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Corrections to radiative rates between atomic configurations

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Configuration-averaged radiative rates in iron plasmas need a correction that depends on the spread of level energies within configurations, with the largest effect for Δn=0 3-3 transitions.

desk verdict A useful and honest application of Klapisch's UTA correction to iron opacity, but the quantitative correction factors for 3-3 transitions are inflated by a missing 3(deltaE/E)^2 term; the qualitative conclusion still holds. read the letter →

arxiv 2509.00207 v1 pith:6VDQ2EJH submitted 2025-08-29 physics.atom-ph physics.plasm-ph

Jean-Christophe Pain , Djamel Benredjem This is my paper · ORCID
classification physics.atom-phphysics.plasm-ph
keywords radiativeopacityconfigurationaveragingunresolvedtransitionarraysironRosselandmeanEinsteincoefficientsdetailedbalanceaccounting
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

The paper argues that standard configuration-averaged radiative rates—which replace all lines between two configurations by a single rate at the mean transition energy—systematically miss the effect of the spread of level energies within each configuration. It extends a previously proposed first-order correction to include the variance of the unresolved transition array, obtaining a multiplicative factor 1 + 3δE/E + 3σ²/E² for spontaneous emission. Applied to iron, the correction barely moves the Rosseland mean at solar-interior conditions (730.986 to 733.582 cm²/g at ρ=0.17 g/cm³, T=182 eV) but is more visible in the cooler, lower-density regime where 3s-3p and 3p-3d Δn=0 arrays dominate, lifting the mean from 7909.54 to 7913.91 cm²/g at ρ=0.01 g/cm³, T=22 eV. The paper also supplies a line-profile ansatz that keeps Kirchhoff's law valid when configuration-averaged Einstein coefficients are used, so the correction can be used in LTE-aware opacity codes.

What carries the argument

The central object is the correction factor in Eq. (7): F = 1 + 3δE_CC'/E_CC' + 3σ²_CC'/E²_CC'. Here E_CC' is the difference of configuration average energies, δE_CC' is the shift of the transition array (the strength-weighted first moment minus the average transition energy), and σ²_CC' is the UTA variance. The factor comes from Taylor-expanding the energy-dependent radial part of the Einstein A coefficient—proportional to (E_u - E_d)³—about the mean transition energy and retaining terms up to second order in the level-energy spread.

What would settle it

Take the first 3p-3d array in Table 5, sum all level-to-level spontaneous-emission Einstein coefficients with equal statistical weights, and compare the exact configuration average with A_CC'(1 + 3δE/E + 3σ²/E²). If the ratio differs from the predicted factor by more than a few percent (or by more than the estimated cubic term), the second-order truncation is falsified. An alternative is a laboratory opacity measurement at ρ=0.01 g/cm³, T=22 eV with enough spectral resolution to isolate the 3-3 feature and compare the enhanced opacity with the uncorrected prediction.

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Extended reading notes

Core claim

The paper's central claim is that configuration-averaged spontaneous-emission rates between atomic configurations should be multiplied by 1 + 3δE_CC'/E_CC' + 3σ²_CC'/E²_CC', where δE_CC' is the unresolved-transition-array (UTA) shift and σ²_CC' is its variance. This factor accounts for the fact that the levels within the initial and final configurations are not degenerate, and the usual replacement of all line energies by the mean configuration-energy difference is only a zeroth-order approximation. The paper demonstrates the impact on iron opacity at two conditions: a high-density, high-temperature case dominated by 2p-nd transitions, and a lower-density, lower-temperature case dominated by

Load-bearing premise

The correction formula assumes δE/E stays small enough that a Taylor series truncated at the quadratic term is accurate; for the 3-3 arrays δE/E is around 0.25–0.30, where the neglected cubic term is no longer negligible.

