QED calculations of the n=2 to n=1 x-ray transition energies in middle- Z heliumlike ions

Abstract

Ab initio QED calculations of the four x-ray transitions from the L to K shell in heliumlike argon, titanium, iron, copper, and krypton are performed. The binding energies for all the n = 1 and n = 2 states are evaluated as well. The calculation approach combines the rigorous QED treatment in the first two orders of the perturbation theory constructed within the extended Furry picture with the third-and higher-order correlation effects evaluated in the Breit approximation. The obtained results are compared with the previous evaluations and available experimental data.

QED tests with highly charged ions

“…As can be seen in figure 19, there are sizable differences at high-Z between the calculations of [206,251,302,303]. The most recent calculations [304], performed for Z = 18, 22, 26, 29, 36 differ only by 2 meV to 4 meV from the calculations of Artemyev et al [206]. The MCDF results [255] correspond to the calculation described in [251], with exact non-relativistic Coulomb correlation energy, relativistic corrections, and magnetic and retardation corrections.…”

“…Figure 27: Differences between experiments and Artemyev et al [206] calculations, compared to the differences between several theoretical results and [206], for the w and x lines. (Plante): [303]; (Drake): [302]; (Indelicato): [251]; (Malyshev): [304]. The fits to the experiment-theory differences, with functions bZ n , n = 0 to 5, for all four lines are also plotted, together with the error bands.…”

“…Another difficulty with many-body methods comes from the gauge dependance of the electron-electron interaction (28). In QED, a diagram or set of diagrams Difference between the calculations using the unified relativistic theory [303], RMBPT, [304], the MCDF method [252,256] and recent improved values [305], and the calculations of Artemyev et al [207] used as a reference. Differences are divided by Z 2 .…”

Many-Electron QED with Redefined Vacuum Approach

“…The question arises: can we perform ab initio QED calculations for many-electron systems? The second-order contributions in α are evaluated only within the state-of-the-art QED calculations for helium-like [21][22][23][24][25][26], lithium-like [27][28][29][30], beryllium-like [31][32][33], boron-like [34][35][36], and sodium-like [37] ions. The computations are so far limited to such selected, relatively simple systems not only due to the complexity of numerical calculations but also because of difficulties in deriving formal expressions.…”

Many-Electron QED with Redefined Vacuum Approach

“…The question arises: can we perform ab initio QED calculations for many-electron systems? The second-order contributions in α are evaluated only within the state-of-the-art QED calculations for helium-like [10][11][12][13][14][15], lithium-like [16][17][18][19], beryllium-like [20][21][22], boron-like [23][24][25], and sodium-like [26] ions. The computations are so far limited to such selected, relatively simple systems not only due to the complexity of numerical calculations but also because of difficulties in deriving formal expressions.…”