron H2 and H3+, and the three-electron He2+ and H+H2 molecular systems. The present work focuses on nuclear configurations near the local minimum of the potential energy surface, but the computations can be repeated also for other structures.

Generalized relativistic small‐core pseudopotentials accounting for quantum electrodynamic effects: Construction and pilot applications

AbstractA simple procedure to incorporate one‐loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape‐consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbersn ≤ 3 for the two former elements andn ≤ 4 for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac–Coulomb–Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two‐valence‐electron atomic systems using the intermediate‐Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high‐accuracy molecular excited state calculations are discussed.

Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation

ABSTRACT The fundamental vibrational excitation energy and the dissociation energy of the main isotopologue of lithium hydride (LiH) are studied by the variational method using all-particle explicitly correlated Gaussian (ECG) basis sets. In this approach, electrons and nuclei are treated on equal footing, i.e. the Born–Oppenheimer approximation is not assumed. The leading relativistic () and the dominating part of the quantum electrodynamics () corrections to the energy levels are accounted for in the framework of the perturbation theory. The fundamental vibrational excitation energy and the dissociation energies obtained in the calculations are well within the error bars of the available experimental data.

Oscillator strengths and interstate transition energies involving [formula omitted] and [formula omitted] states of the Li atom

We report high accuracy calculations of the ground and excited doublet S and P states of lithium atom. Overall, 24 states corresponding to dominant electronic configurations 1s2ns and 1s2np (n=2,…,13) are considered in the framework of the Ritz variational method. The nonrelativistic wave function of each of these states is generated in an independent calculation by expanding it in terms of a large number (K=11,000−17,000) of all-electron explicitly correlated Gaussian functions (ECG) whose nonlinear parameters are extensively optimized with a procedure that employs analytic energy gradient determined with respect to these parameters. The Hamiltonian used in the calculations explicitly depends on the mass of the nucleus. The leading relativistic and quantum electrodynamics (QED) corrections to the energy levels are subsequently computed using the perturbation-theory approach and the variational nonrelativistic wave functions as the zeroth-order functions. As these functions are generated in the finite-nuclear-mass (FNM) calculations, the energy corrections include the nuclear recoil effects. The obtained energy levels allow us to determine highly accurate interstate transition frequencies for both the naturally occurring stable lithium isotopes, 6Li and 7Li, and the lithium atom with an infinitely heavy nucleus, ∞Li. The nonrelativistic wave functions are used to compute the transition dipole moments and the corresponding oscillator strengths. These quantities are reported for 144 S–P transitions of each isotope. The data set generated in this work is considerably more accurate and comprehensive than the data available from the previous theoretical calculations. It can be useful in guiding future spectroscopic measurements of the lithium atom.

Theory of QED radiative corrections to neutrino scattering at accelerator energies

Control over quantum electrodynamics (QED) radiative corrections is critical for precise determination of neutrino oscillation probabilities from observed (anti)neutrino detection rates. It is particularly important to understand any difference between such corrections for different flavors of (anti)neutrinos in charged-current interactions. We provide theoretical foundations for calculating these corrections. Using effective field theory, the corrections are shown to factorize into soft, collinear, and hard functions. The soft and collinear functions contain large logarithms in perturbation theory but are computable from QED. The hard function parametrizes hadronic structure but is free from large logarithms. Using a simple model for the hard function, we investigate the numerical impact of QED corrections in charged-current (anti)neutrino-nucleon elastic cross sections and cross-section ratios at GeV energies. We consider the implications of mass singularity theorems that govern the lepton-mass dependence of cross sections for sufficiently inclusive observables and demonstrate the cancellation of leading hadronic and nuclear corrections in phenomenologically relevant observables.