Editorial extensions

If this is right

  • Detailed-configuration-accounting opacity codes that use only mean configuration energies will systematically underestimate the spontaneous-emission contribution when configurations are close in energy.
  • The correction raises the Rosseland mean opacity for iron at ρ=0.17 g/cm³, T=182 eV from 730.986 to 733.582 cm²/g, a change relevant for comparing with Z-pinch iron opacity measurements.
  • At ρ=0.01 g/cm³, T=22 eV, where 3s-3p and 3p-3d Δn=0 transitions dominate, the correction is larger and lifts the Rosseland mean from 7909.54 to 7913.91 cm²/g, enough to matter for laser opacity experiments and models of β-Cephei-type star envelopes.
  • The first-order shift term dominates the correction in all studied arrays, with the second-order variance term contributing only a few percent of the shift's effect, and the third-order term is negligible for these cases.
  • To maintain Kirchhoff's law with corrected configuration-averaged rates, emission, absorption, and stimulated-emission profiles must be tied together by the prescription given in Section 6, for example starting from a Gaussian, Lorentzian, or Voigt stimulated-emission profile.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The reported numerical correction factors for the 3-3 arrays at ρ=0.01 g/cm³, T=22 eV should be read as order-of-magnitude estimates: since δE/E ≈ 0.25–0.30 there, the next, neglected term in the Taylor expansion plausibly contributes 20–30% of the correction, so the direction and scale are robust but the exact factors are not.
  • The same Taylor-expansion correction should carry over to collisional excitation rates between configurations, where the paper notes the radial factors vary nearly linearly with energy; this could alter non-LTE level populations more strongly than the opacity itself.
  • The profile-consistency prescription offers a concrete test: if the proposed profile relations are implemented in an existing configuration-averaged code, the computed source function in LTE should approach the Planckian; deviations would expose which profile assumption breaks down.
  • The formalism is naturally extendable to other elements and to superconfigurations, and the authors explicitly plan applications to tin, rare earths, and tungsten; for superconfigurations the correction terms involving inverse powers of E_CC' will require averaging over subshell populations.
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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 / 4 minor

Summary. The paper addresses configuration-averaged spontaneous-emission rates in detailed-configuration-accounting opacity codes. It derives a correction factor to the Einstein A coefficient from the UTA shift and variance, extending Klapisch's UTA corrections, and applies it to two iron-plasma cases: 2p-3d and 2p-4d transitions at ρ=0.17 g/cm³, T=182 eV, and 3s-3p and 3p-3d transitions at ρ=0.01 g/cm³, T=22 eV. The paper reports correction tables, opacity spectra, Rosseland means, and a detailed-balance section proposing line-profile relations intended to recover Kirchhoff's law. The main claim is that Δn=0 (3-3) transitions receive large corrections from the UTA shift and variance, and that these corrections matter for iron opacity at conditions relevant to stellar envelopes.

Significance. The method is parameter-free and the tabulated moments and corrections are extensive. The qualitative insight that Δn=0 transitions are most affected is plausible and is supported by the data. However, the central formula is truncated at a point where the omitted term is numerically large for the very transitions the paper emphasizes, so the quantitative results need revision before the method can be considered established. The detailed-balance section is an explicitly imposed consistency ansatz rather than a predictive derivation, which is acceptable as a proposal but should be framed as such.

