Quantum Electrodynamic Corrections Research Articles

Nonadiabatic QED Correction to the Dissociation Energy of the Hydrogen Molecule.

The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1MHz for the dissociation energy, in very good agreement with the parallel measurement [Hölsch etal., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.

Deep core photoionization of iodine in CH3I and CF3I molecules: how deep down does the chemical shift reach?

Hard X-ray electron spectroscopic study of iodine 1s and 2s photoionization of iodomethane (CH3I) and trifluoroiodomethane (CF3I) molecules is presented. The experiment was carried out at the SPring-8 synchrotron radiation facility in Japan. The results are analyzed with the aid of relativistic molecular and atomic calculations. It is shown that charge redistribution within the molecule is experimentally observable even for very deep levels and is a function of the number of electron vacancies. We also show that the analysis of Auger spectra subsequent to hard X-ray photoionization can be used to provide insight into charge distribution in molecules and highlight the necessity of quantum electrodynamics corrections in the prediction of core shell binding energies in molecules that contain heavy atoms.

Theoretical determination of energies, wavelengths, and transition probabilities for EUV and SXR spectral lines in Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII

Energy levels, radiative processes and lifetimes are studied among the 98 lowest levels of the 1s22snl and 1s22pnl (n = 2–4, l = 0–3) configurations of Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII. The GRASP2K (General-purpose Relativistic Atomic Structure Package) is adopted, in which the orbital set is systematically expanded within the orbital space up to n = 9, and the Breit interaction and leading quantum electrodynamical corrections are considered. Results are provided for four types of transitions:electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole. Similar data for the 166 lowest states belonging to the n ≤ 5 configurations are also determined using the second-order relativistic many-body perturbation theory to assess the accuracy of the calculations, taking Sr XXXV as an example. Good agreement is found between results of this work and available values from the Atomic Spectra Database of the National Institute of Standards and Technology and other theoretical reports. The accuracy for energies and radiative rates is estimated to be about 0.02% and 5%, respectively. These accurate theoretical data can aid line identifications in extreme ultraviolet (EUV) and soft X-ray (SXR) spectra. The present work should be useful for diagnostics of hot plasmas in fusion applications.

Theoretical wavelengths, energy levels, lifetimes, and transition probabilities for the silicon isoelectronic sequence Cd XXXV-Ba XLIII, W LXI

We have performed the theoretical calculations of wavelengths and excitation energies from ground state for 56 fine-structure levels as well as of oscillator strengths and radiative decay rates for all the electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels of the terms belonging to the $$3s^{2}3p^{2}$$ , $$3s^{2}3p3d$$ , $$3s3p^{3}$$ , $$3s3p^{2}3d$$ , $$3s^{2}3d^{2}$$ , and $$3p^{4}$$ configurations for the silicon isoelectronic sequence Cd XXXV-Ba XLIII, W LXI. The calculation is based on the multiconfiguration Dirac–Fock approach, and Breit interaction and quantum electrodynamic corrections are included. Electron correlation effects are taken into account by means of the expansions in terms of a basis of configuration state functions. To achieve the accuracy of the data, independent calculation is provided with similar data obtained from the flexible atomic code, taking W LXI as an example. Our results are compared with each other, and other available theories/experimental values and the energy levels/transition rates for a majority of strong transitions are found to be accurate to be better than 0.5%/10%. The present atomic data should be useful in controlled thermonuclear fusion research and technical plasma modeling.

