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Theoretical ab initio Evolution of Satellite Intensity near Threshold for Cu K-shell transitions

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Pith's one-line read Ab initio calculations of copper K-shell spectra recover the measured rise of satellite intensity from the adiabatic to sudden regime and show that near-threshold intensity comes from oxide resonances, not shake processes.

desk verdict Solid ab-initio MCDF satellite library for Cu Kα with a clean high-energy limit; near-threshold shape and oxide peaks still need several fitted multipliers. read the letter →

arxiv 2607.07983 v1 pith:JZF2RCV2 submitted 2026-07-08 physics.atom-ph quant-ph

Daniel Pinheiro , Gonçalo Baptista , César Godinho , André Fernandes , Jorge Machado , Pedro Amaro , Nancy Paul , Martino Trassinelli
show 4 more authors
Miguel Avillez Paul Indelicato José Paulo Santos Mauro Guerra
This is my paper · ORCID
classification physics.atom-phquant-ph
keywords satelliteintensityK-shelltransitionsshakeprobabilitysuddenapproximationmulticonfigurationDirac-FockcopperoxidesX-rayfluorescencenear-thresholdevolution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

When an X-ray photon knocks a copper atom's deepest electron out of its shell, weaker satellite lines appear beside the main K-alpha emission. Their strength grows as the photon energy climbs above the ionization edge, marking the change from adiabatic to sudden shake-off and shake-up. This paper shows that ordinary multiconfiguration Dirac-Fock calculations of every transition rate and every shake probability, followed by a simple overlap of Lorentzian level widths with a Gaussian beam profile, already reproduce that measured rise within experimental error. Below the metallic copper edge the same calculation finds no intensity; the residual signal matches resonant 1s-to-3d and 1s-to-4p excitations of surface Cu(I) and Cu(II) oxides. The result means that high-resolution fluorescence spectra near threshold can be simulated from first principles without free intensity parameters, and that apparent satellites can be oxide fingerprints rather than multi-electron shake.

What carries the argument

An energy-dependent intensity modulation obtained by numerical overlap of each ionized level's Lorentzian (or Heaviside-modified) natural profile with a Gaussian beam-energy distribution; this factor multiplies the ab initio shake-weighted rates so that channels open continuously from threshold to the sudden-approximation limit.

What would settle it

A new high-resolution, oxide-free copper-foil fluorescence scan that still shows residual intensity between 8975 eV and 8998 eV would falsify the claim that the below-threshold signal is solely oxide resonance; conversely, an oxide-free surface whose ratios match the pure-ionization simulation would confirm it.

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Extended reading notes

Core claim

Standard state-of-the-art ab initio methods achieve good agreement with experiment and enable simulation of the intensity evolution near ionization thresholds within a good margin of error; the below-threshold satellite intensity originates from resonant 1s to 3d and 1s to 4p excitations in Cu(I) and Cu(II) oxide phases, which were included in the simulations.

Load-bearing premise

That four process-dependent width multipliers and three oxide intensity normalizations, obtained by fitting the calculated profiles to the published experimental ratios, correctly absorb solid-state and instrumental broadening without introducing uncontrolled bias.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript computes Cu K-shell diagram and satellite transitions with MCDFGME (energies, radiative/non-radiative rates, and sudden-approximation shake probabilities, including a single-shake binomial correction), then builds synthetic Kα1,2 spectra. Near-threshold intensity evolution is modeled by an overlap integral of a Heaviside-modified Lorentzian level profile with a Gaussian beam profile (Eqs. 11–13). High-energy satellite-to-total ratios are compared with Galambosi et al. and with the Thomas and Roy models; residual below-edge intensity is attributed to resonant 1s→3d (Cu(II)) and 1s→4p (Cu(I)) excitations whose strengths and energy shifts are adjusted by nested-sampling fits that also introduce process-dependent width multipliers (Table IV, §IV A).

