The x-ray transitions in Cu- and Ni-like tungsten ions in the 5.19–5.26 Å wavelength range that are relevant as a high-temperature tokamak diagnostic, in particular for JET in the ITER-like wall configuration, have been studied. Tungsten spectra were measured at the upgraded Shanghai- Electron Beam Ion Trap operated with electron-beam energies from 3.16 to 4.55 keV. High-resolution measurements were performed by means of a flat Si 111 crystal spectrometer equipped by a CCD camera. The experimental wavelengths were determined with an accuracy of 0.3–0.4 mÅ. The wavelength of the ground-state transition in Cu-like tungsten from the $3p^{5}3d^{10}4s4d[{(3/2,{(1/2,5/2)}_2]}_{1/2}$ level was measured. All measured wavelengths were compared with those measured from JET ITER-like wall plasmas and with other experiments and various theoretical predictions including cowan, relac, multiconfigurational Dirac-Fock (MCDF), and fac calculations. To obtain a higher accuracy from theoretical predictions, the MCDF calculations were extended by taking into account correlation effects (configuration-interaction approach). It was found that such an extension brings the calculations closer to the experimental values in comparison with other calculations.

We propose a novel approach for the theoretical analysis of the photoinduced high-resolution Kh$\alpha${}1,2 x-ray hypersatellite spectra, which allows us to obtain reliable values of lifetimes of the doubly K-shell ionized states and fundamental information about the relative role of K-shell double photoionization (DPI) mechanisms. It is demonstrated for the first time that the Kh$\alpha${}1,2 hypersatellite natural line broadening observed for selected metal atoms with 20$\le${}Z$\le${}30 can be well reproduced quantitatively by taking into account the influences of the open-shell valence configuration (adopted from predictions of the band-structure method) and the outer-shell ionization and excitation following the DPI process.

Several issues, concerning QED corrections, that are important in precise atomic calculations are presented. The leading QED corrections, self-energy and vacuum polarization, to the orbital energy for selected atoms with 30 ≤ Z ≤ 118 have been calculated. The sum of QED and Breit contributions to the orbital energy is analyzed. It has been found that for ns subshells the Breit and QED contributions are of comparative size, but for np and nd subshells the Breit contribution takes a major part of the QED+Breit sum. It has also, been found that the Breit to leading QED contributions ratio for ns subshells is almost independent of Z. The Z-dependence of QED and Breit+QED contributions per subshell is shown. The fitting coefficients may be used to estimate QED effects on inner molecular orbitals. We present results of our calculations for QED contributions to orbital energy of valence ns-subshell for group 1 and 11 atoms and discuss about the reliability of these numbers by comparing them with experimental first ionization potential data.

Several issues concerning Breit correction to electron-electron interaction in many-electron systems, which are important in precise atomic and molecular calculations, are presented. At first, perturbative versus self-consistent calculations of Breit correction were studied in selected cases. Second, the Z-dependence of Breit contribution per subshell is shown, based on values calculated for selected atoms with 30 ≤ Z ≤ 118. Third, the relations between magnetic and retardation parts of Breit interaction are analyzed. Finally, Gaunt contribution calculated for Kr, Xe, and Rn noble gas atoms and its iso-electronic HBr, HI, and HAt diatomic molecules has been compared to full-Breit atomic calculations. We found that Breit corrections should be treated by self-consistent calculations and that there is a functional dependence of those corrections for subshells as ${\epsilon }_{nl}^{Breit}\left(Z\right)\simeq a\times Z^b$ . We also found that molecular Gaunt corrections are close to their atomic counterparts for inner electrons though they are not for outer orbitals. In any case, accurate calculations must include retardation correction in addition to Gaunt.

We show here results of four-component calculations of nuclear magnetic resonance σ for atoms with 10 ≤ Z ≤ 86 and their ions, within the polarization propagator formalism at its random phase level of approach, and the first estimation of quantum electrodynamic (QED) effects and Breit interactions of those atomic systems by using two theoretical effective models. We also show QED corrections to σ(X) in simple diatomic HX and X₂ (X = Br, I, At) molecules. We found that the Z dependence of QED corrections in bound-state many-electron systems is proportional to Z⁵, which is higher than its dependence in H-like systems. The analysis of relativistic ee (or paramagneticlike) and pp (or diamagneticlike) terms of σ exposes two different patterns: the pp contribution arises from virtual electron-positron pair creation/annihilation and the ee contribution is mainly given by 1s → ns and 2s → ns excitations. The QED effects on shieldings have a negative sign, and their magnitude is larger than 1% of the relativistic effects for high-Z atoms such as Hg and Rn, and up to 0.6% of its total four-component value for neutral Rn. Furthermore, percentual contributions of QED effects to the total shielding are larger for ionized than for neutral atoms. In a molecule, the contribution of QED effects to σ(X) is determined by its highest-Z atoms, being up to −0.6% of its total σ value for astatine compounds. It is found that QED effects grow faster than relativistic effects with Z.

The indirect spin–spin coupling tensor, J, between mercury nuclei in systems containing this element can be of the order of a few kHz and one of the largest measured. We analyzed the physics behind the electronic mechanisms that contribute to the one- and two-bond couplings ⁿJ_Hg–Hg (n = 1, 2). For doing so, we performed calculations for J-couplings in the ionized $X_2^{2+}$ and $X_3^{2+}$ linear molecules (X = Zn, Cd, Hg) within polarization propagator theory using the random phase approximation and the pure zeroth-order approximation with Dirac–Hartree–Fock and Dirac–Kohn–Sham orbitals, both at four-component and zeroth-order regular approximation levels. We show that the “paramagnetic-like” mechanism contributes more than 99.98% to the total isotropic value of the coupling tensor. By analyzing the molecular and atomic orbitals involved in the total value of the response function, we find that the s-type valence atomic orbitals have a predominant role in the description of the coupling. This fact allows us to develop an effective model from which quantum electrodynamics (QED) effects on J-couplings in the aforementioned ions can be estimated. Those effects were found to be within the interval (0.7; 1.7)% of the total relativistic effect on isotropic one-bond ¹J coupling, though ranging those corrections between the interval (−0.4; −0.2)% in Zn-containing ions, to (−1.2; −0.8)% in Hg-containing ions, of the total isotropic coupling constant in the studied systems. The estimated QED corrections show a visible dependence on the nuclear charge Z of each atom X in the form of a power-law proportional to $Z_X^5$ .