major comments (3)
  1. [§3.2, Eq. (7)] Equation (7) is obtained by expanding (E_CC'+x)^3 with x=E_ud-E_CC'. Since the line-strength-weighted mean of x is δ_CC' and the variance is σ²_CC', the exact ratio <E^3>/E_CC'^3 is 1 + 3δ/E + 3σ²/E² + 3δ²/E² + 3δσ²/E³ + δ³/E³ + κ3/E³, where κ3 is the third centered moment. Eq. (7) omits 3δ²/E², which is not negligible for the 3-3 arrays in Tables 5 and 6: δ/E is about 0.25-0.30, so 3δ²/E² is roughly 0.19-0.27, i.e. about 10-15% of the claimed correction factor. For example, in the first row of Table 5, the omitted term is ≈0.24 while the retained terms are ≈0.86, changing the factor from ≈1.9 to ≈2.1. Because Tables 5, 6, and the opacity/Rosseland results of §5.4 are computed from Eq. (7), the numerical corrections are not quantitatively reliable. The sentence in §3.2 acknowledging that the expansion breaks down when C and C' are close in energy describes precisely the 3-3 regime to whi
  2. [Table 5 and §5.4] The tables feeding the opacity results contain internal inconsistencies. In the first row of Table 5, δf(1) is listed as 0.8943, but the columns give 3δ/E = 3×19.8400/69.7124 = 0.8539. This is not a small rounding effect, and similar checks are needed for the other rows. Since the numerical conclusions of §5.4 rest on these tables, all entries should be regenerated from one exact expression and checked for consistency. This is essential even after the missing 3δ²/E² term is restored, because the table inconsistency indicates that the numerical pipeline itself needs verification.
  3. [§5.4 and Conclusion] The reported integrated effect is much smaller than the large rate corrections shown in Tables 5 and 6: the Rosseland mean changes from 730.986 to 733.582 cm²/g (0.36%) in the first case and from 7909.54 to 7913.91 cm²/g (0.055%) in the second. The text uses words such as 'significant' and 'noticeable' for these effects. Large line-by-line rate corrections do not automatically translate into large Rosseland-mean changes, and the paper should quantify the significance claim explicitly and calibrate the abstract and conclusion accordingly. This is not a correctness error in the derivation, but it is important for the astrophysical interpretation.
minor comments (4)
  1. [§6.1] Typo: 'Kirhhoff's law' should be 'Kirchhoff's law'.
  2. [Table 6] The last two rows have configuration labels inconsistent with the stated 3s-3p transition type. For example, '3s2 3p5 3d5 - 2s2 2p6 3s1 3p6 3d5' and '3s1 3p5 3d2 - 2s2 2p6 3s0 3p6 3d2' introduce core shells not present on the left side. These labels should be corrected or explained.
  3. [Table 9 caption] The sentence 'Excluding the pathologic very sharp array, one finds α3 = 5.3822' appears to have a missing sign and decimal point; presumably it should read α3 = -0.53822. Please verify.
  4. [§6.1-6.2] The detailed-balance section is a stated ansatz (following Ref. [32]) rather than a unique derivation. I do not view this as circular, but the manuscript should state explicitly that the resulting profile relations are a modeling choice, that one profile remains arbitrary, and that the plots are illustrative rather than a validation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the correction factor is derived from UTA moments computed from the atomic-structure model and then applied to opacity, not fitted to the reported opacity outputs.

full rationale

The central correction factor in Eq. (7) is obtained by expanding the line-strength-weighted mean of (Eu-Ed)^3 about the configuration-average transition energy E_CC' and expressing the first- and second-order terms through the UTA moments µ1 = E_CC' + δE_CC' and σ²_CC' (Eqs. (6)-(9)). These moments are computed from Slater and spin-orbit integrals in the atomic-structure model, not fitted to the opacity values reported in §5.4. The opacity calculations are applications of the derived factor, and the Rosseland means are outputs, not inputs. The detailed-balance section (§6) explicitly imposes the Planckian form on the line profiles; it is a consistency prescription, not a prediction derived from the correction factor, so no circular reduction is involved. The few self-references ([10], [26]) support auxiliary formalism and the numerical code, and the main result does not depend on an unverified self-citation chain. A possible quantitative concern is the neglect of the 3(δE/E)^2 term in Eq. (7) for Δn=0 arrays with δE/E ≈ 0.25-0.30; that is a truncation accuracy issue, not circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to opacity data. The paper relies on standard atomic structure inputs and on the UTA statistical approximation. The main hidden assumption is the validity of the truncated expansion for the 3-3 transitions, and the profile ansatz for detailed balance is imposed rather than derived.

assumptions (5)
  • domain assumption Configuration-averaged rates can be built from the strength-weighted moments of the transition array (UTA formalism).
    Used throughout Sections 2 and 3; relies on the statistical treatment of many levels as a distribution.
  • domain assumption The Boltzmann population weight can be factorized from the strength-weighted energy moments in Eq. (4).
    Section 2.2 separates the Boltzmann sum from the moment μ3, assuming weak energy dependence of the exponential across the array.
  • domain assumption The Taylor expansion of Θ(E) about E_CC' can be truncated to low order.
    Section 3.1-3.2; the truncation produces Eq. (7) and is not valid when δE/E is large.
  • domain assumption The average-atom model subshell energies and populations in Tables 1 and 4 are accurate.
    Inputs to the corrections; the code [26] is cited but not independently verified.
  • ad hoc to paper A line profile ansatz can be imposed to recover Kirchhoff's law near LTE.
    Section 6.2 sets relations among spontaneous, absorption and stimulated profiles to force the Planckian source function; this is a consistency condition, not derived.

