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Atoms in Dense Plasmas: Models, Applications, and Current Challenges

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Pith's one-line read The thesis claims that a variational free-energy minimization can simultaneously determine the electron structure, the mean ionization, and the ion-fluid correlations of a dense plasma, making pressure ionization an emergent equilibrium…

desk verdict A habilitation synthesis rather than a single new result, but the VAMPIRES model and the generalized Debye-Hückel free-energy functionals are real contributions, and the thesis is refreshingly honest about where it does not yet work. read the letter →

arxiv 2411.18357 v2 pith:FJSYDE54 submitted 2024-11-27 physics.plasm-ph physics.atom-ph

Robin Piron This is my paper · ORCID
classification physics.plasm-phphysics.atom-ph
keywords denseplasmasaverage-atommodelspressureionizationion-ioncorrelationsvariationalfreeenergyvirialtheoremplasmaopacitynon-LTEcollisional-radiativemodeling
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

This thesis tries to establish that atomic models of dense plasmas can be built on a single free-energy principle, instead of grafting screening corrections onto isolated-ion atomic physics. In the VAAQP model, an average atom is immersed in a neutralizing jellium, bound and continuum electrons are treated quantum-mechanically on the same footing, and the model satisfies the virial theorem. In the VAMPIRES model, the ion-fluid pair correlation function becomes a variational variable, so the effective ion-ion potential, the displaced-electron cloud, and the mean ionization are determined together. The author's central claim is that pressure ionization, and the switch from the Debye-Hückel scale to the Wigner-Seitz scale in the decay of the effective potential, emerge from this first-principle treatment of the ion-fluid structure. This matters because opacity, equations of state, and ionization balance in high-energy-density plasmas currently rest on separate, sometimes inconsistent, definitions of the ion and its environment.

What carries the argument

The load-bearing machinery is a first-order cluster expansion of the electron density, $n(\mathbf{R}_1,\dots,\mathbf{R}_{N_i};\mathbf{r}) \approx n_e + \sum_j q(|\mathbf{r}-\mathbf{R}_j|)$, combined with a finite-temperature density-functional free energy for the electrons and a classical-fluid free energy for the ions. The central object is the generalized free-energy functional $\dot{F}\{h,q,n_e\}$ whose variables are the displaced-electron cloud $q(r)$, the jellium density $n_e$, and the ion-ion radial correlation function $h(r)=g(r)-1$; minimizing it under the neutrality constraint reproduces the Ornstein-Zernike equation with the chosen closure and yields the electron self-consistent equation. The special role of the free-energy functionals, which for the Debye-Hückel model were derived here for arbitrary interaction potentials, is that they make the virial theorem hold by construction, so thermodynamic quantities computed from the same functional are consistent with the pressure.

What would settle it

A decisive check would be a strongly coupled plasma, say lithium near the pressure-ionization edge at about 10 eV and several g/$cm^{3}$, where quantum molecular dynamics or X-ray Thomson scattering provides the pair correlation function and mean ionization; if the measured or simulated ionization state departs from VAMPIRES in a way that cavity-based models capture better, the claimed first-principle origin of pressure ionization is not supported.

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Extended reading notes

Core claim

The central claim is that one can write a variational average-atom model whose constrained minimization yields, at the same time, the bound and continuum electron structure, the average ion charge, and the equilibrium structure of the ion fluid. The VAMPIRES model realizes this by combining a first-order cluster expansion of the electron density with a generalized free-energy functional for a classical one-component fluid, taken in either the Debye-Hückel or the hypernetted-chain closure. The author shows that the equations obtained from minimizing this functional fulfill the virial theorem. In this model, the pressure-ionization phenomenon, as well as the switching from the Debye-Hückel-scale to the Wigner-Seitz-scale decay of the effective potential, stems from the accounting for the structure of the ion fluid, and the ionization state of the plasma is obtained from the condition of thermodynamic equilibrium rather than from a heuristic ionization-potential-depression formula.

Load-bearing premise

The load-bearing premise is the first-order cluster expansion: the electron density of the whole plasma is approximated as a uniform background plus a linear sum of spherical one-ion clouds, with all nonlinear overlap of clouds and many-body correlations beyond pairs neglected, while the nuclei are treated as classical particles.

Editorial extensions

If this is right

  • Mean ionization, electron orbitals, and ion-fluid pair correlations follow from one equilibrium minimization, removing the need for an external ionization-potential-depression model.
  • Thermodynamic quantities from the VAAQP and VAMPIRES models satisfy the virial theorem, so thermodynamic and virial pressure agree by construction.
  • In VAAQP-based opacity calculations, pressure ionization does not create discontinuities: a lost bound level reappears as a resonance, keeping the total opacity continuous.
  • In VAMPIRES, pressure ionization coincides with a sharp rise of the effective ion coupling and a shortening of the effective potential range from beyond to inside the Wigner-Seitz radius, giving a distinctive signature of the transition.
  • If correct, the model supports extending atomic modeling to liquid-like, strongly coupled plasmas where the cavity picture of older ion-cell models is questionable.

Reading between the lines

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

  • Editorial inference: extending VAMPIRES to multi-species mixtures and to detailed configurational states, which the author reports as in progress, would give a natural bridge between dense-plasma average-atom models and collisional-radiative modeling.
  • Editorial inference: the weak-coupling limit of VAMPIRES could be made quantitative by checking whether it reproduces the standard continuum-lowering shift plus computable corrections, thereby testing whether any ad hoc suppression of bound states is needed.
  • Editorial inference: the model's steeper pressure-ionization rise than cavity-based models is a testable prediction; comparing mean ionization in X-ray Thomson scattering experiments across the transition would discriminate the mechanism.
  • Editorial inference: because the self-consistent dynamic linear response with continuum channels remained unresolved, frequency-dependent opacity near the plasma frequency is not yet a settled prediction of this framework; fixing the suspected boundary-condition issue would sharpen the collective-effect description.
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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 / 6 minor

Summary. This habilitation thesis reviews and extends variational average-atom models of dense plasmas. After presenting the standard isolated-ion/Saha and ion-in-cell frameworks, the manuscript develops two families of models: VAAQP, an atom-in-jellium average-atom model obtained from a constrained free-energy minimization with a Wigner-Seitz cavity, and VAMPIRES, a more recent model that couples the electronic structure of an ion to the pair structure of the surrounding classical ion fluid through a generalized free-energy functional. Applications to photoabsorption, self-consistent linear response, and non-LTE collisional-radiative modeling are also surveyed. The central scientific claims are that VAMPIRES derives pressure ionization and the crossover from Debye-Hückel- to Wigner-Seitz-scale screening from a first-principles treatment of ion-fluid structure, and that VAAQP and VAMPIRES are thermodynamically consistent in the sense of fulfilling the virial theorem. The derivations are presented in outline form, with key equations given but details deferred to the cited papers.

