# High-Precision Determination of Oxygen K α Transition Energy Excludes Incongruent Motion of Interstellar Oxygen

M. A. Leutenegger, S. Kühn, P. Micke, R. Steinbrügge, J. Stierhof, C. Shah, N. Hell, M. Bissinger, M. Hirsch, R. Ballhausen, et al.

► To cite this version:

M. A. Leutenegger, S. Kühn, P. Micke, R. Steinbrügge, J. Stierhof, et al. High-Precision Determination of Oxygen K α Transition Energy Excludes Incongruent Motion of Interstellar Oxygen. Physical Review Letters, 2020, 125 (24), pp.243001. 10.1103/PhysRevLett.125.243001. hal-04936510

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High-Precision Determination of Oxygen K<sub>α</sub> Transition Energy Excludes Incongruent Motion of Interstellar Oxygen

M. A. Leutenegger<sup>1,∗</sup> S. Kühn,<sup>2</sup> P. Micke,<sup>2,3</sup> R. Steinbrügge,<sup>4</sup> J. Stierhof,<sup>5</sup> C. Shah,<sup>1,2</sup> N. Hell,<sup>6</sup> M. Bissinger,<sup>7</sup>

M. Hirsch,<sup>5</sup> R. Ballhausen,<sup>5</sup> M. Lang,<sup>5</sup> C. Gräfe,<sup>5</sup> S. Wipf,<sup>8</sup> R. Cumbee,<sup>1,9</sup> G. L. Betancourt-Martinez,<sup>10</sup>

S. Park,<sup>11</sup> V. A. Yerokhin,<sup>12</sup> A. Surzhykov,<sup>3,13</sup> W. C. Stolte,<sup>14,†</sup> J. Niskanen,<sup>15,16</sup> M. Chung,<sup>11</sup> F. S. Porter,<sup>1</sup> T. Stöhlker,<sup>8,17,18</sup>

T. Pfeifer,<sup>2</sup> J. Wilms,<sup>5</sup> G. V. Brown,<sup>6</sup> J. R. Crespo López-Urrutia,<sup>2</sup> and S. Bernitt<sup>8,18,17,2</sup>

<sup>1</sup>NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, Maryland 20771, USA

<sup>2</sup>Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

<sup>3</sup>Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany

<sup>4</sup>Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany

<sup>5</sup>Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Sternwartstrasse 7, 96049 Bamberg, Germany

<sup>6</sup>Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, USA

<sup>7</sup>Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany

<sup>8</sup>Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany

<sup>9</sup>Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA

<sup>10</sup>Institut de Recherche en Astrophysique et Planétologie, 9, avenue du Colonel Roche BP 44346, 31028 Toulouse Cedex 4, France

<sup>11</sup>Ulsan National Institute of Science and Technology, 50 UNIST-gil, 44919 Ulsan, Republic of Korea

<sup>12</sup>Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia

<sup>13</sup>Institut für Mathematische Physik, Technische Universität Braunschweig, D-38106 Braunschweig, Germany

<sup>14</sup>Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

<sup>15</sup>Institute for Methods and Instrumentation in Synchrotron Radiation Research G-ISRR, Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany

<sup>16</sup>Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland

<sup>17</sup>GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany

<sup>18</sup>Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena, Germany

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(Received 30 March 2020; revised 19 October 2020; accepted 30 October 2020; published 8 December 2020)

We demonstrate a widely applicable technique to absolutely calibrate the energy scale of x-ray spectra with experimentally well-known and accurately calculable transitions of highly charged ions, allowing us to measure the K-shell Rydberg spectrum of molecular O₂ with 8 meV uncertainty. We reveal a systematic ~450 meV shift from previous literature values, and settle an extraordinary discrepancy between astrophysical and laboratory measurements of neutral atomic oxygen, the latter being calibrated against the aforementioned O₂ literature values. Because of the widespread use of such, now deprecated, references, our method impacts on many branches of x-ray absorption spectroscopy. Moreover, it potentially reduces absolute uncertainties there to below the meV level.

DOI: 10.1103/PhysRevLett.125.243001

The vast majority of baryonic matter in the Universe appears as diffuse gas at temperatures ranging from 10 K to 10 MK [1]. Owing to the presence of elements heavier than hydrogen and helium, which have strong inner-shell absorption features in the 0.2–2 keV band, x-ray observations provide a sensitive means to trace this gas and to determine its properties [2–5]. As oxygen is the third most abundant element in the Universe [6], the strong 1s–2p resonance line from atomic oxygen is especially important for such studies. Its strength provides a measure of the abundance, and its Doppler shift yields the radial velocity.

