keV Energy Research Articles

Differential Cross-section Measurements for 3He Elastic Scattering on 16O and 27Al

In the present work measurements to determine the differential cross section values for the elastic scattering of 3He on 16O and 27Al were carried out at the Ruđer Bošković Institute (RBI) Tandem Accelerator Facility in Zagreb, Croatia, covering the E3He,lab=3500-5600 keV energy range, using four Silicon Surface Barrier (SSB) detectors positioned at the backscattering angles of 130°, 145°, 157.7° and 165ο. The target was constructed at the facility and was comprised of a thin, self-supporting aluminum foil, upon which a thin layer of natB (isotopic ratio: 11B 80.1%, 10B 19.9%), along with 12C, 14N, 16O, was deposited using the sputtering technique. In addition, an ultra-thin layer of 197Au was evaporated on top for wear protection and normalization purposes.

Measurement of scintillation response of CsI[Na] to low-energy nuclear recoils by COHERENT

We present results of several measurements of CsI[Na] scintillation response to 3–60 keV energy nuclear recoils performed by the COHERENT collaboration using tagged neutron elastic scattering experiments and an endpoint technique. Earlier results, used to estimate the coherent elastic neutrino-nucleus scattering (CEvNS) event rate for the first observation of this process achieved by COHERENT at the Spallation Neutron Source (SNS), have been reassessed. We discuss corrections for the identified systematic effects and update the respective uncertainty values. The impact of updated results on future precision tests of CEvNS is estimated. We scrutinize potential systematic effects that could affect each measurement. In particular we confirm the response of the H11934-200 Hamamatsu photomultiplier tube (PMT) used for the measurements presented in this study to be linear in the relevant signal scale region.

CEN X–3 AS SEEN BY MAXI DURING SIX YEARS

The aim of this work is to study both light curve and orbital phase spectroscopy of Cen X-3 taking advantage of the MAXI/GSC observation strategy. These studies allow delimiting the stellar wind properties and its interactions with the compact object. From the analysis of the light curve, we have estimated the orbital period of the binary system and also found possible QPOs around a superorbital period of Psuperorb = 220 ± 5 days. Both orbital phase-averaged and phaseresolved spectra were extracted and analysed in the 2.0–20.0 keV energy range. Two models have described spectra satisfactorily, a partial absorbed Comptonization of cool photons on hot electrons plus a power law, and a partial absorbed blackbody plus a power law, both modified by adding Gaussian lines. The high value of the X-ray luminosity in the averaged spectrum indicates that the accretion mode is not only due to the stellar wind.

Predicted performance of a tangential viewing hard x-ray camera for the DIII-D high field side lower hybrid current drive experiment.

High field side launch of lower hybrid current drive (LHCD) has improved accessibility and penetration over low field side launch on DIII-D. Simulations predict single pass absorption under a wide range of plasma conditions. Hard x-ray (HXR) measurement of LHCD generated fast electron bremsstrahlung (50-250keV) will validate wave propagation and absorption. Emissivity profiles are recovered from one-dimensional inversion of HXR brightness to determine LH damping location, fast electron slowing down time, and some indication of the fast electron energy. The camera will be implemented by populating 32 tangential sightlines of the existing Gamma Ray Imager with Kromek SPEARTM Cadmium Zinc Telluride (CZT) detectors sensitive to 10-1000keV photons with 10keV energy resolution. Expected count rates allow for <0.5ms time resolution. Pulses are processed using 50ns shaping time Cremat CR-200 Gaussian shaping modules and are digitized by 25MHz D-TACQ ACQ216 digitizers. The performance of the HXR camera is evaluated by comparing predicted fast electron density profiles and inverted synthetic brightnesses obtained from the ray-tracing/Fokker-Planck codes GENRAY/CQL3D. Inversions closely matched predicted fast electron profiles for a range of experimental parameters.