Significance. A fully ab-initio MCDF treatment of both shake-off and shake-up channels for Cu Kα, together with an explicit single-shake formula and a transparent modulation integral, is a useful contribution to high-resolution X-ray metrology. The high-energy asymptotic ratio µ∞ ≈ 0.262 matches the calculated total shake probability (0.260) and lies inside the experimental uncertainty, confirming that SA shake probabilities remain a good proxy once all decay channels are open. The oxide-resonance assignment is physically motivated by XANES literature and offers a concrete alternative interpretation of the Galambosi below-edge structure. These strengths are real even if the near-threshold shape is not parameter-free.

major comments (3)
  1. Abstract and §VI claim that “standard state-of-the-art ab initio methods” already achieve good agreement “within a good margin of error” and that below-threshold intensity “was found to originate” from oxide resonances. In practice the rise shape and the three labeled A/B/C peaks are obtained only after nested-sampling optimization of four independent width multipliers (Md ≈ 5, Mo ≈ 7, Mu = 1, Me ≈ 0.54) and three oxide intensity normalizations (Table IV, §IV A). These multipliers rescale the partial widths that enter the modulation integral (Eqs. 11–13), so they alter the predicted energy dependence of each channel rather than acting as mere experimental broadenings. With sparse, high-uncertainty experimental points the fit can absorb residual solid-state or cross-section effects, making the central claim less ab-initio than stated. The abstract and conclusions should be rewritten to di
  2. §III and Table I: approximately 2.9 % of the total shake-up probability is missing because only low-n channels were computed; the missing weight is redistributed proportionally among the existing channels before simulation. Because the redistributed intensity inherits the thresholds of the low-n excitations, the energy dependence of the first rise above the K edge is altered by construction. The manuscript should either (i) quantify the change in the simulated ratio when the missing weight is omitted or placed at a continuum threshold, or (ii) demonstrate that the redistribution does not shift the fitted energy thresholds outside their quoted uncertainties.
  3. §V B and Table V: the oxide species are modeled as free Cu(I)/Cu(II) ions with a single 4p or 3d spectator. The fitted intensity multipliers for peaks B and C reach factors of order 10 (Table IV), which the text attributes either to normalization of the overlap integral or to resonant cross-section enhancement. Without an independent estimate of oxide thickness or of the resonant excitation cross section relative to K-shell ionization, the assignment remains under-constrained. At minimum the paper should report the absolute intensity scale of the oxide contribution relative to bulk Cu and discuss whether a surface oxide of realistic thickness (~100 nm) can produce the observed peak heights.
minor comments (5)
  1. Eq. (1) (Thomas model) and the subsequent fit discussion: the numerical prefactor 15.32 is left unexplained; a brief derivation or reference would help readers reproduce the fit.
  2. Fig. 5 versus Fig. 9: the same experimental points appear with and without oxide contributions; a single multi-panel figure with a clear legend would reduce confusion.
  3. Table I: the two 2J columns are not defined in the caption; a short note that they refer to the total angular momentum of the Cu ground state would improve readability.
  4. Several typographical inconsistencies appear (e.g., “ab initio” vs “abinitio”, missing spaces after commas in author affiliations). A careful copy-edit is needed.
  5. The Roy-model fit (Table II) reports binding energies that differ from theory by many σ for the experimental data set; a short remark on whether this indicates missing physics or simply the limited number of free parameters would be useful.

Circularity Check

2 steps flagged · score 5.0 of 10

Near-threshold rise and oxide A/B/C peaks are reproduced only after nested-fit width multipliers (Md~5, Mo~7) and oxide intensity normalizations rescale the ab-initio modulation integrals against the same Galambosi data.

  1. fitted input called prediction [§IV A, Table IV; modulation Eqs. (11)–(13)]
    "For our initial fits, the direct use of these integrals and the inclusion of energy shifts for each process was not sufficient to reproduce the near threshold region of the experimental data. o we have included a singular width multiplier for the level profile of each process. o These factors, as well as the experimental energy shifts, were adjusted using nested fit. o the final evidence obtained in the fitting is then used to obtain the most likely set of (Md, Mo, Mu, Me) width multipliers through interpolation."