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Pith. "Pith review of Corrections to radiative rates between atomic configurations." pith.science (2026). https://pith.science/paper/6VDQ2EJH

@misc{pith2026250900207,
  author       = {Pith},
  title        = {Pith review of: Corrections to radiative rates between atomic configurations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6VDQ2EJH}},
  note         = {Machine review of arXiv:2509.00207}
}
abstract

The computation of radiative opacity or emissivity of hot dense matter is a challenging task. It requires accounting for an immense number of energy levels and lines across various excitation and ionization states. Whether in local thermodynamic equilibrium (LTE) or non-LTE plasmas, statistical methods provide significant assistance. Many computational codes are based on the Detailed Configuration Accounting approximation, which involves averaged rates between configurations. In that approach, only the mean energies of the configurations are considered, and the effects of the energy distributions of the levels within the initial and final configurations are typically neglected. A long time ago, Klapisch proposed a method to correct the rates. The corresponding formalism includes the energy shift and variance of the Unresolved Transition Array, as well as the average energies of the configurations. We extend this formalism and investigate its impact on opacity calculations in two specific cases: first, the iron experiment conducted at Sandia National Laboratories under conditions similar to those at the base of the Sun's convective zone, dominated by L-shell 2p-$n$d transitions, and second, laser experiments--still for iron--at much lower temperature. The latter measurements shed light on our understanding of the envelopes of $\beta$-Cephei-type stars, where the relevant transitions are intra-M-shell $\Delta n=0$ (3-3) transitions, specifically 3s-3p and 3p-3d, in the XUV range. The issue of ensuring the validity of Kirchhoff's law when plasmas approach LTE is also addressed, and a prescription is proposed, applying both to the standard configuration-to-configuration case and to the aforementioned corrections, which account for the energy distribution of the levels within a configuration.

Figures

Figures reproduced from arXiv: 2509.00207 by the authors.

Figure 1
Figure 1. Kurtosis (α4) versus skewness (α3) for the 2p-3d transition arrays displayed in table 7. Transition array Nb. lines ECC′ δECC′ σ 2 δf(1) δf(2) 2s2 2p5 - 2s2 2p4 4d1 34 1084.4551 5.21226 10.1557 (6.3149) 0.1442×10−1 0.2591×10−4 2s2 2p4 - 2s2 2p3 4d1 97 1154.82365 5.6333 11.8698 (6.5679) 0.1463×10−1 0.2670×10−4 2s2 2p3 - 2s2 2p2 4d1 97 1226.4677 6.0430 12.1352 (6.8281) 0.1478×10−1 0.2420×10−4 2s1 2p5 - 2s1 2p4 4d1 123… view at source ↗
Figure 2
Figure 2. Kurtosis (α4) versus skewness (α3) for the 2p-4d transition arrays reported in table 8. numerical values of the reduced centered moments up to α6 of various 2p-4d transition arrays in an iron plasma at ρ =0.17 g/cm3 and T =182 eV are given in table 8 of A. Six arrays are left-skewed, and 14 are right-skewed. The kurtosis values are all close to 3, indicating that the distributions are nearly Gaussian. Five of them e… view at source ↗
Figure 3
Figure 3. Kurtosis (α4) versus skewness (α3) for the 3p − 3d transition arrays displayed in table 9. -3 -2 -1 0 Skewness α3 0 2 4 6 8 Kurtosis α4 3s-3p transition arrays [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Kurtosis versus skewness for the 3s-3p transition arra [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Opacity of an iron plasma at ρ =0.17 g/cm3 and T =182 eV with and without the corrections. 5.4 Effect on radiative opacity Figures 5 and 6 represent the opacity of an iron plasma at ρ =0.17 g/cm3 and T =182 eV. We can see that the effect of the corrections on spectral …
Figure 6
Figure 6. Figure 6: Opacity of an iron plasma at ρ =0.17 g/cm3 and T =182 eV with and without the corrections. Zoom on the preceding figure over the XUV range. 0 20 40 60 80 100 120 140 160 180 200 Photon energy (eV) 104 105 106 Opacity (cm 2/g) without correction with correction [PITH_F…
Figure 7
Figure 7. Figure 7: Opacity of an iron plasma at ρ =0.01 g/cm3 and T =22 eV with and without the corrections. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Scaled configuration-averaged line profiles in the case of a [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Scaled configuration-averaged line profiles in the case of a [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Scaled configuration-averaged line profiles in the case of [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]