Significance. If the central claims hold, the VAMPIRES model would be a notable conceptual advance: a parameter-free variational scheme in which the average ionization state, the displaced-electron clouds, and the ion-ion pair correlation function are obtained from one free-energy functional, with bound and continuum electrons treated quantum mechanically. The emphasis on thermodynamic consistency and the virial theorem is valuable, and the manuscript honestly documents where the models succeed and where they do not. The comparisons with INFERNO, VAAQP, and selected experimental opacity/Hugoniot data give the work a useful empirical anchor. The limitation of the work is that the load-bearing first-order cluster expansion is uncontrolled in the very strong-coupling regime where VAMPIRES produces its distinctive pressure-ionization prediction, and the manuscript itself reports puzzling strong-coupling behavior. The thesis is therefore significant as a synthesis and as a research program, but the flagship claim about pressure ionization is not yet established at the level of a rigorous, benchmarked result.

major comments (3)
  1. [Sec. 4.3, Eqs. (4.21), (4.25), and Figs. 4.1(c),(e)] The central claim that pressure ionization and the switching from Debye-Hückel- to Wigner-Seitz-scale decay "stems from a first-principle accounting for the structure of the ion fluid" is not established, because the ion-fluid structure and the electron-cloud overlap are both generated by the same uncontrolled first-order cluster expansion. At the densities where the mean ionization jumps, the effective coupling is Γeff ≈ 7.85, h(r) is visibly oscillatory, and the displaced-electron clouds overlap; the expansion neglects all nonlinear cloud-cloud overlap and all correlations beyond pairs. The fulfillment of the virial theorem is a consistency property of the approximate free-energy functional and does not bound the truncation error of the cluster expansion. To support the claim, the manuscript should provide a quantitative estimate of the neglected second-order cluster terms, or benchmark VAMPIRES against an independent method such as DFT-MD or QHNC across the Li 10 eV transition region. Without such a test, the sharp rise of Z* in Fig. 4.1(e) may be an artifact of the ansatz rather than a first-principles pressure-ionization mechanism.
  2. [Sec. 4.4] The manuscript states that results from VAMPIRES in strong-coupling situations are "puzzling" and that the model's weaknesses still need critical assessment. This is precisely the regime in which the pressure-ionization edge and the jump of Z* occur in Fig. 4.1(e). The paper should therefore specify which strong-coupling predictions are considered physically reliable, identify testable quantitative predictions that distinguish VAMPIRES from VAAQP and INFERNO, and state the expected accuracy of the first-order expansion in that regime. As written, the claim in Sec. 4.3 that pressure ionization emerges from first principles is premature.
  3. [Sec. 4.3, Eq. (4.19)] The nuclear degrees of freedom are treated as classical particles through a classical probability distribution over positions and momenta, while electrons are treated quantum mechanically. This is a reasonable approximation at 10 eV, but the manuscript does not quantify its validity for the lower-temperature, higher-density corner of the Li example. A simple estimate of the thermal de Broglie wavelength of the nuclei relative to RWS and to the scale of the ion-ion potential would make the scope of the model precise and would rule out a possible challenge to the pressure-ionization mechanism based on nuclear quantum effects.
minor comments (6)
  1. [Sec. 2.5] In the first sentence, "accouting" should be "accounting".
  2. [Sec. 3.1.1] In the sentence after Eq. (3.4), "Avrogadro's number" should be "Avogadro's number".
  3. [Fig. 3.1 caption] The caption contains "denisty", which should be "density".
  4. [Fig. 2.11 caption] The caption contains "Measurments", which should be "Measurements".
  5. [Fig. 2.2 caption] The caption says the comparisons are shown both without and with suppression, but it would be clearer if the two panels were explicitly labeled as in panel (a) and panel (b) within the caption.
  6. [Sec. 3.6.2 and Sec. 3.7] The text reports that the self-consistent linear response of the quantum VAAQP model remains inconclusive and that the failure may be due to boundary conditions. This is an important caveat for Chapter 3, and it should be stated in the chapter introduction as well as in the research prospects.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the core VAAQP and VAMPIRES models are parameter-free minimizations of stated free-energy functionals, and their central results are emergent outputs checked against external benchmarks.

full rationale

The central models are explicit variational minimizations: for VAAQP, Eq. (2.101) minimizes the free energy with respect to the displaced-electron density and the jellium density; for VAMPIRES, Eq. (4.33) minimizes the approximate free energy with respect to the ion-fluid correlation function h, the electron cloud q, and the background density ne. In both cases the mean ionization Z* = ne/ni is an output of the equilibrium condition, not a fitted input. The pressure-ionization phenomenon and the Debye-Hückel to Wigner-Seitz decay switching are reported as emergent properties of the coupled equations (4.34)-(4.41), illustrated in Fig. 4.1; they are not inserted as pre-imposed values. The first-order cluster expansion of the electron density, Eqs. (2.93) and (4.21), and of the free energy, Eq. (4.25), is an uncontrolled approximation in the strong-coupling regime, and Sec. 4.4 explicitly acknowledges that strong-coupling results are puzzling. That is a correctness and robustness concern, not a circularity: an uncontrolled approximation is still an approximation, not an input disguised as a prediction. The paper's statement that VAMPIRES fulfills the virial theorem is a consistency property of the Debye-Kirkwood charging construction described in Sec. 4.2; the thesis presents it as such rather than as an independent empirical confirmation. External comparisons, including INFERNO, measured silicon opacity, the aluminum Hugoniot, xenon photoabsorption, and NLTE workshop benchmarks, provide independent checks outside the fitted quantities. Self-citations to the author's prior papers supply derivations whose equations are restated in the manuscript, but they do not carry the load by assertion and they do not forbid alternative models through an imported uniqueness claim. No specific step reduces, by the paper's own equations or by self-citation, to its own inputs, so no circularity is established.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central models rest on standard DFT and classical fluid closures plus the specific cluster-expansion and cavity assumptions listed. No fitted parameters set the core physics, but arbitrary line broadenings and a principal-quantum-number cutoff enter illustrative comparisons; no new particles, forces, or dimensions are introduced.

