Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations

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Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations

K. Kubiček, P. H. Mokler, V. Mäckel, J. Ullrich, and J. R. Crespo López-Urrutia

Phys. Rev. A 90, 032508 – Published 22 September 2014

Abstract

For the hydrogenlike ${Ar}^{17 +}$ ion, the $1 s$ Lamb shift was absolutely determined with a $1.4 %$ accuracy based on Lyman- $α$ wavelength measurements that have negligible uncertainties from nuclear size effects. The result agrees with state-of-the-art quantum electrodynamics (QED) calculations, and demonstrates the suitability of Lyman- $α$ transitions in highly charged ions as x-ray energy standards, accurate at the five parts-per-million level. For the heliumlike ${Ar}^{16 +}$ ion the transition energy for the $1 s 2 p^{1} P_{1} \to 1 s^{2}^{1} S_{0}$ line was also absolutely determined on an even higher level of accuracy. Additionally, we present relative measurements of transitions in $S^{15 +}, S^{14 +}$ , and ${Fe}^{24 +}$ ions. The data for the heliumlike $S^{14 +}, {Ar}^{16 +}$ , and ${Fe}^{24 +}$ ions stringently confirm advanced bound-state QED predictions including screened QED terms that had recently been contested.

Received 23 April 2014

DOI:https://doi.org/10.1103/PhysRevA.90.032508

Authors & Affiliations

K. Kubiček^*, P. H. Mokler, V. Mäckel, J. Ullrich, and J. R. Crespo López-Urrutia

Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

^*Present address: Deutsches Elektronen-Synchroton, Notkestraße 85, 22607 Hamburg, Germany; katharina.kubicek@desy.de

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Vol. 90, Iss. 3 — September 2014

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Images

Figure 1
Top: experimental arrangement: an EBIT in combination with a Bond-type flat crystal x-ray spectrometer. Bragg angles can be absolutely determined in a head-on or side-on configuration using the measured crystal rotation angle $Γ$ [11]. Bottom: the sum spectra for a single run each show the Ly- $α$ (right) and the $1 s 2 p^{1} P_{1} \to 1 s^{2}^{1} S_{0} (w), 1 s 2 p^{3} P_{2} \to 1 s^{2}^{1} S_{0} (x)$ and $1 s 2 p^{3} P_{1} \to 1 s^{2}^{1} S_{0} (y)$ [8] lines (left) for $S^{15 +} / S^{14 +}$ and ${Ar}^{17 +} / {Ar}^{16 +}$ ions in head-on and side-on geometry, respectively. A $Z^{2}$ scaling was applied to the photon energy axis. The lines are fitted by Voigt profiles with a FWHM of $\sim 0.7 eV$ (S) and $\sim 1.5 eV$ (Ar). The residues are shown.
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Figure 2
Sum spectrum for a single run showing the Ly- $α$ lines of ${Ar}^{17 +}$ on a linear scale. To the absolute values given along the energy axis a wavelength scale is added at the top. The lines are fitted by Voigt profiles (for details, see text and Table 1). The residues are shown below.
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Figure 3
Top: overview of uncertainties for accurately measured Ly- $α_{1}$ transitions—this work [(pink) triangles], our earlier work [upside down (pink) triangle 9], and results [(gray) circles] reported in [7, 12, 21, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], i.e., the corresponding uncertainties for the $1 s$ ground-state Lamb shift (all scaled by $Z^{4}$ ). Our uncertainties are given as the sum of the statistical and systematic uncertainties. These are compared to the Lamb shift [13, 14] and its main theoretical QED contributions, one-loop self-energy (SE), one-loop vacuum polarization (VP), nuclear size (NS), and the summed-up total second-order two-loop QED terms (top) [32, 33, 34]. For discussion of the two-loop QED contributions, we include the experimental uncertainty of the ground-state Lamb shift in $U^{91 +}$ inferred from the $2 p_{1 / 2} \to 2 s_{1 / 2}$ transition in Li-like $U^{89 +}$ [49] (open diamond). Bottom: uncertainties of the NS corrections in comparison with experimental $1 s$ ground-state Lamb-shift uncertainties. (Pink) Triangles: Uncertainty of our current values for $S^{15 +}$ and ${Ar}^{17 +}$ . Open diamond: uncertainty in $U^{91 +}$ from [49] deduced from Li-like transitions.
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Figure 4
Comparison of theoretical two-electron QED terms [31] for the $1 s^{2}^{1} S_{0}$ and $1 s 2 p^{1} P_{1}$ states of heliumlike ions to the uncertainties of earlier experimental results [23, 24, 25, 26, 27, 28, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61] (gray circles), and our earlier [upside down (pink) triangles 9, 22] and present values [(pink) triangles]. (The earlier ${Ar}^{16 +}$ data point [9] did not include some systematic uncertainties included in the present work.) Our uncertainties are given as the sum of the statistical and systematic uncertainties. All data are scaled by $Z^{3}$ .
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