Differential Cross-section Measurements for Deuteron Elastic Scattering on 11B

The implementation of boron in several fields, such as in the creation of p-type semiconductors in electronics, has created the need for the accurate quantitative determination of its depth profile concentrations in near surface layers of various matrices. In the framework of IBA techniques, a combination of Elastic Backscattering Spectroscopy (EBS), along with Nuclear Reaction Analysis (NRA), has been proposed in order to address the current needs for boron depth profiling, based on the use of a proton beam. Deuterons offer superior mass resolution with respect to protons, having similar stopping power values, but, unfortunately, the lack of experimental datasets concerning the deuteron elastic scattering on boron impedes their use. Thus, in the present work, the first set of measurements for the 11B(d,d0) differential cross sections covering the Ed,lab=1300-1860 keV energy range for the backscattering angles of 150°, 160° and 170° was carried out. The study was conducted at the 5.5 MV Tandem Accelerator of the Institute of Nuclear and Particle Physics, in the National Center of Scientific Research “Demokritos”, Athens, Greece. The target was a thin, self-supporting aluminum foil, upon which a thin natB (isotopic ratio: 11B 80.1%, 10B 19.9%) layer was deposited using the sputtering technique at RBI, Zagreb, Croatia, followed by the evaporation of an ultra-thin layer of 197Au on top for wear protection and normalization purposes. The outgoing particles were detected using 6 Silicon Surface Barrier (S.S.B.) detectors and the differential cross sections for the elastic scattering were determined from the resulting spectra via the relative measurement technique.

Swift and XMM–Newton observations of an RS CVn-type eclipsing binary SZ Psc: superflare and coronal properties

ABSTRACT We present an in-depth study of a large and long duration (&amp;gt;1.3 d) X-ray flare observed on an RS CVn-type eclipsing binary system SZ Psc using observations from Swift observatory. In the 0.35–10 keV energy band, the peak luminosity is estimated to be 4.2 × 1033 $\rm {erg}~\rm {s}^{-1}$. The quiescent corona of SZ Psc was observed ∼5.67 d after the flare using Swift observatory, and also ∼1.4 yr after the flare using the XMM–Newton satellite. The quiescent corona is found to consist of three temperature plasma: 4, 13, and 48 MK. High-resolution X-ray spectral analysis of the quiescent corona of SZ Psc suggests that the high first ionization potential (FIP) elements are more abundant than the low-FIP elements. The time-resolved X-ray spectroscopy of the flare shows a significant variation in the flare temperature, emission measure, and abundance. The peak values of temperature, emission measure, and abundances during the flare are estimated to be 199 ± 11 MK, 2.13 ± 0.05 × 1056 cm−3, 0.66 ± 0.09 $\rm {Z}_{\odot }$, respectively. Using the hydrodynamic loop modelling, we derive the loop length of the flare as 6.3 ± 0.5 × 1011 cm, whereas the loop pressure and density at the flare peak are derived to be 3.5 ± 0.7 × 103 dyn cm−2 and 8 ± 2 × 1010 cm−3, respectively. The total magnetic field to produce the flare is estimated to be 490 ± 60 G. The large magnetic field at the coronal height is supposed to be due to the presence of an extended convection zone of the subgiant and the high orbital velocity.

Spectral and timing properties of the recently discovered Be/X-ray pulsar eRASSUJ 052914.9−662446

ABSTRACT We have presented NuSTAR and Swift observations of the newly discovered Be/X-ray pulsar eRASSU J052914.9−662446. This is the first detailed study of the temporal and spectral properties of the pulsar using 2020 observations. A coherent pulsation of 1411.5 ± 0.5 s was detected from the source. The pulse profile was found to resemble a simple single-peaked feature that may be due to emission from the surface of the neutron star only. Pulse profiles are highly energy dependent. The variation of the pulse fraction of the pulse profiles is found to be non-monotonic with energy. The 0.5–20 keV Swift and NuSTAR simultaneous can be fitted well with power law modified by high-energy cut-off of ∼5.7 keV. The NuSTAR luminosity in the 0.5–79 keV energy range was ∼7.9 × 1035$\text{erg}\,\text{s}^{ -1}\,$. The spectral flux in 3–79 keV shows modulation with the pulse phase.