free parameters (2)
  • ad hoc spectral line broadening = 1 eV (Fig. 3.4) and 4 eV (Fig. 3.7)
    Added to opacity and transmission spectra to mimic physical broadening and instrumental resolution; chosen by hand and not derived from the model.
  • principal quantum number cutoff = n <= 8
    Used in the Saha and average-atom isolated-ion comparisons of Fig. 2.1 to render partition functions finite; acknowledged by the author as an arbitrary limitation.
assumptions (5)
  • ad hoc to paper First-order cluster expansion of electron density and free energy (Eqs. (2.93), (4.21), (4.25)): total density is jellium plus a sum of spherical displaced-electron clouds, with the free energy truncated at the same order.
    Central approximation of VAAQP and VAMPIRES; it assumes linear additivity of electron clouds and is uncontrolled at strong coupling, as the author acknowledges in Sec. 4.4.
  • domain assumption Local density approximation (LDA) for exchange-correlation free energy (Eqs. (2.31), (2.98)).
    Standard DFT approximation used throughout; limits accuracy of total energies, ionization balance, and spectral features.
  • domain assumption Classical treatment of nuclei with pair interactions derived from spherical electron clouds (Eqs. (4.19), (4.24)).
    Nuclei are treated as indistinguishable classical particles; quantum nuclear effects and non-pair interactions are neglected.
  • domain assumption HNC or DH closure for the ion-fluid pair correlation (Eqs. (4.34)-(4.35)).
    Approximate closures for classical fluids; each is valid in a limited coupling regime, and the choice affects the ion structure and the electron potential.
  • ad hoc to paper Wigner-Seitz cavity hypothesis in VAAQP (Eq. (2.99)).
    Surrounding ions are represented as a uniform neutralizing background excluded from a spherical cavity; this is a modeling assumption that VAMPIRES later attempts to relax.

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Cite this review

Pith. "Pith review of Atoms in Dense Plasmas: Models, Applications, and Current Challenges." pith.science (2026). https://pith.science/paper/FJSYDE54

@misc{pith2026241118357,
  author       = {Pith},
  title        = {Pith review of: Atoms in Dense Plasmas: Models, Applications, and Current Challenges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FJSYDE54}},
  note         = {Machine review of arXiv:2411.18357}
}
read the original abstract

Modeling plasmas in terms of atoms or ions is theoretically appealing for several reasons. When it is relevant, the notion of atom or ion in a plasma provides us with an interpretation scheme of the plasma's microscopic structure. From the standpoint of quantitative estimation of plasma properties, atomic models of plasma allow extending many theoretical tools of atomic physics to plasmas. This notably includes the statistical approaches to the detailed accounting for excited states, or the collisional-radiative modeling of non-equilibrium plasmas, which is based on the notion of atomic processes. This habilitation thesis is mostly focused on the studies to which the author has contributed in the field of atomic modeling of dense, non-ideal plasmas. The studies to which the author contributed in the field of collisional-radiative modeling of non-LTE plasmas are also addressed, and the prospect of bridging with dense-plasma models is sketched.

Figures

Figures reproduced from arXiv: 2411.18357 by the authors.

Figure 2
Figure 2. presents a comparison between the mean ionization: [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 2
Figure 2. – Mean ionization [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 2
Figure 2. – Schematic view of the delocalization of a bound orbital, with a resonance appearing in the [PITH_FULL_IMAGE:figures/full_fig_p027_2.png] view at source ↗
Figures from the paper (25 more)
Figure 2
Figure 2. Figure 2: – Schematic picture of the Thomas-Fermi model. [PITH_FULL_IMAGE:figures/full_fig_p029_2.png]
Figure 2
Figure 2. Figure 2: – Mean ionization [PITH_FULL_IMAGE:figures/full_fig_p030_2.png]
Figure 2
Figure 2. Figure 2: shows the density of states obtained from the INFERNO model for silicon at 5 eV tem [PITH_FULL_IMAGE:figures/full_fig_p032_2.png]
Figure 2
Figure 2. Figure 2: – Density of states obtained from the INFERNO model in the case of silicon at 5 eV tem [PITH_FULL_IMAGE:figures/full_fig_p033_2.png]
Figure 2
Figure 2. Figure 2: – Schematic pictures of an impurity in a jellium (a), and of an ion-in-jellium model such as [PITH_FULL_IMAGE:figures/full_fig_p034_2.png]
Figure 2
Figure 2. Figure 2: shows an example comparison of results from the isolated-ion, INFERNO, and VAAQP [PITH_FULL_IMAGE:figures/full_fig_p036_2.png]
Figure 2
Figure 2. Figure 2: – Principal Hugoniot of Aluminum. Comparison of the results from VAAQP, INFERNO [PITH_FULL_IMAGE:figures/full_fig_p038_2.png]
Figure 3
Figure 3. Figure 3: – Continuum-continuum contribution to the opacity of a silicon plasma at 5 eV temperature [PITH_FULL_IMAGE:figures/full_fig_p043_3.png]
Figure 3
Figure 3. Figure 3: shows the oscillator strengths at two matter densities between which the 5p subshell gets [PITH_FULL_IMAGE:figures/full_fig_p044_3.png]
Figure 3
Figure 3. Figure 3: – Differential oscillator strengths for the [PITH_FULL_IMAGE:figures/full_fig_p045_3.png]
Figure 3
Figure 3. Figure 3: – Example of a 6-component classical plasma, typical of the charge-state distribution of [PITH_FULL_IMAGE:figures/full_fig_p048_3.png]
Figure 3
Figure 3. Figure 3: shows the charge state distributions obtained for iron at 40 eV temperature, at various [PITH_FULL_IMAGE:figures/full_fig_p049_3.png]
Figure 3
Figure 3. Figure 3: displays the results of the present approach [30], using the heuristic coefficient [PITH_FULL_IMAGE:figures/full_fig_p052_3.png]
Figure 3
Figure 3. Figure 3: shows the photoabsorption cross-section of Aluminum at temperature [PITH_FULL_IMAGE:figures/full_fig_p053_3.png]
Figure 3
Figure 3. Figure 3: – Photoabsorption cross-section of Aluminum at temperature [PITH_FULL_IMAGE:figures/full_fig_p054_3.png]
Figure 3
Figure 3. Figure 3: displays the result of a self-consistent dynamic linear response calculation using the same [PITH_FULL_IMAGE:figures/full_fig_p055_3.png]
Figure 4
Figure 4. Figure 4: presents results from the VAMPIRES model for lithium at 10 eV temperature. First, one [PITH_FULL_IMAGE:figures/full_fig_p065_4.png]
Figure 4
Figure 4. Figure 4: – Results from the VAMPIRES model for lithium at 10 eV temperature. Pair correlation [PITH_FULL_IMAGE:figures/full_fig_p066_4.png]
Figure 5
Figure 5. Figure 5: – Mean ionization of Iron in thermodynamic equilibrium, defined as [PITH_FULL_IMAGE:figures/full_fig_p075_5.png]
Figure 5
Figure 5. Figure 5: – Comparison between results from the DEDALE and AVERROES codes on Iron emissivity [PITH_FULL_IMAGE:figures/full_fig_p076_5.png]
Figure 5
Figure 5. Figure 5: b present the interpretation of an experiment performed on the ELFIE laser facility during [PITH_FULL_IMAGE:figures/full_fig_p077_5.png]
Figure 5
Figure 5. Figure 5: – Interpretation of an L-shell spectroscopy experiments using the DEDALE code. The [PITH_FULL_IMAGE:figures/full_fig_p078_5.png]
Figure 5
Figure 5. Figure 5: shows the comparison of the simulated radiant intensity on the DMX axis, compared to the [PITH_FULL_IMAGE:figures/full_fig_p080_5.png]
Figure 5
Figure 5. Figure 5: – Radiant intensity as a function of time of a silver X-ray source driven by the OMEGA [PITH_FULL_IMAGE:figures/full_fig_p081_5.png]
Figure 5
Figure 5. Figure 5: a displays the total electron-ion elastic-scattering cross-section for a silicon plasma at a [PITH_FULL_IMAGE:figures/full_fig_p082_5.png]