To enable this science, space instruments such as the Chandra High Energy Transmission Grating Spectrometer

(HETGS) have been calibrated to better than 100 km s⁻¹ [7,8]. The stability of this calibration has been tracked on orbit through repeated observations of soft x-ray transitions from highly charged ions (HCI), specifically of H- and He-like ions of elements such as neon, oxygen, and nitrogen, in the coronae of stars with small and known radial velocities [9,10] or of supernova remnants [11], and verified through observations with other space instruments such as the XMM-Newton Reflection Grating Spectrometer (RGS) [12] and x-ray sensitive CCDs [13]. For the 1s–2p oxygen resonance line, the HETGS has yielded radial velocity measurements with an uncertainty as low as 13 km s⁻¹ [14]. Surprisingly, Gorczyca et al. [15] showed that
<figure><img src="image_3.png" /><figcaption>FIG. 1. Scheme for simultaneous measurements of resonant fluorescence spectra of highly charged ions trapped in a compact electron beam ion trap equipped with an off-axis electron gun [25] and photoabsorption spectra of molecular gases in a separated gas cell downstream. A monochromatic synchrotron radiation beam, which is slowly scanned in energy, passes through both the ion trap and the gas cell, thus eliminating the effect of temporal drifts and providing a stable mutual reference for the spectra of ionized and neutral species.</figcaption></figure>

averaging measurements of this line over different lines of sight in the Galaxy did not yield a value close to the rest value as was expected. The average wavelength differed from the best laboratory value [16–18] by an amount equivalent to ~340 km s⁻¹, i.e., outside the laboratory and HETGS uncertainties. RGS data also appear to require a shift of ~380 km s⁻¹, when compared with theory calibrated against the same laboratory measurements [19]. To put this shift in context, the Galactic escape velocity in the vicinity of the Solar System is (580 ± 63) km s⁻¹ [20].

The traditional calibration standard for the laboratory measurements of the atomic oxygen spectrum was the conveniently measurable absorption spectrum of molecular oxygen. Its value was established by electron energy loss spectroscopy (EELS) measurements [21,22]. Conversely, the absolute wavelength calibration of the grating spectrometers of Chandra and XMM-Newton outlined above primarily relies on soft x-ray transitions from H-like and He-like ions of elements such as neon, oxygen, and nitrogen in objects with well-known radial velocities.

In this Letter, we introduce an independent, accurate laboratory calibration technique in order to help resolve this puzzling and significant discrepancy between space-based and laboratory energy calibration methods. We measure the molecular oxygen Rydberg spectrum simultaneously with x-ray lines from He-like ions; specifically, we present a new high-precision measurement of the K-shell absorption spectrum of molecular oxygen using the well-known 1s-np resonance transitions (i.e., 1s² ¹S₀ – 1snp ¹P₁) of He-like O⁶⁺ and N⁵⁺ as calibration references. This reduces the uncertainty of the laboratory standard to only 4 km s⁻¹, unveils a significant calibration error in the hitherto used standard, and brings the laboratory energy scale into agreement with the calibration of space-based instruments. Our method overcomes current limitations and outperforms the accuracy of existing soft x-ray calibration standards by at least 3 orders of magnitude.

Our setup (Fig. 1) was installed at beamline U49-2/PGM-1 [23,24] of the synchrotron-radiation facility

BESSY-II (Helmholtz-Zentrum Berlin), where an undulator delivers linearly polarized light to a plane-grating monochromator, with typical photon fluxes of 10¹² s⁻¹ in the energy range of 500–600 eV. An exit slit width of 10 µm yielded a full-width-at-half-maximum (FWHM) resolution of 69 meV (E/ΔE = 8320) at 574 eV.