    The multipliers rescale the very partial widths ΓiP that enter the intensity-modulation integral F claimed to model the adiabatic-to-sudden evolution from first principles. Optimizing Md≈5, Mo≈7, Mu=1, Me≈0.54 (and the associated energy shifts) against the Galambosi satellite-ratio data forces the simulated rise shape to match that data; the subsequent “good agreement” is therefore not an independent prediction of the ab-initio rates plus unadjusted modulation.

  2. fitted input called prediction [§IV A, Table IV; Figs. 9–10; abstract claim on oxide origin]
    "as this intensity originates from different atomic structures (Cu(I) and Cu(II)) present in the sample in unknown amounts, and the excitation probabilities could not be normalized ab initio to the ionization, a normalization multiplier to the intensity was required. o Intensity o A 0.14±0.08 o B 13±3 o C 9±1. Below-threshold satellite intensity was found to originate from resonant 1s→3d and 1s→4p excitations in Cu(I) and Cu(II) oxide phases respectively, which were included in our simulations."

    The abstract’s claim that the below-threshold intensity “was found to originate” from the oxide resonances is obtained only after free intensity multipliers (as large as ×13) are fitted so that the added A/B/C peaks reproduce the sparse experimental points. Without those normalizations the oxide contributions would not match the observed ratios; the origin assignment is therefore a fitted explanation rather than an ab-initio prediction.

full rationale

The high-energy asymptotic satellite ratio µ∞ ≈ 0.262 is essentially the MCDF total-shake probability (0.260) and is therefore an independent ab-initio result. The energy-dependent shape that rises from the K-edge, however, is generated by the overlap integral F (Eqs. 11–13) whose Lorentzian widths ΓiP are subsequently multiplied by four free process-dependent factors (Md, Mo, Mu, Me) that are optimized, together with energy shifts and three oxide intensity normalizations, by nested sampling to maximize Bayesian evidence on the Galambosi et al. satellite-ratio points. Without those multipliers the pure ab-initio modulation “was not sufficient to reproduce the near threshold region.” Consequently the claimed “good agreement o within a good margin of error” and the assignment of below-threshold intensity to Cu(I)/Cu(II) 1s→4p/3d resonances are partially forced by construction rather than pure first-principles predictions. The circularity is only partial because the asymptotic value and the qualitative inclusion of oxide channels remain independent of the fit.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The load-bearing claim rests on the validity of the sudden-approximation shake formula, the MCDF wave-functions, the ad-hoc width multipliers, and the modeling of surface oxides as free Cu(I)/Cu(II) ions. Four continuous multipliers and three intensity normalizations are fitted to the target data; the oxide identification is taken from XANES literature but renormalized freely.

free parameters (6)
  • diagram width multiplier Md = 5
    Scales the Lorentzian width of diagram levels; fitted by nested sampling to maximize evidence against experimental ratios (Table IV, Md=5±4/3).
  • shake-off width multiplier Mo = 7
    Same role for shake-off channels; fitted (Mo=7±10/5).
  • shake-up width multiplier Mu = 1.0
    Fixed near 1 after evidence scan; still a free choice.
  • excitation width multiplier Me = 0.54
    Scales oxide resonance widths; fitted (Me=0.54±0.03).
  • oxide intensity normalizations (A,B,C) = 0.14 / 13 / 9
    Absolute scale of Cu(I)/Cu(II) resonant contributions relative to ionization; three free factors (Table IV).
  • energy shifts for diagram, shake-off, shake-up, oxide levels = -7 to -10 eV range
    Compensate for solid-state Fermi-level and chemical shifts absent from the free-atom calculation; fitted (Table IV).
assumptions (4)
  • domain assumption Sudden-approximation monopole shake probabilities computed from MCDF orbital overlaps correctly give the high-energy satellite intensity ratio.
    Invoked throughout Sections II E–F and used as the asymptotic limit of the modulation function.
  • ad hoc to paper The adiabatic-to-sudden crossover can be represented by a simple overlap integral of a Heaviside-modified Lorentzian level profile with a Gaussian beam profile.
    Introduced in Section II G; not derived from time-dependent Schrödinger equation but shown to mimic Thomas’s exponential form.
  • domain assumption Surface Cu oxides can be modeled as free Cu(I) and Cu(II) ions with only 1s→4p and 1s→3d excitations retained.
    Section V B; justified by XANES peak assignments but ignores ligand-field multiplet structure.
  • ad hoc to paper Missing high-n shake-up probability (~3 %) may be redistributed proportionally among the calculated low-n channels without distorting the energy dependence.
    Section III, after Table I.
invented entities (1)
  • Effective Lorentzian / Gaussian profiles with Heaviside cut-offs
    purpose: Enforce the asymmetric rise of ionization cross-section and normalize the modulation integral to unity far above threshold.
    Defined by Eqs. (11)–(13); no independent experimental verification outside the present fit.