High energy millihertz quasi-periodic oscillations in 1A 0535 + 262 with Insight-HXMT challenge current models

ABSTRACT We studied the millihertz quasi-periodic oscillation (mHz QPO) in the 2020 outburst of the Be/X-ray binary 1A 0535 + 262 using Insight-HXMT data over a broad energy band. The mHz QPO is detected in the 27–120 keV energy band. The QPO centroid frequency is correlated with the source flux and evolves in the 35–95 mHz range during the outburst. The QPO is most significant in the 50–65 keV band, with a significance of ∼8σ, but is hardly detectable (&amp;lt;2σ) in the lowest (1–27 keV) and highest (&amp;gt;120 keV) energy bands. Notably, the detection of mHz QPO above 80 keV is the highest energy at which mHz QPOs have been detected so far. The fractional rms of the mHz QPO first increases and then decreases with energy, reaching the maximum amplitude at 50–65 keV. In addition, at the peak of the outburst, the mHz QPO shows a double-peak structure, with the difference between the two peaks being constant at ∼0.02 Hz, twice the spin frequency of the neutron star in this system. We discuss different scenarios explaining the generation of the mHz QPO, including the beat frequency model, the Keplerian frequency model, the model of two jets in opposite directions, and the precession of the neutron star, but find that none of them can explain the origin of the QPO well. We conclude that the variability of non-thermal radiation may account for the mHz QPO, but further theoretical studies are needed to reveal the physical mechanism.

Polarization constraints on the X-ray corona in Seyfert Galaxies: MCG-05-23-16

ABSTRACT We report on the first observation of a radio-quiet active galactic nucleus (AGN) in polarized X-rays: the Seyfert 1.9 galaxy MCG-05-23-16. This source was pointed at with the Imaging X-ray Polarimetry Explorer (IXPE) starting on 2022 May 14 for a net observing time of 486 ks, simultaneously with XMM-Newton (58 ks) and NuSTAR (83 ks). A polarization degree Π smaller than 4.7 per cent (at the 99 per cent confidence level) is derived in the 2–8 keV energy range, where emission is dominated by the primary component ascribed to the hot corona. The broad-band spectrum, inferred from a simultaneous fit to the IXPE, NuSTAR, and XMM-Newton data, is well reproduced by a power law with photon index Γ = 1.85 ± 0.01 and a high-energy cutoff EC = 120 ± 15 keV. A comparison with Monte Carlo simulations shows that a lamp-post and a conical geometry of the corona are consistent with the observed upper limit, a slab geometry is allowed only if the inclination angle of the system is less than 50°.

Boron neutron capture therapy for the treatment of lung cancer and assessment of dose received by organs at risk

Recent studies on boron neutron capture therapy (BNCT) have focused on investigating the appropriate neutron sources based on accelerators for neutron production, such as 7Li(p,n)7 Be. The therapeutic abilities of BNCT have been studied for the possible treatment of lung cancer using thermal and epithermal neutron beams. For neutron transport, the Monte Carlo N-particle transport code was used, and doses in the organs of different Oak Ridge National Laboratory phantoms were evaluated. The right lung was meshed with voxels to obtain depth-dose distributions using 1 eV, 10 eV, 100 eV, 1 keV, 5 keV, 8 keV and 10 keV energy sources. These results suggest that BNCT with an epithermal neutron beam can be used to treat lung cancer. By evaluating the biological dose rate and dose-depth distribution curves in healthy tissues and tumors by simulating a lung phantom, the quantities in the phantom were also evaluated. Our calculations show that with increasing boron concentration applied to the tumor, the dose is increased and the 100 eV energy source has the greatest effect on the tumor dose.

Three-year annual modulation search with COSINE-100

COSINE-100 is a direct detection dark matter experiment that aims to test DAMA/LIBRA's claim of dark matter discovery by searching for a dark matter-induced annual modulation signal with NaI(Tl) detectors. We present new constraints on the annual modulation signal from a dataset with a 2.82 yr livetime utilizing an active mass of 61.3 kg, for a total exposure of 173 kg$\cdot$yr. This new result features an improved event selection that allows for both lowering the energy threshold to 1 keV and a more precise time-dependent background model. In the 1-6 keV and 2-6 keV energy intervals, we observe best-fit values for the modulation amplitude of 0.0067$\pm$0.0042 and 0.0051$\pm$0.0047 counts/(day$\cdot$kg$\cdot$keV), respectively, with a phase fixed at 152.5 days.