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Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    Mandelbaum, M

    P. Mandelbaum, M. Finkenthal, J. L. Schwob, and M. Klapisch. Int erpretation of the quasicontinuum band emitted by highly ionized rare-earth elements in the 70–100- ˚ A range. Phys. Rev. A , 35:5051– 5059, 1987

    work page 1987

  2. [2]

    Mandelbaum, J

    P. Mandelbaum, J. F. Seely, A. Bar-Shalom, and M. Klapisch. Effec t of configuration mixing on 3d-4f transitions in highly ionized Ga-, Zn-, and Cu-like ions. Phys. Rev. A , 44:5744–5751, 1991

    work page 1991

  3. [3]

    Mandelbaum, J

    P. Mandelbaum, J. F. Seely, D. R. Kania, and R. L. Kauffman. 3d-4 p x-ray spectrum emitted by highly ionized uranium from a laser-produced plasma in the λ 3.8-4.4 ˚ A wavelength range. Phys. Rev. A , 45:7484–7487, 1992

    work page 1992

  4. [4]

    Bauche-Arnoult, J

    C. Bauche-Arnoult, J. Bauche, and M. Klapisch. Variance of the distributions of energy levels and of the transition arrays in atomic spectra. Phys. Rev. A , 20:2424, 1979

    work page 1979

  5. [5]

    Peyrusse

    O. Peyrusse. Atomic configuration averages and non-local the rmodynamical equilibrium plasma spectroscopy calculations. J. Phys. B: At. Mol. Opt. Phys. , 32:683–700, 1999

    work page 1999

  6. [6]

    A superconfiguration model for broadband spect roscopy of non-LTE plasmas

    O Peyrusse. A superconfiguration model for broadband spect roscopy of non-LTE plasmas. J. Phys. B: At. Mol. Opt. Phys. , 33:4303–4321, 2000

    work page 2000

  7. [7]

    Hansen, J

    S.B. Hansen, J. Bauche, C. Bauche-Arnoult, and M.F. Gu. Hybrid atomic models for spectroscopic plasma diagnostics. High Energy Density Phys. , 3(1):109–114, 2007

    work page 2007

  8. [8]

    Abdallah and M

    J. Abdallah and M. E. Sherrill. The reduced detailed configuration a ccounting (RDCA) model for NLTE plasma calculations. High Energy Density Phys. , 4:124–130, 2008

    work page 2008

Show all 43 references
  1. [9]

    S. B. Hansen, J. Bauche, and C. Bauche-Arnoult. Superconfig uration widths and their effects on atomic models. High Energy Density Phys. , 7:27–37, 2011

    2011

  2. [10]

    Benredjem and J.-C

    D. Benredjem and J.-C. Pain. Excitation and ionization by electro n impact in transition and super- transition arrays. submitted to Phys. Rev. E , 2025

    2025

  3. [11]

    Winhart, K

    G. Winhart, K. Eidmann, C. A. Iglesias, and A. Bar-Shalom. Meas urements of extreme uv opacities in hot dense Al, Fe, and Ho. Phys. Rev. E , 53:R1332–R1335, 1996

    1996

  4. [12]

    Turck-Chi` eze, M

    S. Turck-Chi` eze, M. Le Pennec, J. E. Ducret, J. P. Colgan, D. P. Kilcrease, C. J. Fontes, F. Gilleron, J.-C. Pain, and N. Magee. Detailed opacity comparison for an improve d stellar modeling of the envelopes of massive stars. Astrophys. J. , 823:78, 2016

    2016

  5. [13]

    Poirier and F

    M. Poirier and F. de Gaufridy de Dortan. A comparison between d etailed and configuration- averaged collisional-radiative codes applied to nonlocal thermal equ ilibrium plasmas. J. Appl. Phys. , 101:063308, 2007. 20