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Pith. "Pith review of Theoretical ab initio Evolution of Satellite Intensity near Threshold for Cu K-shell transitions." pith.science (2026). https://pith.science/paper/JZF2RCV2

@misc{pith2026260707983,
  author       = {Pith},
  title        = {Pith review of: Theoretical ab initio Evolution of Satellite Intensity near Threshold for Cu K-shell transitions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JZF2RCV2}},
  note         = {Machine review of arXiv:2607.07983}
}
abstract

In this work, we have investigated the evolution of satellite intensity near the ionization threshold for Cu K-shell transitions through theoretical methods. Employing standard state-of-the-art ab initio methods, we have calculated all Cu K-shell transitions and simulated the full K$\alpha_1$ and K$\alpha_2$ spectrum where all transition parameters, as well as shake probabilities were determined theoretically. Through these calculations we show that standard state-of-the-art ab initio methods achieve good agreement with experiment and enable us to simulate the intensity evolution near ionization thresholds within a good margin of error. Below-threshold satellite intensity was found to originate from resonant 1s$\rightarrow$3d and 1s$\rightarrow$4p excitations in Cu(I) and Cu(II) oxide phases respectively, which were included in our simulations.

Figures

Figures reproduced from arXiv: 2607.07983 by the authors.

Figure 2
Figure 2. FIG. 2. Simulated Cu K [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Stem plots or stick spectra of some of the satellite [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Evolution of the line shape of the simulated K shell [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Evolution of the intensity ratio of the satellite lines, respective to the total K [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Visual representation of the final evidence interpola [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Set of simulations performed around the point (5.5, [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Final evidence curves used to determine the uncer [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Evolution of the intensity ratio of the satellite lines, respective to the total K [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Evolution of the intensity ratio of the satellite lines, respective to the total K [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison between the theoretical results for satel [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]

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Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    The length gauge was considered for all radiative transition rates

    was used. The length gauge was considered for all radiative transition rates. For the non-radiative rates, the continuum-electron wavefunctions were obtained by solving the Dirac-Fock equations with the same atomic potential of the initial state. Here, no relaxation was allowed in both initial and final states. In addition, the details of the adiabatic in...

    work page

  2. [2]

    Ultra-high- accuracy x-ray spectroscopy of transition metal oxides and rare earths

    To make this comparison, an adjustment of the the- oretical energy thresholds has to be made. This is due to the Fermi energy which arises from solid state effects and is not considered in the isolated atom model used FIG. 3. Stem plots or stick spectra of some of the satellite transitions included in the simulations. Transitions for the Cu(I) and Cu(II) ...

    work page arXiv 2025

  3. [3]

    T. D. Thomas, Transition from adiabatic to sudden ex- citation of core electrons, PHYSICAL REVIEW LET- TERS5, 10.1103/PhysRevLett.52.417 (1984). 15

    work page doi:10.1103/physrevlett.52.417 1984

  4. [4]