We used PolarX-EBIT [25], an electron beam ion trap (EBIT) employing a novel off-axis electron gun leaving the main axis obstacle-free, to produce and store HCI by means of its monoenergetic electron beam. The photon beam merges on the longitudinal axis of PolarX-EBIT with the electron beam [26–28], and passes through the device to the absorption cell downstream. An electron beam at an energy of 420 eV (300 eV), well below the K-shell excitation energies of O⁶⁺ (N⁵⁺), produces and traps the ions for study from injected N₂ and residual H₂O that are dissociated by it. These choices of electron-beam energy suppress excitation of soft x-ray transitions in the energy band of interest both by electron impact and resonant as well as nonresonant photorecombination processes. A low beam current of only ~1.1 mA reduces ion heating and its associated Doppler broadening, as originally shown by Beiersdorfer et al. [29].

Fluorescence photons from the decay of photoexcited ions were detected with two (one vertical, the other horizontal) silicon drift detectors (SDDs) mounted side-on to the photon beam axis. Photon events were recorded with a multichannel data acquisition (DAQ) system. Since the photon beam was horizontally polarized, the signal was stronger in the vertical detector for *J* = 0–1 transitions [30]. This effect is most pronounced for the 1s–2p transitions and decreases for 1s–np transitions with higher principal quantum number *n* due to depolarization effects in alternate decay paths. The transition energy does not depend on polarization.

Two meters downstream from PolarX-EBIT, a cell continuously fed with O₂ gas using a needle valve and pumped down to keep a constant pressure of ~10⁻⁶ mbar is installed (Fig. 1). A 30 nm SiN foil separated the vacua of
<figure><img src="image_4.png" /><figcaption>FIG. 2. Example of a calibration scan. We recorded ~15000 counts in the vertical SDD in a 15-min scan. The best-fit model is the sum of two cocentered Gaussians, reflecting a nonideal instrumental line shape, and has a FWHM of 69 meV. The centroid of the 1s–2p resonance transition of He-like O$^{6+}$ has a statistical uncertainty of 0.3 meV, while the theoretical uncertainty is 0.53 meV.</figcaption></figure>

the gas cell and PolarX-EBIT. For detection of single photoions produced by absorption of the soft x rays in the gas, we used a channeltron. Its electronic pulses were amplified, pulse-height discriminated, and passed to the DAQ system. Background was negligible when the x-ray beam was off; while on, but without O₂ gas injection, residual gaseous H₂O (at ~10⁻⁷ mbar) leads to weak O K-shell transitions cleanly distinguishable from that of O₂ [31].

The photon energy is selected by rotations of the monochromator plane grating and its ancillary mirror that are measured with high resolution encoders. Regular

calibrations are needed because of thermal drifts in the positions of beamline optical components, encoder errors, and shifts in the x-ray source position caused by adjustments to the storage ring orbit parameters. We slowly scanned the photon energy across the ranges of interest; at each position, our DAQ system recorded the grating and mirror angles, nominal photon energy, counts from SDDs and channeltrons, and storage ring current.

We show an example calibration scan of the 1s–2p transition of He-like O$^{6+}$ in Fig. 2. Within a 15-min-long measurement, it achieved a statistical uncertainty for the centroid position of 0.3 meV, smaller than the theoretical uncertainty of the transition energy and better than 1 ppm in precision. We performed similar scans of the 1s–np transitions of O$^{6+}$ and N$^{5+}$ up to $n = 7$.

Repeated scans displayed drifts of the photon energy on the order of 50–300 meV on timescales of several hours to days. Consecutive scans of the same line sometimes showed drifts of 10–30 meV within 50 min. Slow, smooth shifts while scanning over a 1 eV scan region of the O₂ Rydberg spectrum in the gas cell did not exceed 40 meV; thus we assume a systematic uncertainty proportional (40 meV per eV) to the separation from the nearest 1s–np calibration line of N$^{5+}$ (see Supplemental Material [32]).

We therefore simultaneously calibrated the O₂ 1s–π* transition and Rydberg series with the 1s–5p, 1s–6p, and 1s–7p transitions of N$^{5+}$ in the same broad scans. We used transition energies for N$^{5+}$ from Yerokhin and Surzhykov [33], which are calculated with techniques [34,35] that have been experimentally benchmarked to 1.5 ppm for 1s–2p transitions in He-like Ar [36]. The theoretical uncertainty for the 1s–5p, 6p, 7p transition energies is estimated to be 0.3 meV [33]. Our recalibrated spectra are shown in Fig. 3, together with best-fit peak positions and previously