Direct measurement of the ionization quenching factor of nuclear recoils in germanium in the keV energy range

This article reports the measurement of the ionization quenching factor in germanium for nuclear recoil energies in the keV range. Precise knowledge of this factor in this energy range is highly relevant for coherent elastic neutrino-nucleus scattering and low mass dark matter searches with germanium-based detectors. Nuclear recoils were produced in a thin high-purity germanium target with a very low energy threshold via irradiation using monoenergetic neutron beams. The energy dependence of the ionization quenching factor was directly measured via kinematically constrained coincidences with surrounding liquid scintillator based neutron detectors. The systematic uncertainties of the measurements are discussed in detail. With measured quenching factors between 0.16 and 0.23 in the 0.4 keV_{nr} to 6.3 keV_{nr} energy range, the data are compatible with the Lindhard theory with a parameter k of 0.162 pm ,0.004 (stat + sys).

Multicell accelerating structure driven by a lens-focused THz pulse

Recently, gradients on the order of $1\text{ }\text{ }\mathrm{GV}/\mathrm{m}$ have been obtained with single-cycle ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{ps}$) THz pulses produced by the conversion of high peak power laser radiation, in nonlinear crystals ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{mJ}$, 1 ps, up to 3% conversion efficiency). Such high intensity radiation can be utilized for charged particle acceleration. For efficient acceleration, a large number of accelerating cells have to be stacked together with delay lines in order to provide proper timing between accelerating fields and moving electrons. Additionally, THz pulses in individual cells need to be focused transversely to maximize the accelerating gradient. This focusing is currently done by the tapering of the waveguide. In this paper, we propose instead to use dielectric lenses for the robust focusing of THz pulses in accelerating cells. Each lens is made from the same material as the delay line in a monolithic unit. We have fabricated prototype units from quartz and silicon. Such an approach simplifies the fabrication and alignment of the multicell accelerating structure. We present a design in which a 100 microJoule THz pulse produces a 600 keV energy gain in a 5-mm long 10-cell accelerating structure for an ultrarelativistic electron. This approach can be extended to nonrelativistic particles.

The SVOM/ECLAIRs image trigger with wavelet-based background correction optimised with a one-year simulation of observations

Context. The Space-based multi-band astronomical Variable Objects Monitor (SVOM) mission under development will carry four instruments, and in particular the coded-mask telescope named ECLAIRs, with a large field of view of about 2 sr, operating in the 4–150 keV energy band. The trigger software on board ECLAIRs will search for high-energy transients such as gamma-ray bursts and peculiar behaviour (e.g. strong outbursts) from known X-ray sources, in order to repoint the satellite to perform follow-up observations with the onboard narrow field of view instruments. Aims. The image trigger, one of the two algorithms implemented in the software on board ECLAIRs, produces images over periods of exposure ranging from 20 s to 20 min during which the Earth can cross the field of view. The Cosmic X-ray Background and contributions from known X-ray sources are expected to dominate the ECLAIRs astrophysical and instrumental background and must be taken into account and corrected prior to coded-mask image deconvolution in order to optimise the sensitivity to faint transients. Methods. To correct these background components, we implemented and studied a traditional fitting method and a new method based on wavelet decomposition of the detector image. In order to study and to assess the performance of these methods, we performed a 1-yr simulation of the image trigger on board ECLAIRs. From the images produced during this realistic observation scenario of the SVOM mission, we also defined a way to analyse the sky images to search for new sources. Results. We present the algorithms behind the image trigger on board SVOM/ECLAIRs. We show that the wavelet method we implemented provides similar results in terms of cleaning performance compared to the traditional fitting method, and has the benefit of not requiring any assumption on the shape of the background on the detector. We also calibrate the detection threshold to be adaptive and based on the quality of the reconstructed sky image.

Investigation of statistical correlation of negative parity energy levels in Tm nucleus with A=170

In this paper, the statistical properties of 1- to 7- negative parity levels in the 170Tm nucleus are considered with emphasis on the nearest neighbor spacing distribution in the framework of random matrix theory. The latest available experimental data for different negative parity energy levels in the E≤ 3000 keV region are used to classifiy in different sequences and are analysed. The Berry – Robnik distribution function and the least square extraction method have been used to determine the parameter of distribution function in considered sequences. The results show the adaptation of the statistical behavior of all considered negative parity levels with the Wigner distribution function and therefore, the statistical correlation of such levels. Also, the strong correlations are yield for the sequences prepared by levels with odd spin values while the 2- levels show a weak correlation and a Poisson-like behavior. The dependence of the statistical behavior of the negative parity levels to the energy was investigated which suggests the maximum correlation in the 1300 <E < 2100 keV energy region.