    D. Sier, J. W. Dean, N. T. T. Tran, T. Kirk, C. Q. Tran, J. F. W. Mosselmans, S. Diaz-Moreno, and C. T. Chantler, High-accuracy measurement, advanced theory and analysis of the evolution of satellite transitions in manganese kαusing xr-herfd, IUCrJ11, 620 (2024)

    work page 2024

  5. [5]

    Y. Ito, T. Tochio, H. Oohashi, and A. M. Vlaicu, Con- tribution of the [1s3d] shake process to kα1,2 spectra in 3d elements, Radiation Physics and Chemistry75, 1534 (2006)

    work page 2006

  6. [6]

    Y. Ito, T. Tochio, M. Yamashita, S. Fukushima, A. M. Vlaicu, Syrocki, K. S labkowska, E. Weder, M. Polasik, K. Sawicka, P. Indelicato, J. P. Marques, J. M. Sampaio, M. Guerra, J. P. Santos, and F. Parente, Structure of high-resolution kβ1,3 x-ray emission spectra for the ele- ments from ca to ge, Physical Review A97, 1 (2018)

    work page 2018

  7. [7]

    Y. Ito, T. Tochio, S. Fukushima, A. Taborda, J. M. Sam- paio, J. P. Marques, F. Parente, P. Indelicato, and J. P. Santos, Experimental and theoretical determination of the kα2/kα1 intensity ratio for zinc, Journal of Quan- titative Spectroscopy and Radiative Transfer151, 295 (2015)

    work page 2015

  8. [8]

    Y. Ito, T. Tochio, H. Ohashi, M. Yamashita, S. Fukushima, M. Polasik, K. S labkowska, Syrocki, E. Szyma´ nska, J. Rzadkiewicz, P. Indelicato, J. P. Mar- ques, M. C. Martins, J. P. Santos, and F. Parente, Kα1,2 x-ray linewidths, asymmetry indices, and [km] shake probabilities in elements ca to ge and comparison with theory for ca, ti, and ge, Physical Revi...

    work page 2016

Show all 56 references
  1. [9]

    M. H. Mendenhall, A. Henins, L. T. Hudson, C. I. Szabo, D. Windover, and J. P. Cline, High-precision measurement of the x-ray cu kαspectrum, Journal of Physics B: Atomic, Molecular and Optical Physics50, 10.1088/1361-6455/aa6c4a (2017)

    2017 doi

  2. [10]

    Galambosi, H

    S. Galambosi, H. Sutinen, A. Mattila, K. H¨ am¨ al¨ ainen, R. Sharon, C. C. Kao, and M. Deutsch, Near-threshold multielectronic effects in the cukα 1,2 x-ray spectrum, Physical Review A - Atomic, Molecular, and Optical Physics67, 5 (2003)

    2003

  3. [11]

    St¨ ohr, R

    J. St¨ ohr, R. Jaeger, and J. J. Rehr, Transition from adi- abatic to sudden core-electron excitation: N2 on ni(100), Physical Review Letters51, 821 (1983)

    1983

  4. [12]

    T. A. Carlson and M. O. Krause, Atomic readjustment to vacancies in the k and l shells of argon, Physical Review 137, A1655 (1965)

    1965

  5. [13]

    M. Roy, J. D. Lindsay, S. Louch, and S. J. Gurman, Multiple-electron excitation in x-ray absorption: a sim- ple generic model, Journal of Synchrotron Radiation8, 1103 (2001)

    2001

  6. [14]

    Guerra, J

    M. Guerra, J. M. Sampaio, G. R. V´ ılia, C. A. Godinho, D. Pinheiro, P. Amaro, J. P. Marques, J. Machado, P. In- delicato, F. Parente, and J. P. Santos, Fundamental Pa- rameters Related to Selenium Kαand KβEmission X-ray Spectra, Atoms9, 8 (2021)

    2021

  7. [15]

    Pinheiro, A

    D. Pinheiro, A. Fernandes, C. Godinho, J. Machado, G. Baptista, F. Grilo, L. Sustelo, J. M. Sampaio, P. Amaro, R. G. Leit˜ ao, J. P. Marques, F. Parente, P. In- delicato, M. de Avillez, J. P. Santos, and M. Guerra, K- and l-shell theoretical fluorescence yields for the fe ison...