The relativistic computations of spectral lines of 129Xe I

Abstract In this paper, we present our achievement on the relativistic computations of the spectral lines for the levels belonging to the 6s[k]J, 4f[k]J, 5d[k]J, 6p[k]J, 7s[k]J, 5f[k]J, 6d[k]J, 7p[k]J and 8s[k]J intermediate Rydberg series in the heavy xenon-129 isotope. These spectral lines are identified by the energy levels, the transition rates, the oscillator strengths, the Lande gj-factors and the magnetic dipole hyperfine constant. Inasmuch as the transitions from the ground state to the 4f and 5f levels in addition to the 6p and 7p levels are forbidden by electric dipole selection rules, we computed all the 5p55d–5p5nf (4 ≤ n ≤ 5), 5p55d–5p5np (6 ≤ n ≤ 7), 5p56s–5p5np (6 ≤ n ≤ 7), 5p57s–5p56p, 5p56d–5p5nf (4 ≤ n ≤ 5), 5p56d–5p5np (6 ≤ n ≤ 7), 5p57s–5p57p and 5p58s–5p5np (6 ≤ n ≤ 7) transition arrays. The present accurate values of spectral lines are obtained by using the well-established multiconfiguration Dirac-Hartree-Fock (MCDHF) method in conjunction with the relativistic configuration interaction (RCI) calculations. The RCI calculations encompass further electron correlation effects. These effects include static electron-valence and core-valence correlation and core polarizations effects, the Breit and quantum electrodynamics (QED) corrections in addition to the effect of nuclear charge distribution. To provide a context for information in the accuracy associated with these values, a detailed comparison of our data with other experimental and theoretical data available in the database is made. On the whole, a good agreement has generally been observed for most of the spectral lines. These newcomers to the area of database with insights into nuclear fusion research, as they may provide diagnostic information on magnetically confined plasmas, they could be a reference point for the identification and de-blending of new spectral lines provided by astrophysics observations and space research.

Accurate wavenumber measurements for the S0(0), S0(1), and S0(2) pure rotational Raman lines of D2

AbstractWe present accurate measurements for the wavenumbers of the S0(0), S0(1), and S0(2) pure rotational Raman lines in D2. Our measurements improve the accuracy of the previously available experimental data by an order of magnitude. They also show complete agreement with the state‐of‐the‐art ab initio calculations of the D2 rotational splitting, which include both relativistic and Quantum electrodynamics (QED) corrections.

Theoretical study of energy levels and radiative properties of Be-like W70+

We report an extensive theoretical study of the Be-like W70+ spectrum in a wide energy range. We present accurate calculated 215 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn′l′ (n = 2, n′ = 2–7 Ɩ = s, p Ɩ′ = s, p, d, f, g), which may be useful ion for fusion plasma research. We have identified wavelengths of extreme ultraviolet (EUV) and X-ray transitions using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method implemented in the GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. Transition data are reported for multipole transitions from the ground state. We have discussed discrepancy graphically with available results. We have also graphically explained the convergence in excitation energies with active sets. We predict new energy levels and transition parameters where no other experimental or theoretical results are available. The present complete set of results should be of help in line identification and the interpretation of spectra, as well as in modeling and diagnostics of fusion plasmas.

Extended atomic structure calculations for energy levels and radiative data of Xe XLIII

We report an extensive and elaborate theoretical study of atomic data for Xe XLIII. We have calculated energies for the lowest 141 fin. structure levels by using Multi-Configuration Dirac Fock (MCDF) method. We have also considered Quantum Electrodynamics (QED) and Breit corrections in our calculations. We have presented the radiative data for electric dipole (E1) transitions among lowest 141 levels. We have made comparisons of our calculated excitation energies and EUV (Extreme Ultraviolet) transition wavelengths with the theoretically computed and experimentally observed energy levels and wavelengths at Electron Beam Ion Trap (EBIT) and a good agreement is achieved. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code (FAC). Additionally, we have provided new atomic data for Xe XLIII which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and detection and investigation of EUV and Soft X-ray (SXR) spectral lines.

Testing atomic wave functions in the nuclear vicinity: The hyperfine structure with empirically deduced nuclear and quantum electrodynamic effects

Calculations of the magnetic hyperfine structure rely on the input of nuclear properties -- nuclear magnetic moments and nuclear magnetization distributions -- as well as quantum electrodynamic (QED) radiative corrections for high-accuracy evaluation in heavy atoms. The uncertainties associated with assumed values of these properties limit the accuracy of hyperfine calculations. For example, for the heavy alkali-metal atoms Cs and Fr, these uncertainties may amount collectively to almost 1\% or 2\%, respectively. In this paper we propose a method for removing the dependence of hyperfine structure calculations on assumed values of nuclear magnetic moments and nuclear magnetization distributions by determining these effects empirically from measurements of the hyperfine structure for high states. The method is valid for $s$, $p_{1/2}$, and $p_{3/2}$ states of alkali-metal atoms and alkali-metal-like ions. We have shown that for $s$ states the dependence on QED effects may also be removed to high accuracy. The ability to probe the electronic wave functions, through hyperfine comparisons, with significantly increased accuracy is important for the analysis of atomic parity violation measurements and may enable the accuracy of atomic parity violation calculations to be improved. More broadly, it opens the way for further development of high-precision atomic many-body methods.