    2007

  6. [14]

    On various validity criteria for the configuration avera ge in collisional–radiative codes

    M Poirier. On various validity criteria for the configuration avera ge in collisional–radiative codes. J. Phys. B: At., Mol. Opt. Phys. , 41:025701, 2008

    2008

  7. [15]

    Bar-Shalom, M

    A. Bar-Shalom, M. Klapisch, and J. Oreg. Electron collision excita tions in complex spectra of ionized heavy atoms. Phys. Rev. A , 38:1773–1784, 1988

    1988

  8. [16]

    Bauche, C

    J. Bauche, C. Bauche-Arnoult, and M. Klapisch. Transition arr ays in the spectra of ionized atoms. Adv. At. Mol. Phys. , 23:131–195, 1988

    1988

  9. [17]

    Klapisch

    M. Klapisch. A UTA approach to the collisional radiative model for ionization balance. In Proceed- ings of The Tenth International Colloquium on UV and X-Ray Sp ectroscopy of Astrophysical and Laboratory Plasmas, Berkeley, 1993. February 1992

    1993

  10. [18]

    Bauche and C

    J. Bauche and C. Bauche-Arnoult. Theory of complex spectra from laser plasmas , pages 325–355. Springer US, Boston, MA, 1994

    1994

  11. [19]

    Karazija

    R. Karazija. Sums of atomic quantities and mean characteristic s of spectra. Mokslas, Vilnius , page 272, 1991

    1991

  12. [20]

    Karazija

    R. Karazija. Evaluation of explicit expressions for mean charac teristics of atomic spectra. Acta Phys. Hungarica, 70:367–379, 1991

    1991

  13. [21]

    Karazija and S

    R. Karazija and S. Kucas. Summation of atomic quantities over a ll many-electron quantum numbers. Lith. J. Phys. , 35:155–170, 1995

    1995

  14. [22]

    J. Oreg, W. H. Goldstein, A. Bar-Shalom, and M. Klapisch. Config uration average of general n-body symmetrical tensor operators. J. Comput. Phys. , 91:460–477, 1990

    1990

  15. [23]

    Bar-Shalom and M

    A. Bar-Shalom and M. Klapisch. NJGRAF — An efficient program for calculation of general re- coupling coefficients by graphical analysis, compatible with NJSYM. Comput. Phys. Commun. , 50:375–393, 1988

    1988

  16. [24]

    J. E. Bailey, T. Nagayama, G. P. Loisel, G. A. Rochau, C. Blancar d, J. Colgan, Ph Cosse, G. Faus- surier, C. J. Fontes, F. Gilleron, I. Golovkin, S. B. Hansen, C. A. Ig lesias, D. P. Kilcrease, J. J. MacFarlane, R. C. Mancini, S. N. Nahar, C. Orban, J.-C. Pain, A. K. P radhan...

    2015

  17. [25]

    Buldgen, J.-C Pain, P

    G. Buldgen, J.-C Pain, P. Coss´ e, C. Blancard, F. Gilleron, A. K. P radhan, C. J. Fontes, J. Col- gan, A. Noels, J. Christensen-Dalsgaard, M. Deal, S. V. Ayukov, V . A. Baturin, A. V. Oreshina, R. Scuflaire, C. Pin¸ con, Y. Lebreton, T. Corbard, P. Eggenberg er, P. Hakel, and ...

    2025

  18. [26]

    J.-C. Pain. Solar opacity calculations: recent theoretical adva nces prompted by laser and Z-pinch experiments. Solar Phys. , 299:140, 2024

    2024

  19. [27]

    S. J. A. J. Salmon, P. Eggenberger, J. Montalb´ an, A. Miglio, A. Noels, G. Buldgen, F. Moyano, and G. Meynet. Asteroseismology of β Cephei stars: The stellar inferences tested in hare and hound exercises. Astron. AStrophys., 659:A142, 2022

    2022

  20. [28]

    Moskalik and W

    P. Moskalik and W. A. Dziembowski. New opacities and the origin of t he β Cephei pulsation. Astron. Astrophys., 256:L5–L8, 1992

    1992

  21. [29]

    R. F. Stellingwerf. Helium ionization driving in Beta Cephei stars. Astron. J. , 83:1184–1189, 1978

    1978

  22. [30]