    2022

  8. [16]

    J. P. Marques, J. M. Sampaio, J. P. Santos, P. Indeli- cato, and F. Parente, Theoretical fluorescence yields and widths of the K shell and the L subshells, for the Ne, Ar, and Kr isoelectronic sequences, X-Ray Spectrometry49, 69 (2020)

    2020

  9. [17]

    Guerra, J

    M. Guerra, J. M. Sampaio, T. I. Madeira, F. Parente, P. Indelicato, J. P. Marques, J. P. Santos, J. Hoszowska, J. C. Dousse, L. Loperetti, F. Zeeshan, M. M¨ uller, R. Unterumsberger, and B. Beckhoff, Theoretical and experimental determination of l -shell decay rates, line widt...

    2015

  10. [18]

    J. P. Desclaux, A multiconfiguration relativistic DIRAC- FOCK program, Computer Physics Communications9, 31 (1975)

    1975

  11. [19]

    Indelicato and J

    P. Indelicato and J. P. Desclaux, Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions, Physical Review A42, 5139 (1990)

    1990

  12. [20]

    Indelicato, J

    P. Indelicato, J. P. Santos, S. Boucard, and J.-P. De- sclaux, QED and relativistic corrections in superheavy elements, The European Physical Journal D45, 155 (2007)

    2007

  13. [21]

    J. P. Santos, F. Parente, S. Boucard, P. Indelicato, and J. P. Desclaux, X-ray energies of circular transitions and electron screening in kaonic atoms, Physical Review A 71, 032501 (2005)

    2005

  14. [22]

    P. O. L¨ owdin, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals, and convergence problems in the method of configurational interaction, Physical Review 97, 1474 (1955)

    1955

  15. [23]

    T. A. Carlson and C. W. Nestor, Calculation of electron shake-off probabilities as the result of x-ray photoioniza- tion of the rare gases, Physical Review A8, 2887 (1973)

    1973

  16. [24]

    T. V. B. Nguyen, H. A. Melia, F. I. Janssens, and C. T. Chantler, Multiconfiguration dirac-hartree-fock theory for copper kαand kβdiagram lines, satellite spectra, andab initiodetermination of single and double shake probabilities, Physical Review A105, 022811 (2022)

    2022

  17. [25]

    A. G. Kochur and V. A. Popov, Probabilities of multi- ple shake processes in sudden approximation, Journal of Physics B: Atomic, Molecular and Optical Physics39, 3335 (2006)

    2006

  18. [26]

    F. Wang, J. Shi, E. Stambulchik, and G. Zhao, Atomic data for modeling of cold photoionized copper, The Eu- ropean Physical Journal D79, 82 (2025)

    2025

  19. [27]

    Chernysheva and V

    L. Chernysheva and V. Yarzhemsky, Photoionization cross-sections of valence shells of 3d-elements in vuv-soft x-ray spectral region, Atomic Data and Nuclear Data Ta- bles158, 101650 (2024)

    2024

  20. [28]

    Dawra, M

    D. Dawra, M. Dimri, A. K. Singh, A. K. S. Jha, R. K. Pandey, and M. Mohan, Theoretical calculations of the photoionization cross sections for the ground and lowest two excited states of ni xviii ion, The European Physical Journal D76, 59 (2022)

    2022

  21. [29]

    A. K. Singh, D. Dawra, M. Dimri, A. K. S. Jha, and M. Mohan, Relativistic r-matrix calculations of photoion- ization cross sections of cu xviii, The European Physical Journal D73, 85 (2019)

    2019

  22. [30]