Short range interactions in the hydrogen atom

In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$, satisfying $\left|\delta V\right|\ll\left|V_{C}\right|$ over the whole range of the radial variable $r$. The other possible addition to $V_{C}$ is a potential arising due to the finite size of the atomic nucleus and as a matter of fact, can be larger than $V_{C}$ in a very short range. We focus here on the latter and show that the electric potential of the proton displays some undesirable features. Among others, the energy content of the electric field associated with this potential is very close to the threshold of $e^+e^-$ pair production. We contrast this large electric field of the Maxwell theory with one emerging from the non-linear Euler-Heisenberg theory and show how in this theory the short range electric field becomes smaller and is well below the pair production threshold.

Proposal of highly accurate tests of Breit and QED effects in the ground state 2p5 of the F-like isoelectronic sequence

We propose that the ground term transition, 2p5P3/22-P1/22, for ions in the F-like isoelectronic sequence could be used to accurately test current methods to compute Breit and quantum-electrodynamic (QED) effects. These systems are of interest since correlation is small due to what we will label Layzer quenching. Using the multiconfiguration Dirac-Hartee-Fock method, we investigate how correlation, Breit and QED corrections vary along the sequence and show that QED dominates over correlation already for Z≈20. We also investigate the behavior of different QED effects as a function of the nuclear charge and find that the self-energy dominates for the mid-Z range (40-80), but then decreases to change sign for Z≈90. For a few elements between Z=85 and 90 the vacuum polarization is the leading term, while for higher Z the two QED contributions cancel. This opens up the possibility for these ions to carefully test the frequency-dependent transverse photon correction. The uncertainties of the treatment of the well-understood frequency-independent Breit correction and correlation are expected to be at least three orders of magnitude smaller than the QED and frequency-dependent transverse photon corrections for high Z. In this work we also compare and evaluate the results from three different methods to compute self-energies. (Less)

Radiative corrections to the Coulomb law and model of dense quantum plasmas: Dispersion of longitudinal waves in magnetized quantum plasmas

Two kinds of quantum electrodynamic radiative corrections to electromagnetic interactions and their influence on the properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction is considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of radiative corrections are related to the nonlinearity of the Maxwell equations for the strong electromagnetic field. Their contribution in the spectrum of transverse waves of magnetized plasmas is briefly discussed. At the consideration of the Langmuir wave spectrum, we included the effect of different distributions of the spin-up and spin-down electrons revealing in the Fermi pressure shift.

Theoretical calculation of Kα and Kβ X-ray satellite and hypersatellite structures for hollow argon atoms

A systematical knowledge of the satellite and hypersatellite structures of X-ray transitions is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed explanation of the complex structures of X-ray satellites and hypersatellites are crucial for understanding the X-ray emission mechanism and the hollow atom formation mechanism. In this paper, the Kα and Kβ X-ray satellite and hypersatellite structure are theoretically studied for hollow argon atoms with the relativistic multiconfiguration Dirac-Fock (MCDF) method, which includes the Breit and quantum electro-dynamics (QED) corrections. To check the applicability of the method, the transition energies and rates of the diagram lines for Ar are calculated,. and the results are in agreement with previously published data. Then the MCDF calculations of the transition energies and probabilities of Kα 1, 2 (K →L3, 2) and Kβ 1, 3 (K → M3, 2) X-ray satellites and hypersatellites, which originate from the argon atoms with additional vacancies in the L shell, are carried out. To obtain the overall profile of the K X-ray spectrum, the diagram lines are integrated with the satellites and hypersatellites on the assumption that the intensity is proportional to the corresponding transition probability and each discrete line has a Gaussian distribution profile with a full width at half maximum (FWHM) value of 20 eV. From the convoluted profile, we can obtain the dependence of the average transition energy and relative transition intensity of the satellites and hypersatellites on the initial hollow configuration. It is found that the transition energy shift increases linearly with the number of spectator vacancies in the L shell increasing. For instance, the energy shift of the Kα satellite caused by L-shell hole is about 20 eV, and that of the Kβ satellite is 48 eV. While for hypersatellite, the energy shift increases greatly due to the double ionization in the K shell. The energy shift increment of Kα and Kβ hypersatellites corresponding to L vacancy are 21 and 52 eV, respectively. Finally, four simple empirical formulae for estimating the energy shifts of the Kα, Kβ X-ray satellites and hypersatellite for Ar atom with any number of L-shells vacancies are deduced by using the least square method. These results are useful in explaining various K X-ray spectra and better understanding the collision process.