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Reference graph

Works this paper leans on

289 extracted references · 71 canonical work pages

  1. [1]

    Kippenhahn and A

    R. Kippenhahn and A. Weigert. Stellar Structure and Evolution. Springer-Verlag, 1989

    1989

  2. [2]

    At matter density of 10−3 g.cm−3, the 7d bound orbital is delocalized, but still contributes a sharp resonance in the continuum

    ATOMIC PHYSICS OF NON-LTE PLASMAS 79 / 102 At high energies, the Born approximation behavior (plane-wave incoming and outgoing electrons) is recovered. At matter density of 10−3 g.cm−3, the 7d bound orbital is delocalized, but still contributes a sharp resonance in the continuum. At matter density of10−1 g.cm−3, the same occurs for the 3d bound orbital. A...

  3. [3]

    S. L. Shapiro and S. A. Teukolsky. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. Wiley, 1983

    1983

  4. [4]

    E. U. Condon and G. H. Shortley. The Theory of Atomic Spectra. Cambridge University Press, 1935

    1935

  5. [5]

    error bars TROLL w

    ATOMIC PHYSICS OF NON-LTE PLASMAS 77 / 102 0 50 100 150 200 250 300 350 400 0 0 .5 1 1 .5 2 (a) radiant intensity (GW.sr −1) time (ns) DMX w. error bars TROLL w. ICARE 0 20 40 60 80 100 120 140 0 0 .5 1 1 .5 2 (b) radiant intensity (GW.sr −1) time (ns) DMX w. error bars TROLL w. ICARE Figure 5.5 – Radiant intensity as a function of time of a silver X-ray ...

  6. [6]

    The main shortfalls of models based on the notion of continuum lowering are rather well identified

    Conclusions Atomic models of dense plasmas in themselves are still an active field of research, facing open questions as regards their theoretical foundations. The main shortfalls of models based on the notion of continuum lowering are rather well identified. However, models used in order to go beyond the continuum lowering picture are still mostly based ...

  7. [7]

    D. Mihalas. Stellar Atmospheres. W H Freeman & Co, 1978

    1978

  8. [8]

    R. D. Cowan. The Theory of Atomic Structure and Spectra. University of California Press, 1981

    1981

Show all 289 references
  1. [9]

    Froese-Fischer

    C. Froese-Fischer. The Hartree-Fock Method for Atoms: A Numerical Approach . John Wiley & Sons Inc., 1977

    1977

  2. [10]

    I. P . Grant. Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation . Springer, 2006

    2006

  3. [11]

    G. Racah. Theory of Complex Spectra. I. Phys. Rev., 61:186–197, 1942

    1942

  4. [12]

    G. Racah. Theory of Complex Spectra. II. Phys. Rev., 62:438–462, 1942

    1942

  5. [13]

    G. Racah. Theory of Complex Spectra. III. Phys. Rev., 63:367–382, 1943

    1943

  6. [14]

    S. A. Moszkowski. On the Energy Distribution of Terms and Line Arrays in Atomic Spectra. Progress of Theoretical Physics, 28:1–23, 1962

    1962

  7. [15]

    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, 20:2424–2439, 1979

    1979

  8. [16]

    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. II. Configurations with more than two open subshells. Phys. Rev. A, 25:2641–2646, 1982

    1982

  9. [17]

    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. III. Case of spin-orbit-split arrays. Phys. Rev. A, 31:2248–2259, 1985

    1985

  10. [18]

    F . Perrot. Correlated fluctuations of electron populations in high temperature plasmas. Physica A, 150:357–370, 1988

    1988

  11. [19]

    Bar-Shalom, J

    A. Bar-Shalom, J. Oreg, W. H. Goldstein, D. Shvarts, and A. Zigler. Super-transition-arrays: A model for the spectral analysis of hot, dense plasma. Phys. Rev. A, 40(6):3183–3193, 1989

    1989

  12. [20]

    Blenski, A

    T. Blenski, A. Grimaldi, and F . Perrot. A superconfiguration code based on the local density approximation. J. Quant. Spectrosc. Radiat. Transf., 65:91–100, 2000

    2000

  13. [21]

    Mixed UTA and detailed line treatment for mid-Z opacity and spectral calculations