<figure><img src="image_5.png" /><figcaption>FIG. 3. Recalibration of the O₂ soft x-ray absorption spectrum by simultaneously measuring K$_{δ}$ (1s–5p), K$_{e}$ (1s–6p), and K$_{ζ}$ (1s–7p) transitions in He-like N$^{5+}$ as energy references. Positions of spectral features in O₂ from the literature [21,37] (dashed red vertical markers) are compared with our measurements (full red vertical markers), clearly showing the energy offset (see Table I). The vertical scales are different for the two spectral regions shown.</figcaption></figure>
<table><caption>TABLE I. Energies measured for selected peaks in the O₂ Rydberg series compared with measurements from Tanaka *et al.* [37] (labeled T08 below). Peak labels and assignments are as in that work. Uncertainties of T08 are relative, and do not include the absolute error of the calibration standard used.</caption><thead><tr><th rowspan="2">Peak</th><th colspan="3">Energy (eV)</th><th colspan="2">Assignment</th></tr><tr><th>This work</th><th>T08</th><th>Shift</th><th><sup>4</sup>Σ<sup>-</sup></th><th><sup>2</sup>Σ<sup>-</sup></th></tr></thead><tbody><tr><td>s1</td><td>539.377(35)</td><td>538.95(4)</td><td>0.427</td><td>3sσν = 0</td><td></td></tr><tr><td>p1</td><td>540.641(58)</td><td>540.22(4)</td><td>0.421</td><td>3pπ</td><td></td></tr><tr><td>s6</td><td>541.089(40)</td><td>540.67(4)</td><td>0.419</td><td>3pσν = 0</td><td></td></tr><tr><td>s7</td><td>541.313(31)</td><td>540.89(4)</td><td>0.423</td><td>3pσν = 1</td><td></td></tr><tr><td>s8</td><td>541.530(22)</td><td>541.09(4)</td><td>0.440</td><td>3pσν = 2</td><td></td></tr><tr><td>s12</td><td>542.249(8)</td><td>541.80(4)</td><td>0.449</td><td>4pσν = 0</td><td>3p'σν = 0</td></tr><tr><td>s13</td><td>542.459(19)</td><td>542.02(5)</td><td>0.439</td><td>4pσν = 1</td><td>3p'σν = 1</td></tr><tr><td>s14</td><td>542.683(24)</td><td>542.25(5)</td><td>0.433</td><td>4dσ</td><td></td></tr></tbody></table>

published reference positions [37] tracing their calibration to the original EELS measurements [21,22].

To get the best possible calibration for the strongest feature (s12) in the O₂ Rydberg series, we used the 1s-7p resonance of N⁵⁺, separated from it by only 158 meV, with a calculated energy of 542.090 57(31) eV. The peaks appear in the scan only 4 min apart, avoiding systematic shifts affecting longer timescales. We derived a peak energy of 542.249(8) eV, with an uncertainty of 5 meV from counting statistics on the N⁵⁺ 1s-7p transition, an estimated 3 meV systematic contribution from the fits of neighboring peaks, and 6 meV from drift due to the 158 meV separation from N⁵⁺ 1s-7p. We assign a larger 12 meV uncertainty to the nearest peak at 542.459(19) eV (s13) to account for its greater sensitivity to the fit model of the dominant s12 peak, in addition to the 15 meV drift uncertainty. For all other peaks (Table I), uncertainties are dominated by those of the drift; all peaks are referenced to N⁵⁺ 1s-7p, with the exception of π* (N⁵⁺ 1s-5p) and s1 (N⁵⁺ 1s-6p).

Our result for peak s12 differs by 0.449 eV (-248 km s⁻¹) from the value that was originally measured by Hitchcock and Brion [22] and that has been used as a standard in numerous works (see, e.g., Refs. [37-39]), including for atomic oxygen [16,17]. We find similar shifts for the rest of the O₂ Rydberg series. However, the peak of the 1s-π* transition, which is calibrated with respect to the N⁵⁺ 1s-5p transition, is measured to be 530.92(6) eV, which is shifted by only 0.12 eV from the value reported by Wight and Brion [21], well within their quoted uncertainty of 0.2 eV. It is not clear why the shift in the calibration of the O₂ Rydberg series is 0.33 eV larger, since Hitchcock and Brion [22] referenced the Rydberg series against 1s-π*. Real peak shifts of the temperature-dependent rovibrational distribution in 1s-π* and the quoted 0.1 eV energy uncertainties might explain this.