    Sardar, M

    S. Sardar, M. Bilal, M. A. Bari, R. T. Nazir, A. Han- nan, M. Salahuddin, and M. H. Nasim, Dirac r -matrix calculations of photoionization cross-sections of ni xiii, Monthly Notices of the Royal Astronomical Society458, 1504 (2016)

    2016

  23. [31]

    chao Liu, Spin-orbit components of resonant satellite photoionization of atomic cu, Chinese Physics Letters13, 899 (1996)

    J. chao Liu, Spin-orbit components of resonant satellite photoionization of atomic cu, Chinese Physics Letters13, 899 (1996). 16

    1996

  24. [32]

    A. W. Fliflet and H. P. Kelly, Photoionization of the 3 d , 3 p , and 3 s subshells of zn i, Physical Review A13, 312 (1976)

    1976

  25. [33]

    Sabbatucci and F

    L. Sabbatucci and F. Salvat, Theory and calculation of the atomic photoeffect, Radiation Physics and Chemistry 121, 122 (2016)

    2016

  26. [34]

    I. E. Brumboiu, O. Eriksson, and P. Norman, Atomic photoionization cross sections beyond the electric dipole approximation, Journal of Chemical Physics150, 10.1063/1.5083649 (2019)

    2019 doi

  27. [35]

    Kavˇ ciˇ c and M.ˇZitnik, Shake-up and shake-off pro- cesses (2023) pp

    M. Kavˇ ciˇ c and M.ˇZitnik, Shake-up and shake-off pro- cesses (2023) pp. 653–658

    2023

  28. [36]

    Deslattes, E

    R. Deslattes, E. K. Jr., P. Indelicato, L. de Billy, E. Lin- droth, J. Anton, J. Coursey, D. Schwab, C. Chang, R. Sukumar, K. Olsen, and R. Dragoset, X-ray transi- tion energies (version 1.2) (2005), [Accessed 16-03-2026]

    2005

  29. [37]

    Trassinelli, The nested fit data analysis program (MDPI AG, 2019) p

    M. Trassinelli, The nested fit data analysis program (MDPI AG, 2019) p. 14

    2019

  30. [38]

    M. Trassinelli, Bayesian data analysis tools for atomic physics, Nuclear Instruments and Methods in Physics Re- search, Section B: Beam Interactions with Materials and Atoms408, 301 (2017)

    2017

  31. [39]

    Guerra, P

    M. Guerra, P. Amaro, J. P. Santos, and P. Indelicato, Rel- ativistic calculations of screening parameters and atomic radii of neutral atoms, Atomic Data and Nuclear Data Tables117-118, 439 (2017)

    2017

  32. [40]

    Sanson, Exafs spectroscopy: a powerful tool for the study of local vibrational dynamics (2021)

    A. Sanson, Exafs spectroscopy: a powerful tool for the study of local vibrational dynamics (2021)

    2021

  33. [41]

    E. A. Stern, D. E. Sayers, and F. W. Lytle, Ex- tended x-ray-absorption fine-structure technique. iii. determination of physical parameters, NUMBER11, https://doi.org/10.1103/PhysRevB.11.4836 (1975)

    1975 doi

  34. [42]

    Beccara, G

    S. Beccara, G. Dalba, P. Fornasini, R. Grisenti, F. Ped- eriva, A. Sanson, D. Diop, and F. Rocca, Local thermal expansion in copper: Extended x-ray-absorption fine- structure measurements and path-integral monte carlo calculations, Physical Review B - Condensed Matter and Mate...