    S Mazevet and J Abdallah. Mixed UTA and detailed line treatment for mid-Z opacity and spectral calculations. Journal of Physics B: Atomic, Molecular and Optical Physics, 39:3419, 2006

    2006

  14. [22]

    C. A. Iglesias and V. Sonnad. Partially resolved transition array model for atomic spectra. High Energy Density Physics, 8:154–160, 2012

    2012

  15. [23]

    Ralchenko

    Yu. Ralchenko. Modern Methods in Collisional-Radiative Modeling of Plasmas. Springer, 2016

    2016

  16. [24]

    Baranger

    M. Baranger. Simplified Quantum-Mechanical Theory of Pressure Broadening. Phys. Rev., 111:481–493, 1958. 83 84 / 102 7. REFERENCES

    1958

  17. [25]

    I. I. Sobel’man, L. A. Vainshtein, and E. A. Yukov.Excitation of Atoms and Broadening of Spectral Lines. Springer Berlin, Heidelberg, 1995

    1995

  18. [26]

    D. B. Boercker, C. A. Iglesias, and J. W. Dufty. Radiative and transport properties of ions in strongly coupled plasmas. Phys. Rev. A, 36:2254–2264, 1987

    1987

  19. [27]

    Talin, A

    B. Talin, A. Calisti, L. Godbert, R. Stamm, R. W. Lee, and L. Klein. Frequency-fluctuation model for line-shape calculations in plasma spectroscopy. Phys. Rev. A, 51:1918–1928, 1995

    1918

  20. [28]

    Stambulchik and Y

    E. Stambulchik and Y . Maron. Stark effect of high-n hydrogen-like transitions: quasi- contiguous approximation. Journal of Physics B: Atomic, Molecular and Optical Physics , 41:095703, 2008. URL: https://dx.doi.org/10.1088/0953-4075/41/9/095703, doi:10. 1088/0953-4075/41/9/095703

    2008 doi

  21. [29]

    T. A. Gomez, T. Nagayama, P . B. Cho, D. P . Kilcrease, C. J. Fontes, and M. C. Zammit. Introduc- tion to spectral line shape theory. J. Phys. B: At. Mol. Opt. Phys., 55:034002, 2022

    2022

  22. [30]

    J. M. Ziman. A theory of the electrical properties of liquid metals. I: The monovalent met- als. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics , 6:1013–1034, 1961

    1961

  23. [31]

    R. Piron. Variational Average-Atom in Quantum Plasmas (VAAQP). PhD thesis, École Polytech- nique, 2009. URL: https://theses.hal.science/tel-00446558

    2009

  24. [33]

    Piron and T

    R. Piron and T. Blenski. Average-atom model calculations of dense-plasma opacities: Review and potential applications to white-dwarf stars. Contributions to Plasma Physics , 58:30–41,

  25. [34]

    Danel, P

    J.-F . Danel, P . Blottiau, L. Kazandjian, R. Piron, and M. Torrent. Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements. Phys. of Plasmas, 21:102701, 2014. doi:10.1063/1.4897190

    2014 doi

  26. [35]

    Caizergues

    C. Caizergues. Réponse linéaire dynamique et auto-cohérente des atomes dans les plasmas quantiques. PhD thesis, Université Paris-Sud 11, 2015. URL: https://theses.hal.science/ tel-01154056

    2015

  27. [36]

    Caizergues, T

    C. Caizergues, T. Blenski, and R. Piron. Linear response of a variational average atom in plasma: Semi-classical model. High Energy Density Physics, 12:12 – 20, 2014. doi:10.1016/j.hedp. 2014.04.004

    2014 doi

  28. [37]

    Caizergues, T

    C. Caizergues, T. Blenski, and R. Piron. Dynamic linear response of atoms in plasmas and photo-absorption cross-section in the dipole approximation. High Energy Density Physics, 18:7 – 13, 2016. doi:10.1016/j.hedp.2015.11.001

    2016 doi

  29. [38]

    Blenski and R

    T. Blenski and R. Piron. Free-energy functional of the Debye-Hückel model of two-component plasmas. High Energy Density Physics, 24:28–32, 2017. doi:10.1016/j.hedp.2017.05.005

    2017 doi

  30. [39]

    Danel, L

    J.-F . Danel, L. Kazandjian, and R. Piron. Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics. Phys. Rev. E, 93:043210, 2016. doi:10.1103/PhysRevE.93.043210

    2016 doi

  31. [40]

    Danel, L

    J.-F . Danel, L. Kazandjian, and R. Piron. Equation of state of carbon in the warm dense matter regime from density-functional theory molecular dynamics. Phys. Rev. E , 98:043204, 2018. doi:10.1103/PhysRevE.98.043204

    2018 doi

  32. [41]

    Piron and T

    R. Piron and T. Blenski. Free-energy functional of the Debye-Hückel model of simple fluids.Phys. Rev. E, 94:062128, 2016. doi:10.1103/PhysRevE.94.062128

    2016 doi

  33. [42]

    Gilleron and R

    F . Gilleron and R. Piron. The fast non-LTE code DEDALE. High Energy Density Physics , 17:219–230, 2015. doi:10.1016/j.hedp.2015.07.001

    2015 doi

  34. [43]

    Piron and T

    R. Piron and T. Blenski. Simpler free-energy functional of the Debye-Hückel model of fluids and the non-uniqueness of free-energy functionals in the theory of fluids. Phys. Rev. E, 99:052134,

  35. [44]

    J. C. Slater. A Simplification of the Hartree-Fock Method. Phys. Rev., 81:385–390, 1951

    1951

  36. [45]

    Piron and T

    R. Piron and T. Blenski. Variational average-atom model of electron-ion plasma with correlations and quantum bound electrons. arXiv:1904.13289, 2019. doi:10.48550/arXiv.1904.13289

    1904 doi arXiv

  37. [46]

    Blenski and R

    T. Blenski and R. Piron. Variational atomic model of plasma accounting for ion radial correlations and electronic structure of ions. Phys. Rev. E, 107:035209, 2023. doi:10.1103/PhysRevE. 107.035209

    2023 doi

  38. [47]

    J. C. Slater. The Self Consistent Field and the Structure of Atoms. Phys. Rev., 32:339–348, 1928

    1928

  39. [48]

    R. Piron. Atomic Models of Dense Plasmas, Applications, and Current Challenges. Atoms, 12:26, 2024. doi:10.3390/atoms12040026