    N. R. Simon. A plea for reexamining heavy element opacities in star s. Astrophys. J. , 260:L87–L90, 1982. 21

    1982

  23. [31]

    V. A. Makhrov, A. Y. Sechin, and A. N. Starostin. Theory of no nstationary transfer of resonance radiation under conditions of partial frequency redistribution. Sov. Phys. JETP , 70:623–631, 1990

    1990

  24. [32]

    Busquet, M

    M. Busquet, M. Klapisch, and A. Bar-Shalom. Absorption and em ission profiles of unresolved arrays near local thermodynamic equilibrium. J. Quant. Spectrosc. Radiat. Transfer , 81:255–263, 2003

    2003

  25. [33]

    Y. K. Zemtsov and A. N. Starostin. Does the probability for spo ntaneous emission depend on the density and the temperature? Sov. Phys. JETP , 76:186–199, 1993

    1993

  26. [34]

    D. C. Mayes, B. A. Hobbs, R. F. Heeter, T. S. Perry, H. M. Joh ns, Y. P. Opachich, M. Hohenberger, P. A. Bradley, E. C. Dutra, C. J. Fontes, E. Gallardo-Diaz, M. H. Mo ntgomery, H. F. Robey, M. S. Wallace, and D. E. Winget. Overview of oxygen opacity experiments a t the Nation...

    2025

  27. [35]

    P. R. Sen Sarma, M. T. Belmonte, and S. Mar. Characterisation of a hollow-cathode lamp to measure accurate branching fractions of rare-earth elements. Eur. Phys. J. D , 78:76, 2024

    2024

  28. [36]

    Kasen, B

    D. Kasen, B. Metzger, J. Barnes, E. Quataert, and E. Ramire z-Ruiz. Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event. Nature, 551:80–84, 2017

    2017

  29. [37]

    Hirai, H

    T. Hirai, H. Maier, M. Rubel, Ph. Mertens, R. Neu, E. Gauthier, J . Likonen, C. Lungu, G. Mad- daluno, G.F. Matthews, R. Mitteau, O. Neubauer, G. Piazza, V.Philipp s, B. Riccardi, C. Ruset, and I. Uytdenhouwen. R & D on full tungsten divertor and beryllium w all for JET ITER-l...

    2007

  30. [38]

    Ralchenko, J

    Y. Ralchenko, J. N. Tan, J. D. Gillaspy, J. M. Pomeroy, and E. Silv er. Accurate modeling of benchmark x-ray spectra from highly charged ions of tungsten. Phys. Rev. A , 74:042514, 2006

    2006

  31. [39]

    Benredjem, G

    D. Benredjem, G. Mondet, A. Calisti, F. Gilleron, and J.-C. Pain. O pacity of germanium and silicon in ICF plasmas. In Abdul A. S. Awwal, editor, High Power Lasers for Fusion Research II , volume 8602, page 860205. International Society for Optics and Photon ics, SPIE, 2013

    2013

  32. [40]

    Jarrah, D

    W. Jarrah, D. Benredjem, J.-C. Pain, and J. Dubau. NLTE opac ity calculations: C-Si and C-Ge mixtures. High Energy Density Phys. , 24:64–74, 2017

    2017

  33. [41]

    M. M. Al-Rabban. Term structure of 4d-electron configuratio ns and calculated spectrum in Sn- isonuclear sequence. J. Quant. Spectrosc. Radiat. Transfer , 97:278–316, 2006

    2006

  34. [42]

    Sheil, O

    J. Sheil, O. O. Versolato, A. J. Neukirch, and J. Colgan. Multiply- excited states and their con- tribution to opacity in CO2 laser-driven tin-plasma conditions. J. Phys. B: At., Mol. Opt. Phys. , 54(3):035002, jan 2021

    2021

  35. [43]

    asymmetry of the distribution

    J. Sheil, O. Versolato, V. Bakshi, and H. Scott. Review of the 1s t EUV Light Sources Code Com- parison Workshop. Atoms, 11(10), 2023. A Numerical values of high-order moments up to α6 The exact values of the moments up to α6 for 2p-3d and 2p-4d transition arrays for an iron p...

    2023

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.