    2003 doi

  35. [43]

    Fornasini, S

    P. Fornasini, S. A. Beccara, G. Dalba, R. Grisenti, A. Sanson, M. Vaccari, and F. Rocca, Extended x-ray- absorption fine-structure measurements of copper: Local dynamics, anharmonicity, and thermal expansion, Physi- cal Review B - Condensed Matter and Materials Physics 70, 1 (2004)

    2004

  36. [44]

    Gaur and B

    A. Gaur and B. D. Shrivastava, A comparative study of the methods of speciation using x-ray absorption fine structure, Acta Physica Polonica A121, 647 (2012)

    2012

  37. [45]

    K. I. Shimizu, H. Maeshima, H. Yoshida, A. Satsuma, and T. Hattori, Ligand field effect on the chemical shift in xanes spectra of cu(ii) compounds, Physical Chemistry Chemical Physics3, 862 (2001)

    2001

  38. [46]

    Klysubun, Y

    W. Klysubun, Y. Thongkam, S. Pongkrapan, K. Won- In, J. T-Thienprasert, and P. Dararutana, Xas study on copper red in ancient glass beads from thailand, inAna- lytical and Bioanalytical Chemistry, Vol. 399 (2011) pp. 3033–3040

    2011

  39. [47]

    L. K. H. K. Alwis, M. R. Mucalo, B. Ingham, and P. Kap- pen, A combined sniftirs and xanes study of electrically polarized copper electrodes in dmso and dmf solutions of cyanate (nco-), thiocyanate (ncs-) and selenocyanate (ncse-) ions, Journal of The Electrochemical Society16...

    2015

  40. [48]

    W. Xu, Y. Zhang, K. Ishii, H. Wadati, Y. Zhu, Z. Guo, Q. Diao, Z. Hong, H. Han, and L. Zhao, Experimen- tal and theoretical investigation of high-resolution x- ray absorption spectroscopy (hr-xas) at the cu k-edge for cu2znsnse4, Condensed Matter8, 10.3390/cond- mat8010008 (2023)

    2023 doi

  41. [49]

    I. A. Pankin and A. V. Soldatov, Pecularities of xanes simulations for cu(ii) sites in square-planar coordination in cu-exchanged zeolites, Journal of Surface Investigation 16, 934 (2022)

    2022

  42. [50]

    Y. P. Liu, C. Gao, J. L. Zeng, J. M. Yuan, and J. R. Shi, Atomic data of cu i for the investigation of element abun- dance, Astrophysical Journal, Supplement Series211, 10.1088/0067-0049/211/2/30 (2014)

    2014 doi

  43. [51]

    A. K. Pradhan and S. N. Nahar, The opacity project: R-matrix calculations for opacities of high-energy- density astrophysical and laboratory plasmas, Atoms13, 10.3390/atoms13100085 (2025)

    2025 doi

  44. [52]

    S. N. Nahar, L. Zhao, W. Eissner, and A. K. Pradhan, R- matrix calculations for opacities.ii. photoionization and oscillator strengths of iron ions fexvii, fexviii and fexix 10.48550/arXiv.2308.14854 (2023)

    2023 doi arXiv

  45. [53]

    C. T. Chantler, J. A. Lowe, and I. P. Grant, Multiconfig- uration dirac-fock calculations in open-shell atoms: Con- vergence methods and satellite spectra of the copper kα photoemission spectrum, Physical Review A - Atomic, Molecular, and Optical Physics82, 10.1103/Phys- RevA....

    2010 doi

  46. [54]

    Deutsch, G

    M. Deutsch, G. Holzer, J. Hartwigs, J. Wolf, M. Fritsch, and E. Forster, Kαand kβx-ray emis- sion spectra of copper, PHYSICAL REVIEW A51, https://doi.org/10.1103/PhysRevA.51.283 (1995)

    1995 doi

  47. [55]

    W. C. Sauder, J. R. Huddle, J. D. Wilson2, and R. E. Lavilla, Detection of multiplet structure in cu kα1,2 by means of a monolithic double crystal spectrometer, PHYSICS LETTERS63, https://doi.org/10.1016/0375- 9601(77)90914-8 (1977)

    1977 doi

  48. [56]

    Mukoyama and K

    T. Mukoyama and K. Taniguchi, Atomic excitation as the result of inner-shell vacancy production, PHYSICAL RE- VIEW A36, https://doi.org/10.1103/PhysRevA.36.693 (1987)

    1987 doi

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