    2024 doi

  40. [49]

    B. R. Judd. Second Quantization and Atomic Spectroscopy . The Johns Hopkins University Press, 1967

    1967

  41. [50]

    Talman and William F

    James D. Talman and William F . Shadwick. Optimized effective atomic central potential. Phys. Rev. A, 14:36–40, 1976

    1976

  42. [51]

    Klapisch

    M. Klapisch. A program for atomic wavefunction computations by the parametric potential method. Computer Physics Communications, 2:239–260, 1971

    1971

  43. [52]

    Gaigalas, S

    G. Gaigalas, S. Fritzsche, and I. P . Grant. Program to calculate pure angular momentum coeffi- cients in jj-coupling. Computer Physics Communications, 139:263–278, 2001

    2001

  44. [53]

    L. I. Schiff. Quantum Mechanics. Mc Graw - Hill, 1968

    1968

  45. [54]

    M. N. Saha. Ionization in the solar chromosphere. Philos. Mag., 40:472–488, 1920

    1920

  46. [55]

    A. P . Yutsis, I. B. Levinson, and V. V. Vanagas.Mathematical apparatus of the theory of angular momentum. Israel Program for Scientific Translations Ltd., 1962

    1962

  47. [56]

    Bar-Shalom and M

    A. Bar-Shalom and M. Klapisch. NJGRAF — An efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM. Computer Physics Com- munications, 50:375–393, 1988

    1988

  48. [57]

    W. Kohn, L. J. Sham, et al. Self-consistent equations including exchange and correlation effects. Phys. Rev., 140(4A):A1133–A1138, 1965

    1965

  49. [58]

    J. C. Slater. The Theory of Complex Spectra. Phys. Rev., 34:1293–1322, 1929

    1929

  50. [59]

    J. C. Slater. The virial and molecular structure. J. Chem. Phys., 1:687, 1933

    1933

  51. [60]

    M. N. Saha. On a Physical Theory of Stellar Spectra. Proc. R. Soc. London Ser. A, 99:135–153, 1921

    1921

  52. [61]

    Hohenberg and W

    P . Hohenberg and W. Kohn. Inhomogeneous Electron Gas. Phys. Rev., 136(3B):B864–B871, 1964

    1964

  53. [62]

    D. G. Hummer and Dimitri Mihalas. The Equation of State for Stellar Envelopes. I. an Occupation Probability Formalism for the Truncation of Internal Partition Functions. Ap. J., 331:794, August

  54. [63]

    N. D. Mermin. Thermal properties of the inhomogeneous electron gas. Phys. Rev. , 137(5A):A1441–A1443, 1965

    1965

  55. [64]

    Debye and E

    P . Debye and E. Hückel. Zur Theorie des Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Phys. Z., 24:185–206, 1923

    1923

  56. [65]

    J. C. Stewart and K. D. Pyatt. Lowering of ionization potentials in plasmas.Astrophysical Journal, 144:1203–1211, 1966

    1966

  57. [66]

    Hans R. Griem. High-Density Corrections in Plasma Spectroscopy. Phys. Rev., 128:997–1003, Nov 1962. URL: https://link.aps.org/doi/10.1103/PhysRev.128.997, doi:10.1103/ PhysRev.128.997. 86 / 102 7. REFERENCES

    1962 doi

  58. [67]

    Levinson

    N. Levinson. On the Uniqueness of the Potential in a Schrödinger Equation for a Given Asymp- totic Phase. Danske Vidensk. Selsk. K. Mat.-Fys. Medd., 25(9), 1949

    1949

  59. [68]

    C. Deutsch. Equilibrium Properties of Two-Component Classical Plasmas. Annals of Physics, 115:404–441, 1978

    1978

  60. [69]

    The Levinson theorem

    Zhong-Qi Ma. The Levinson theorem. J. Phys. A: Mathematical and General , 39:R625–R659, 2006

    2006

  61. [70]

    T. Morita. Theory of Classical Fluids: Hyper-Netted Chain Approximation, I. Prog. Theor. Phys., 20:920–938, 1958

    1958

  62. [71]

    T. Morita. Theory of Classical Fluids: Hyper-Netted Chain Approximation, II. Prog. Theor. Phys., 21:361–382, 1959

    1959

  63. [72]

    Bargmann

    V. Bargmann. On the number of bound states in a central field of force. Proc. Nat. Acad. Sci. , 38:961–966, 1952

    1952

  64. [73]

    J. M. Jauch. On the Relation Between Scattering Phase and Bound States. Helv. Phys. Acta, 30:143–156, 1957

    1957

  65. [74]

    A. I. Larkin. Thermodynamic functions of a low-temperature plasma. JETP, 38:1896–1898, 1960

    1960

  66. [75]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.djvu. Dover Publication, Inc, New Y ork, 1965

    1965

  67. [76]

    C. Kittel. Quantum Theory of Solids. Wiley, 1991

    1991

  68. [77]

    Ebeling, W

    W. Ebeling, W. D. Kraeft, D. Kremp, and G. Röpke. Energy Levels in Hydrogen Plasmas and the Planck-Larkin Partition Function – a Comment. Astrophysical Journal, 290:24–27, 1985

    1985

  69. [78]

    Uhlenbeck

    Erich Beth and George E. Uhlenbeck. The quantum theory of the non-ideal gas. II. Behaviour at low temperatures. Physica, 4:915–924, 1937

    1937

  70. [79]

    F . J. Rogers. Occupation Numbers for Reacting Plasmas: The Role of the Planck-Larkin Partition Function. Astrophysical Journal, 310:723, 1986

    1986

  71. [80]

    W. Ebeling. Equation of State and Saha Equation of Partially Ionized Plasmas. Physica, 38:378–388, 1968

    1968

  72. [81]

    W. Ebeling. Statistical Derivation of the Mass-Action Law for Interacting Gases ans Plasmas. Physica, 73:573–584, 1974

    1974

  73. [82]

    E. Fermi. Über die Wahrscheinlichkeit der Quantenzustände. Zeitschrift für Physik, 26:54–56, 1924

    1924

  74. [83]

    F . J. Rogers. On The Compensation Of Bound And Scattering State Contributions To The Parti- tion Function. Phys. Lett., 61A:358–360, 1977

    1977

  75. [84]

