A new benchmark of soft X-ray transition energies of $$\mathrm {Ne}$$ Ne , $$\mathrm {CO}_2$$ CO 2 , and $$\mathrm {SF}_6$$ SF 6 : paving a pathway towards ppm accuracy

Eur. Phys. J. D (2022)76:38 https://doi.org/10.1140/epjd/s10053-022-00355-0 THE EUROPEAN PHYSICAL JOURNAL D Regular Article – Atomic Physics A new benchmark of soft X-ray transition energies of Ne, CO2, and SF6: paving a pathway towards ppm accuracy J. Stierhof1,a , S. Kühn2 , M. Winter3,4 , P. Micke2,5 , R. Steinbrügge6 , C. Shah2,7,8 , N. Hell8 , M. Bissinger1, M. Hirsch1, R. Ballhausen1 , M. Lang1, C. Gräfe1, S. Wipf9 , R. Cumbee7,10 , G. L. Betancourt-Martinez11 , S. Park12 , J. Niskanen13 , M. Chung12 , F. S. Porter7 , T. Stöhlker9,14,15 , T. Pfeifer2 , G. V. Brown8 , S. Bernitt2,9,14,15 , P. Hansmann3 , J. Wilms1 , J. R. Crepso López-Urrutia2 , and M. A. Leutenegger7 1 Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität ErlangenNürnberg, Sternwartstr. 7, 96049 Bamberg, Germany 2 Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 3 Institute of Theoretical Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen, Germany 4 CNRS, Institut NEEL, Université Grenoble Alpes, CNRS, Institut NEEL, 25 rue des Martyrs BP 166, 38042 Grenoble Cedex 9, France 5 CERN, 1211 Geneva 23, Switzerland 6 Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany 7 NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, USA 8 Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550, USA 9 Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany 10 Department of Astronomy, University of Maryland, College Park, MD 20742, USA 11 Institut de Recherche en Astrophysique et Planétologie, 9, avenue du Colonel Roche BP 44346, 31028 Toulouse Cedex 4, France 12 Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan, South Korea 13 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 14 GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany 15 Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena, Germany Received 30 November 2021 / Accepted 23 January 2022 © The Author(s) 2022 Abstract. A key requirement for the correct interpretation of high-resolution X-ray spectra is that transition energies are known with high accuracy and precision. We investigate the K-shell features of Ne, CO2 , and SF6 gases, by measuring their photo ion-yield spectra at the BESSY II synchrotron facility simultaneously with the 1s–np fluorescence emission of He-like ions produced in the Polar-X EBIT. Accurate ab initio calculations of transitions in these ions provide the basis of the calibration. While the CO2 result agrees well with previous measurements, the SF6 spectrum appears shifted by ∼0.5 eV, about twice the uncertainty of the earlier results. Our result for Ne shows a large departure from earlier results, but may suffer from larger systematic effects than our other measurements. The molecular spectra agree well with our results of time-dependent density functional theory. We find that the statistical uncertainty allows calibrations in the desired range of 1–10 meV, however, systematic contributions still limit the uncertainty to ∼40–100 meV, mainly due to the temporal stability of the monochromator energy scale. Combining our absolute calibration technique with a relative energy calibration technique such as photoelectron energy spectroscopy will be necessary to realize its full potential of achieving uncertainties as low as 1–10 meV. 1 Introduction High-resolution astrophysical X-ray spectroscopy has become routine in the last 20 years, with diffraction grating spectrometers on Chandra and XMM-Newton providing resolving powers of Δλ/λ ∼ 1000 [1–4]. These instruments have enabled the measurements of the cona ditions in the emitting plasmas, e.g., through observations of the triplets from He-like ions, precision Doppler velocity and line shape measurements in a variety of astrophysical plasmas, including stellar coronae and winds, cataclysmic variables, X-ray binaries containing neutron stars and black holes, supernova remnants, or outflows in active galactic nuclei [5–11, e.g.,]. Due to the success of these measurements, future astrophysi- e-mail: (corresponding author) 0123456789().: V,-vol 123 38 Page 2 of 13 cal X-ray observatories such as XRISM, Athena, Arcus, or Lynx, envision spectral resolving powers as high as 5000, implying the ability to accurately determine centroids to 10 ppm, or 3 km s−1 absolute Doppler velocity [12–17]. These instruments will open up the field of spatially resolved, high-resolution X-ray spectroscopy, and will allow scientists to access techniques that are currently not available to X-ray astronomy such as X-ray Fine Structure Absorption measurements for solids [18], the imaging of velocity fields in galaxy clusters [19], or diagnosing the properties of the Warm and Hot Intergalactic Medium [20]. The ground and on-orbit calibration of existing and future instruments as well as the interpretation of the existing and future observations require accurately calibrated atomic transition energies [4,21, e.g.,]. In oneand two-electron ions, these energies are calculable with part per million (ppm) accuracy for the astrophysically relevant atomic numbers less than 30 [22–25, e.g.,], and theory has been experimentally benchmarked with precision as good as 10 ppm [26,27, e.g.,]. Inner shell transition energies in less-ionized species, neutral atoms, molecules, and solids, are far more challenging to calculate accurately, and thus must be obtained experimentally. These experiments, however, rely on existing soft X-ray calibration standards, which have limitations to their accuracy. We recently found a discrepancy in the extensively used standard of the Rydberg transitions of molecular oxygen of almost 0.5 eV [28], thus resolving a tension between astrophysical and laboratory measurements of transitions of atomic oxygen [29], which had been calibrated against this molecular standard [30]. Such discrepancies raise the question of whether other commonly-used soft Xray standards may have errors of comparable magnitude, given that many such standards are based on similar experimental techniques using electron energy loss spectroscopy (EELS). Even if the error in the earlier molecular oxygen standard is an outlier, the typical experimental precision of soft X-ray standards obtained with EELS is still of order 0.1 eV (or 100 ppm at 1 keV), which is far too large to fully exploit the capabilities of current and future Xray astronomical and ground based facilities, and not precise enough for the calibration needs of many future instruments. Modern synchrotron facilities are capable of sufficient photon fluxes and resolving powers that determining centroids of peaks with (...truncated)