Ground-state hyperfine splitting for Rb, Cs, Fr, Ba+ , and Ra+

We have systematically investigated the ground-state hyperfine structure for alkali-metal atoms ^{87}Rb, ^{133}Cs, ^{211}Fr and alkali-metal-like ions ^{135}Ba^+, ^{225}Ra^+, which are of particular interest for parity violation studies. The quantum electrodynamic one-loop radiative corrections have been rigorously evaluated within an extended Furry picture employing core-Hartree and Kohn-Sham atomic potentials. Moreover, the effect of the nuclear magnetization distribution on the hyperfine structure intervals has been studied in detail and its uncertainty has been estimated. Finally, the theoretical description of the hyperfine structure has been completed with full many-body calculations performed in the all-orders correlation potential method.

Calculation of Araki-Sucher correction for many-electron systems

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

Multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for Ni XXV

We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn′l′ (n = 2, n′ = 2, 3, 4, 5, Ɩ = s,p Ɩ′ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.

Theory of the Lamb shift in muonic tritium and the muonic He3 ion

Due to recent experimental efforts on light muonic atoms, we consider the quantum electrodynamics (QED) theory of two-body muonic atoms, namely, of those with $A=3$. Here we present the results for the Lamb shift and fine structure up to the order ${\ensuremath{\alpha}}^{5}m$ for the $n=2$ levels, which in particular include (1) pure QED contributions, (2) the coefficient to the ${r}_{N}^{2}$ term with QED corrections (where ${r}_{N}$ is the rms nuclear charge radius), and (3) the general expressions for the nuclear-structure contributions consistent with the presented QED theory. We revisit theory for the muonic helium-3 ion by rechecking all the relevant theoretical contributions and develop a theory of muonic tritium. We also reestimate the uncertainty of the nuclear-structure contribution.

Quantum Electro-dynamic Corrections of 1s1/2 Energy Level in Hydrogen like Atoms

Quantum Electro-dynamic Corrections of 1s1/2 Energy Level in Hydrogen like Atoms

Model operator approach to the relativistic Lamb shift calculations in many-electron atoms and highly charged molecular ions

The quantum electrodynamics (QED) corrections to the alkali metal ionization potentials and to the ground-state energy of the U92+-U91+ one-electron quasi-molecule are evaluated with the use of the model operator approach. The QED contributions to the ionization energies in the alkali metals are obtained both by averaging the model operator with the valence electron wave functions and by incorporating the QED operator into the Dirac–Coulomb–Breit Hamiltonian. The two-center calculations of the vacuum-polarization and self-energy contributions to the Lamb shift in the one-electron quasi-molecule are performed for the different values of the internuclear distances (from the chemical distances up to the critical ones), the more simplified evaluation in the monopole approximation is also considered. The results of the calculations are compared with the theoretical predictions obtained previously in the framework of the ab initio approaches.

Radiative transition rates of 1s2s(3S)3p levels for Li-like ions with [formula omitted

Energy and radiative transition rates of the 1s2s (1,3S) 3p levels of Li-like ions with 5⩽Z⩽10 are calculated using a multiconfiguration Dirac-Fock approach including quantum-electrodynamic and electronic correlation corrections. The importance of the electronic correlation on the radiative transition probabilities is assessed in detail.