    R. Latter. Temperature Behavior of the Thomas-Fermi Statistical Model for Atoms. Phys. Rev., 99(6):1854–1870, 1955

    1955

  76. [85]

    K. F . Herzfeld. Über die Wahrscheinlichkeit der Quantenzustände. Annalen der Physik, 51:261, 1916

    1916

  77. [86]

    H. C. Urey. The Distribution of Electrons in the Various Orbits of the Hydrogen Atom. Astrophys- ical Journal, 59:1, 1924

    1924

  78. [87]

    R. Latter. Atomic Energy Levels for the Thomas-Fermi and Thomas-Fermi-Dirac Potential. Phys. Rev., 99:510–519, 1955

    1955

  79. [88]

    R. P . Feynman, N. Metropolis, and E. Teller. Equation of State of Elements Based on the Gener- alized Fermi-Thomas Theory. Phys. Rev., 75(10):1561–1573, 1949

    1949

  80. [89]

    Ishikawa and B

    K. Ishikawa and B. U. Felderhof. High-frequency photoabsorption by an ion immersed in a plasma as calculated from Bloch’s hydrodynamic model. Physica A, 253:541–554, 1998

    1998

  81. [90]

    P . A. M. Dirac. Note on exchange phenomena in the Thomas atom.Proc. Cambridge Phil. Soc., 26:376–385, 1930

    1930

  82. [91]

    D. A. Kirzhnits. Quantum corrections to the Thomas-Fermi equation. JETP, 5:64, 1957

    1957

  83. [92]

    B. F . Rozsnyai. Relativistic Hartree-Fock-Slater Calculations for Arbitrary Temperature and Mat- ter Density. Phys. Rev. A, 5(3):1137–1149, 1972

    1972

  84. [93]

    J. A. Ball, J. A. Wheeler, and E. L. Firemen. Photoabsorption and Charge Oscillation of the Thomas-Fermi Atom. Rev. Mod. Phys., 45:333, 1973

    1973

  85. [94]

    Wigner and F

    E. Wigner and F . Seitz. On the Constitution of Metallic Sodium. II.Phys. Rev., 46:509–524, 1934

    1934

  86. [95]

    J. C. Slater and H. M. Krutter. The Thomas-Fermi Method for Metals. Phys. Rev., 47:559–568, 1935

    1935

  87. [96]

    D. A. Liberman. Self-consistent field model for condensed matter. Phys. Rev. B , 20(12):4981–4989, 1979

    1979

  88. [97]

    Massacrier, M

    G. Massacrier, M. Böhme, J. Vorberger, F . Soubiran, and B. Militzer. Reconciling ionization energies and band gaps of warm dense matter derived with ab initio simulations and average atom models. Phys. Rev. Research, 3:023026, 2021

    2021

  89. [98]

    Wigner and F

    E. Wigner and F . Seitz. On the Constitution of Metallic Sodium. Phys. Rev., 43:804–810, 1933

    1933

  90. [99]

    B. I. Bennett and D. A. Liberman. INFERNO. Technical Report LA-10309-M, Los Alamos National Laboratory, 1985

    1985

  91. [100]

    N. W. Ashcroft and N. D. Mermin. Solid State Physics. Harcourt College Publishers, 1976

    1976

  92. [101]

    Rosmej, K

    F . Rosmej, K. Bennadji, and V. S. Lisitsa. Effect of dense plasmas on exchange-energy shifts in highly charged ions: An alternative approach for arbitrary pertubation potentials. Phys. Rev. A, 84:032512, 2011

    2011

  93. [102]

    Li and F

    X. Li and F . Rosmej. Quantum-number-dependent energy level shifts of ionsin dense plasmas: A generalized analytical approach. Euro. Phys. Lett., 99:33001, 2012

    2012

  94. [103]

    D. A. Liberman. I NFERNO : a better model of atoms in dense plasmas. J. Quant. Spectrosc. Radiat. Transf., 27:335, 1982

    1982

  95. [104]

    Beiersdorfer, G

    P . Beiersdorfer, G. Brown, A. McKelvey, R. Shepherd, D. J. Hoarty, C. R. D. Brown, M. P . Hill, L. M. R. Hobbs, S. F . James, J. Morton, and L. Wilson. High-resolution measurments of Cl 15+ line shifts in hot, solid-density plasmas. Phys. Rev. A, 100:012511, 2019

    2019

  96. [105]

    Wilson, V

    B. Wilson, V. Sonnad, P . Sterne, and W. Isaacs. P URGATORIO - a new implementation of the INFERNO algorithm. J. Quant. Spectrosc. Radiat. Transf., 99:658–679, 2006

    2006

  97. [106]

    Pénicaud

    M. Pénicaud. An average atom code for warm matter: application to aluminum and uranium. Journal of Physics: Condensed Matter, 21:095409, 2009

    2009

  98. [107]

    Massacrier and J

    G. Massacrier and J. Dubau. A theoretical approach to N-electron ionic structure under dense plasma conditions: I. Blue and red shift. J. Phys. B: At. Mol. Opt. Phys., 23:2459S–2469S, 1990

    1990

  99. [108]

    Iglesias

    C. Iglesias. On spectral line shifts from analytic fits to the ion-sphere model potential. High Energy Density Physics, 30:41–44, 2019

    2019

  100. [109]

    Manninen, R

    M. Manninen, R. Nieminen, P . Hautojärvi, and J. Arponen. Electrons and positrons in metal vacancies. Phys. Rev. B, 12(10):4012–4022, 1975

    1975

  101. [110]

    Li and F

    X. Li and F . Rosmej. Analytical approach to level delocalization and line shifts in finite tempera- ture dense plasmas. Phys. Lett. A, 384:126478, 2020. 88 / 102 7. REFERENCES

    2020

  102. [111]

    Ionization potential depression in dense iron plasmas near solid density

    Jiaolong Zeng, Chen Y e, Y ongjun Li, and Jianmin Yuan. Ionization potential depression in dense iron plasmas near solid density. Results in Physics, 40:105836, 2022

    2022

  103. [112]

    Blenski and B

    T. Blenski and B. Cichocki. Variational theory of average-atom and superconfigurations in quan- tum plasmas. Phys. Rev. E, 75:056402, 2007

    2007

  104. [113]

    Arponen, P

    J. Arponen, P . Hautojärvi, R. Nieminen, and E. Pajanne. Charge density and positron annihilation at lattice defects in aluminium. J. Phys. F: Metal Physics, 3(6):2092–2108, 1973

