Relativistic and QED corrections to one-bond indirect nuclear spin-spin couplings in X2 2+ and X3 2+ ions (X = Zn, Cd, Hg).

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 nJHg-Hg (n = 1, 2). For doing so, we performed calculations for J-couplings in the ionized X2 2+ and X3 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 ZX 5.

FLUKA Simulations of Kß/Kα Intensity Ratios of Copper in Ag-Cu Alloys.

The numerical simulations of Cu Kα and Cu Kß fluorescence lines induced by Rh X-ray tube and by monoenergetic radiation have been presented. The copper Kß/Kα intensity ratios for pure elements as well as for Ag-Cu alloys have been modeled. The results obtained by use of the FLUKA code, based on the Monte-Carlo approach, have been compared to available experimental and theoretical values. A visible relationship was found between the simulated Kß/Kα intensity ratios and the copper content of the Ag-Cu alloy: as the Cu content increases, the Kß/Kα coefficient decreases. The results can play role in elemental material analysis, especially in archaeometry.

Relativistic and QED effects on NMR magnetic shielding constant of neutral and ionized atoms and diatomic molecules.

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.

QED effects on individual atomic orbital energies.

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.

Breit corrections to individual atomic and molecular orbital energies.

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 εnlBreit(Z)≃a×Zb. 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.