We recalibrated the dataset of McLaughlin *et al.* [17] using our measured energy for the strongest Rydberg peak (s12) at 542.249(8) eV. The fitting uncertainty for this peak

<table><caption>TABLE II. Recalibrated energies for atomic oxygen (in eV) compared with previous works (G13, Gorczyca *et al.* [15]; M13, McLaughlin *et al.* [17]; L13, Liao *et al.* [40]). Doppler shifts relative to our work given in km s⁻¹; sh. refers to shifted (see text). The XMM results are for Mkn 421, while the Chandra results are for a weighted average of multiple lines of sight. ALS refers to measurements at the Advance Light Source.</caption><thead><tr><th>Source</th><th>1s-2p</th><th>Δv</th><th>1s-3p<sup>4</sup>P</th><th>Δv</th></tr></thead><tbody><tr><td>This work</td><td>527.26(4)</td><td></td><td>541.645(12)</td><td></td></tr><tr><td>G13 XMM</td><td>527.28(5)</td><td>-11(36)</td><td>541.93(28)</td><td>-158(155)</td></tr><tr><td>G13 XMM, sh.</td><td>527.30(5)</td><td>-22(36)</td><td>541.95(28)</td><td>-169(155)</td></tr><tr><td>G13 Chandra</td><td>527.44(9)</td><td>-102(56)</td><td>541.72(18)</td><td>-42(100)</td></tr><tr><td>G13 Chandra, sh.</td><td>527.26(9)</td><td>-11(56)</td><td></td><td></td></tr><tr><td>L13 Chandra</td><td>527.39(2)</td><td>-74(25)</td><td></td><td></td></tr><tr><td>M13 ALS</td><td>526.79(4)</td><td>267(32)</td><td>541.19(4)</td><td>252(22)</td></tr></tbody></table>

was 7 meV, yielding a net calibration uncertainty of 11 meV. We then performed a new fit of the nearby 1s-3p⁴P line of atomic oxygen, which had an 8 meV fit uncertainty, yielding a total uncertainty of 14 meV. Finally, we fitted the 1s-2p line of atomic oxygen, obtaining a best-fit value of 527.26(4) eV. Here the uncertainty is dominated by scan-to-scan calibration shifts across the 14.4 eV separating 1s-2p and 1s-3p⁴P.

Our recalibrated line energies for 1s-2p and 1s-3p⁴P in neutral oxygen are much closer to previously published astrophysical values for neutral gas in the intergalactic medium, as shown in Table II. Independently from each other, Gorczyca *et al.* [15] and Liao *et al.* [40] averaged Chandra spectra for multiple lines of sight in the Galaxy. Gorczyca *et al.* [15] also analyze a high signal-to-noise XMM-Newton RGS spectrum of Mkn 421. In Table II we show both the values of the line position determined using the instrumental wavelength calibration and the values as corrected by Gorczyca *et al.* based on observed shifts of the O VII line relative to the most precise laboratory measurements [21.601 95 Å, 573.949 eV] [41]. Our results for 1s-2p disagree with the Chandra averages at the level of 0.13-0.18 eV, corresponding to a velocity of -75-100 km s⁻¹, and agree with the Mkn 421 value from the RGS within uncertainties. This disagreement may reflect some combination of real astrophysical velocities such as motion of the absorbers with respect to the Galactic rotation, or residual calibration uncertainties. Indeed, Gorczyca *et al.* [15] indicate that in the case of XTE J1817-330, observations of the O VII 1s-2p line by Gatuzz *et al.* [14] are shifted by ~9 mÅ with respect to laboratory measurements [41]. Correcting for this shift, Gorczyca *et al.* [15] find a line energy of 527.26(9) eV, fully consistent with the laboratory value found here. A more advanced description of the O VII line as a blend of
absorption and emission components by Liao et al. [40] gives a quantitatively similar result for the shift. Taken together with our new calibration, this implies an astro-physical origin of this 9 mÅ shift, corresponding to a velocity of 115 km s⁻¹, which is larger than expected from either the barycentric correction of the satellite’s motion or from the rotational velocity of the Galaxy on the line of sight toward XTE J1817–330, and therefore may suggest an association of the absorber with this x-ray binary.