Hard x-ray spectrometer calibrations using a portable120kV x-ray source.

A Cauchois transmission-crystal hard x-ray spectrometer was calibrated by using a portable, compact, battery-powered tungsten x-ray source having 120 peak kilovoltage. The source emission region was characterized by recording high-resolution 2D x-ray images and was found to be composed of three emission regions having a 400 µm overall extent. The absolutely calibrated source fluence was measured by using a calibrated silicon drift detector and was in good agreement with the spectrum calculated by the SpekPy code. High-resolution spectra of the W Kα and Kβ lines in the 57-70keV energy range were recorded on image plate detectors by the Cauchois spectrometer and provided excellent calibrations of the spectrometer's dispersion and spectral resolution. The minimal effect of the source size in the spectral lines recorded on the spectrometer's Rowland circle and the source-size broadening of the spatial lines recorded well beyond the Rowland circle were analyzed. The integrated reflectivity of the spectrometer's quartz (101) crystal was measured by using the absolutely calibrated 59.318keVW Kα1 spectral line emission and was in agreement with previous integrated reflectivity measurements performed at the National Institute of Standards and Technology. The well-characterized portable120kV x-ray source provides a convenient and cost-effective way to accurately calibrate the sensitivity, dispersion, spectral resolution, and source-size broadening in the spectra recorded by high-resolution x-ray spectrometers operating in the hard x-ray range. The absolutely calibrated source fluence can also be used to calibrate x-ray detectors at energies in the 40-100keV energy range.

The faintest solar coronal hard X-rays observed with FOXSI

Context. Solar nanoflares are small impulsive events releasing magnetic energy in the corona. If nanoflares follow the same physics as their larger counterparts, they should emit hard X-rays (HXRs) but with a rather faint intensity. A copious and continuous presence of nanoflares would result in a sustained HXR emission. These nanoflares could deliver enormous amounts of energy into the solar corona, possibly accounting for its high temperatures. To date, there has not been any direct observation of such persistent HXRs from the quiescent Sun. However, the quiet-Sun HXR emission was constrained in 2010 using almost 12 days of quiescent solar off-pointing observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). These observations set 2σ upper limits at 3.4 × 10−2 photons s−1 cm−2 keV−1 and 9.5 × 10−4 photons s−1 cm−2 keV−1 for the 3–6 keV and 6–12 keV energy ranges, respectively. Aims. Observing faint HXR emission is challenging because it demands high sensitivity and dynamic range instruments. The Focusing Optics X-ray Solar Imager (FOXSI) sounding rocket experiment excels in these two attributes when compared with RHESSI. FOXSI completed its second and third successful flights (FOXSI-2 and -3) on December 11, 2014, and September 7, 2018, respectively. This paper aims to constrain the quiet-Sun emission in the 5–10 keV energy range using FOXSI-2 and -3 observations. Methods. To fully characterize the sensitivity of FOXSI, we assessed ghost ray backgrounds generated by sources outside of the field of view via a ray-tracing algorithm. We used a Bayesian approach to provide upper thresholds of quiet-Sun HXR emission and probability distributions for the expected flux when a quiet-Sun HXR source is assumed to exist. Results. We found a FOXSI-2 upper limit of 4.5 × 10−2 photons s−1 cm−2 keV−1 with a 2σ confidence level in the 5–10 keV energy range. This limit is the first-ever quiet-Sun upper threshold in HXR reported using ∼1 min observations during a period of high solar activity. RHESSI was unable to measure the quiet-Sun emission during active times due to its limited dynamic range. During the FOXSI-3 flight, the Sun exhibited a fairly quiet configuration, displaying only one aged nonflaring active region. Using the entire ∼6.5 min of FOXSI-3 data, we report a 2σ upper limit of ∼10−4 photons s−1 cm−2 keV−1 for the 5–10 keV energy range. Conclusions. The FOXSI-3 upper limits on quiet-Sun emission are similar to that previously reported, but FOXSI-3 achieved these results with only 5 min of observations or about 1/2600 less time than RHESSI. A possible future spacecraft using hard X-ray focusing optics like those in the FOXSI concept would allow enough observation time to constrain the current HXR quiet-Sun limits further, or perhaps even make direct detections. This is the first report of quiet-Sun HXR limits from FOXSI and the first science paper using FOXSI-3 observations.

