Benchmarking high-field few-electron correlation and QED contributions in ${\mathrm{Hg}}^{75+}$ to ${\mathrm{Hg}}^{78+}$ ions. I. Experiment

The photorecombination of highly charged few-electron mercury ions ${\mathrm{Hg}}^{75+}$ to ${\mathrm{Hg}}^{78+}$ has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays $(65–76\mathrm{keV})$ and scanning the electron beam energy $(45–54\mathrm{keV})$ over the $KLL$ dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within $\pm 4\mathrm{eV}$ (relative) and $\pm 14\mathrm{eV}$ (absolute). At this level of experimental accuracy, it becomes possible to make a detailed comparison to various theoretical approaches and methods, all of which include quantum electrodynamic (QED) effects and finite nuclear size contributions (for a $1s$ electron, these effects can be as large as 160 and $50\mathrm{eV}$, respectively). In He-like ${\mathrm{Hg}}^{78+}$, a good agreement between the experimental results and the calculations has been found. However, for the capture into Li-, Be-, and B-like ions, significant discrepancies have been observed for specific levels. The discrepancies suggest the need for further theoretical and experimental studies with other heavy ions along these isoelectronic sequences.

Figure 1

Sketch of the dielectronic (DR) and radiative recombination (RR) processes of He-like ions (initial state) in collisions with free electrons.

Figure 2

(Color online) Logarithmic 2D contour-map (x-ray counts as a function of electron energy and x-ray energy) of photorecombination of highly charged mercury ions showing $KLL$ DR resonances, which appear as bright spots at particular electron energies ($KLL$: promotion of a bound $K$ shell electron to an $L$ shell and simultaneous capture of a free electron into another $L$ shell). The two continuous diagonal bands correspond to x rays due to RR processes into $J=1∕2$ (upper) and $J=3∕2$ (lower) levels of the $L$ shell, respectively.

Figure 3

Overall scheme of the data acquisition system.

Figure 4

Projections on the electron energy axis of $480\mathrm{eV}$ wide slices made along the RR $n=2$, $J=1∕2$ band (see the labeled cuts in Fig. 2). On the right side, the variable photon energies $E_{\gamma }$ (sum of the electron beam energy $E_e$ and the ionization potential of the corresponding charge state) are indicated in keV.

Figure 5

Projections of the slices along the RR $n=2$, $J=3∕2$ band. $E_{\gamma }$ and $E_e$ are the photon and electron beam energies in keV, respectively.

Figure 6

(Color online) Difference (in eV) between experimental and theoretical results (black open squares for ${\mathrm{MCDF}}_S$, triangles for configuration-interaction Dirac-Fock-Sturm (CI-DFS), rhombus for relativistic many-body perturbation theory (QMB) including first-order QED and second-order relativistic many-body effects, and circles for ${\mathrm{MCDF}}_M$ for the DR resonance energies for capture into He- to B-like mercury ions. Note that in this plot, the experimental energies are referred to the theoretical value of the DR $1s2s^2$ resonance of each individual calculation, in contrast to Table where the experimental results were pinned to the theoretical value of the $1s2s^2$ ${\mathrm{MCDF}}_S$ calculation. The error bars shown in the plot are those of the relative scale and not those of the absolute one.

Figure 7

(Color online) Deviations (in eV) of the various calculations from the present experimental results on the energy separation between DR resonances.

Figure 8

(Color online) Two projections onto the x-ray axis of a single data set. The two peaks (single lines) always present in these types of projections correspond to the RR $n=2$, $J=1∕2$ and $J=3∕2$ bands, respectively. (a) Projection of the resonance (filled area) into Li-like states in the $K{L}_{12}{L}_{12}$ region. (b) Projection of resonance (filled areas) into B-like states in the $K{L}_{12}{L}_3$ region.

Figure 9

(Color online) Differences between the observed x-ray energies and the ${\mathrm{MCDF}}_S$ (open squares), the ${\mathrm{MCDF}}_M$ (closed circles), and QMB (open rhombus) calculations. The error bars shown are those of the measured x-ray energies.