There is a growing need for reliable, easily reproducible energy calibration references over the whole x-ray band at modern high-flux radiation sources of steadily improving resolution and stability. Advanced synchrotron-radiation sources [42] and free-electron lasers [43,44] serve many x-ray absorption and scattering applications in biology, materials science, physical chemistry, as well as condensed-matter, atomic, and molecular physics [45]. Subtle chemical, isotopic, and crystallographic x-ray absorption shifts are studied in a plethora of x-ray absorption near-edge structure (XANES), extended as well as near-edge x-ray absorption fine structure (EXAFS, NEXAFS) experiments [46] and with sophisticated theory [47]. Future radiation sources based on high-harmonic generation [48] will also require accurate photon-energy references.

Calibration based on EELS suffers, i.a., from systematic effects in the measurement of voltages applied to macroscopic electrodes. In view of the present results, it can be assumed that some unknown or underestimated uncertainties were extant but were not included by Hitchcock and Brion [22], and were not corrected since then. Other sophisticated methods to determine the dispersion function of grating or crystal spectrometers are hindered by natural limitations of the measurement techniques for distances, angles, grating spacing, and crystal lattice constants [49–51]. Furthermore, all these input parameters are sensitive to thermal shifts and mechanical vibrations. The K-shell and L-shell lines of neutral atoms, widely used as x-ray energy standards [52], suffer from the presence of multiple blended satellite transitions that cannot be calculated with the high accuracy now possible for few-electron ions. They also display asymmetric line profiles affected by chemical and solid-state effects. Absorption edges used for calibration [53] are broader than those, and show even larger susceptibility to environmental influences.

In contrast, x-ray fluorescence lines in HCI are symmetric [27,28], and can be, by choice of their multipolarity, as narrow as necessary for a given application. Their transition probabilities and level lifetimes span many orders of magnitude, and their energies are far more stable than other standards. This is true under all values of temperature and electron density conceivable for our device conceivable values of temperature and electron density—e.g., extrapolating from Ref. [54] for an electron-density effect on $K_β$ (1s–3p) of He-like Cl in an EBIT yields a shift lower than 1 neV—and recommends them as inherently superior

references. Furthermore, since space observatories often use naturally occurring HCI transitions for calibration, comparing them with the identical ones from an EBIT is straightforward. This can help when transitions from other isoelectronic sequences (e.g., in Ref. [55]) with larger theoretical uncertainties than the He- and H-like systems are investigated.

The here introduced method is the most accurate presently available, being based on ab initio calculations of He-like systems that have become extremely reliable during the past decades [56–58], with uncertainties reduced to a level well below 1 meV in the recent work of Yerokhin and Surzhykov [33]. Hydrogenic transitions [59,60], which could in principle also be used with our method, reach below the part-per-billion uncertainty level, basically only limited by uncertainties on the nuclear size parameters. Following an analogous approach to optical frequency metrology with atoms and ions, x-ray energy references based on HCI can become ideal tools not only for calibration, but also for fundamental physics studies [61] relying on exquisitely accurate measurements of photon energies and their shifts. Fully exploiting this technique, however, requires long-term stability of the experimental setup to a level of 1 K in temperature and microns in mechanical stability, which are achievable in current state-of-the-art facilities.

Financial support was provided by the Max-Planck-Gesellschaft (MPG) and Bundesministerium für Bildung und Forschung (BMBF) through Project No. 05K13SJ2. We thank HZB for the allocation of synchrotron radiation beamtime at BESSY II. Work by C. S. was supported by the Deutsche Forschungsgemeinschaft (DFG) Project No. 266229290 and by an appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight Center, administered by Universities Space Research Association under contract with NASA. Work by UNIST was supported by the National Research Foundation of Korea (No. NRF-2016R1A5A1013277). Work by LLNL was performed under the auspices of the U.S. Department of Energy under Contract No. DE-AC52-07NA27344 and supported by NASA grants to LLNL. M. A. L. and F. S. P. acknowledge support from NASA’s Astrophysics Program. Work by G. V. B. was supported by a NASA Space Technology Research Fellowship. Work by R. C. was supported by an appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight Center.

<footnote>*maurice.a.leutenegger@nasa.gov</footnote>

<footnote>†Present address: Nevada National Security Site, Mission Support and Test Services, Livermore operations, Livermore, California 94551, USA.</footnote>

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