An Insight-HXMT View of the mHz Quasi-regular Modulation Phenomenon in the Black Hole X-Ray Binary 4U 1630–47

Here we report the spectral-timing results of the black hole X-ray binary 4U 1630–47 during its 2021 outburst using observations from the Hard X-ray Modulation Telescope (Insight-HXMT). Type C quasi-periodic oscillations (QPOs) in ∼1.6–4.2 Hz and quasi-regular modulation (QRM) near 60 mHz are detected during the outburst. The mHz QRM has a fractional rms of ∼10%–16% in the 8–35 keV energy band with a Q factor (frequency/width) of ∼2–4. Benefiting from the broad energy band of Insight-HXMT, we study the energy dependence of the ∼60 mHz QRM in 1–100 keV for the first time. We find that the fractional rms of the mHz QRM increases with photon energy, while the time lags of the mHz QRM are soft and decrease with photon energy. Fast recurrence of the mHz QRM, in a timescale of less than 1 hr, has been observed during the outburst. During this period, the corresponding energy spectra moderately change when the source transitions from the QRM state to the non-QRM state. The QRM phenomenon also shows a dependence with the accretion rate. We suggest that the QRM could be caused by an unknown accretion instability aroused from the corona.

L‐Value and Energy Dependence of 0.1–50 keV O+, He+, and H+ Ions for CME and CIR Storms Over the Entire Van Allen Probes Era

AbstractOur studies report the first observation of L‐value and energy sorted correlation of differential fluxes of 0.1–50 keV O+, He+, and H+ ions with different geophysical parameters for 29 Coronal Mass Ejected (CME) and 40 Corotating Interaction Region (CIR)‐driven geomagnetic storms during the entire Van Allen Probes era. For both solar wind drivers, ions with ≥1 keV energies show more variability in response to the solar wind changes, while the lower energy (&lt;1 keV) ions are relatively stable. During the in‐storm interval, O+ ions show maximum flux enhancement and become further prominent during CME storms. O+ ion (≥10 keV) fluxes show good correlation with − VswBz, and Sym‐H index during CME‐driven storms in the L ∼2.5–5.5. Apart from this, the average duration of persistence (〈Δt〉) for enhanced fluxes is higher for CIR‐driven storms with &gt;&gt; at E ≤ 50 keV in the L ∼2.5–5.5. Moreover, the observed value of 〈Δt〉i (where i is O+, H+ or He+) increases with the increasing L. We discuss the plausible mechanisms to provide a comprehensive overview of L‐values and energy sorted O+, He+ and H+ ion dynamics for two different categories of solar wind drivers.

Theoretical study of the enhancement of saturable absorption of Kr under x-ray free-electron laser

The generation of hollow atoms will reduce the probability of light absorption and provide a high-quality diffraction image in the experiment. In this paper, we calculated the ionization rate of the Kr atom under x-ray free-electron laser (XFEL) using Hartree–Fock–Slater model and simulated the ionization model of Kr atom using Monte–Carlo method to determine the response of the hollow atom of Kr atom to the XFEL photon energy. Calculating the correlation between the total photoionization cross-section of the ground state of Kr atom and the photon energy, we determined three particular photon energies of 1.75 keV, 1.90 keV, and 14.30 keV. The dynamics simulation under the experimental condition’s 17.50 keV photon energy was achieved by implementing the Monte–Carlo method and calibrating the photon flux modeling parameters. Consequently, our calculated data are more consistent with experimental phenomena than previous theoretical studies. The saturable absorption of Kr at 1.75 keV, 1.90 keV, 14.30 keV, and 17.50 keV energies was further investigated by using the optimized photon flux model theory. We compared the statistics on main ionization paths under those four specific photon energies and calculated the population changes of various Kr hollow atoms with different configurations. The results demonstrate that the population of hollow atoms produced at the critical ionization photon energy is high. Furthermore, the change of population with respect to position is smooth, which shows a significant difference between the generation mode of ions with low and high photon energies. The result is important for the study of medium- and high-Z element hollow atoms, which has substantial implications for the study of hollow atoms with medium and high charge states, as well as for the scaling of photon energy of free electron lasers.