    1973

  105. [114]

    Piron and T

    R. Piron and T. Blenski. Variational average-atom in quantum plasmas (VAAQP) – Recent progress, virial theorem and applications to the equation-of-state of warm dense Be.High Energy Density Physics, 7:346–352, 2011. doi:10.1016/j.hedp.2011.06.006

    2011 doi

  106. [115]

    Jena and K

    P . Jena and K. S. Singwi. Electronic structure of hydrogen in simple metals. Phys. Rev. B, 17(9):3518–3524, 1978

    1978

  107. [116]

    Blenski and B

    T. Blenski and B. Cichocki. Variational approach to the average-atom-in-jellium and superconfigurations-in-jellium models with all electrons treated quantum-mechanically. High En- ergy Density Physics, 3:34–47, 2007

    2007

  108. [117]

    G. I. Kerley. Perturbation theory and the thermodynamic properties of fluids. II. The CRIS model. The Journal of Chemical Physics, 73:478–486, 1980. doi:10.1063/1.439898

    1980 doi

  109. [118]

    Piron and T

    R. Piron and T. Blenski. Variational-average-atom-in-quantum-plasmas (VAAQP) code and virial theorem: Equation-of-state and shock-Hugoniot calculations for warm dense Al, Fe, Cu, and Pb. Phys. Rev. E, 83:026403, 2011. doi:10.1103/PhysRevE.83.026403

    2011 doi

  110. [119]

    L. D. Landau and E. M. Lifshitz. Electrodynamics of Continuous Media. Pergamon Press, 1960

    1960

  111. [120]

    B. U. Felderhof, G. W. Ford, and E. G. D. Cohen. Cluster Expansion for the Dielectric Constant of a Polarizable Suspension. J. Stat. Phys., 28(1):135–164, 1982

    1982

  112. [121]

    G. I. Kerley. Perturbation theory and the thermodynamic properties of fluids. I. General theory. The Journal of Chemical Physics, 73:469–477, 1980. doi:10.1063/1.439842

    1980 doi

  113. [122]

    Błe ´nski and B

    T. Błe ´nski and B. Cichocki. Linear response of partially ionized, dense plasmas. Laser Part. Beams, 10(2):299–309, 1992

    1992

  114. [123]

    A. V. Bushman, I. V. Lomonosov, K. V. Khishchenko, V. P . Kopyshev, E. A. Kuzmenkov, V. E. Kogan, P . R. Levashov, and I. N. Lomov. IHED Shock Wave Database – http://www.ihed.ras.ru/rusbank/. URL: http://www.ihed.ras.ru/rusbank

  115. [124]

    B. U. Felderhof, T. Blenski, and B. Cichocki. Dielectric function of an electron-ion plasma in the optical and X-ray regime. Physica A, 217:161–174, 1995

    1995

  116. [125]

    A. L. Fetter and J. D. Walecka. Quantum Theory of Many-Particle Systems. Dover Publication, Inc, 2003

    2003

  117. [126]

    L. D. Landau and E. M. Lifshitz. Statistical Physics. Pergamon Press, 1959

    1959

  118. [127]

    Zangwill and P

    A. Zangwill and P . Soven. Density-functional approach to local-field effects in finite systems: photoabsorption in the rare gases. Phys. Rev. A, 21:1561–1572, 1980

    1980

  119. [128]

    Blenski and B

    T. Blenski and B. Cichocki. Polarizability of partially ionized, dense plasmas (application to photo- absorption calculations). Journal of Quantitative Spectroscopy and Radiative Transfer, 51:49–58, 1994

    1994

  120. [129]

    A. K. Dhara and S. K. Ghosh. Density-functional theory for time-dependent systems. Phys. Rev. A, 35:442–444, 1987

    1987

  121. [130]

    Gauge invariance and relativistic radiative transitions

    I P Grant. Gauge invariance and relativistic radiative transitions. Journal of Physics B: Atomic and Molecular Physics, 7:1458, 1974. doi:10.1088/0022-3700/7/12/007

    1974 doi

  122. [131]

    M. J. Stott and E. Zaremba. Linear-response theory within the density-functional formalism: Application to atomic polarizabilities. Phys. Rev. A, 21(4):12–23, 1980

    1980

  123. [132]

    F . Perrot. A new approximation for calculating free-free absorption in hot dense plasmas. Laser Part. Beams, 14:731–748, 1996

    1996

  124. [133]

    Runge and E

    E. Runge and E. K. U. Gross. Density-Functional Theory for Time-Dependent Systems. Phys. Rev. Lett., 52:997–1000, 1984

    1984

  125. [134]

    Y a. B. Zel’dovich and Yu. P . Raizer.Physics of shock waves and high-temperature hydrodynamic phenomena. Academic Press, 1968

    1968

  126. [135]

    S. K. Ghosh and A. K. Dhara. Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields. Phys. Rev. A, 38:1149–1158, 1988

    1988

  127. [136]

    H. A. Bethe and E. E. Salpeter. Quantum Mechanics of One- and Two-Electron Atoms. Springer- Verlag, 1957

    1957

  128. [137]

    B. W. Shore. On the threshold behaviour of bound-bound and bound-free photoabsorption for the screened Coulomb potentials. J. Phys. B, 8:2023–2040, 2019

    2023

  129. [138]

    H. A. Kramers. On the theory of X-ray absorption and of the continuous X-ray spectrum. Philo- sophical Magazine Series 6, 46(275):836–871, 1923

    1923

  130. [139]

    D. A. Liberman, J. R. Albritton, B. G. Wilson, and W. E. Alley. Self-consistent-field calculations of atoms and ions using a modified local-density approximation. Phys. Rev. A, 50:171–176, 1994

    1994

  131. [140]

    W. B. Somerville. The continuous absorption coefficient of the negative hydrogen molecular ion. Astrophysical Journal, 139:192–197, 1964

    1964

  132. [141]

    M. Ashkin. Radiative Absorption Cross Section of an Electron in the Field of an Argon Atom. Phys. Rev., 141:41–44, 1966

    1966

  133. [142]

    Shalitin, J

    D. Shalitin, J. Stein, and Akiva Ron. Level and line broadening for Thomas-Fermi atoms at finite temperature. Phys. Rev. A, 29:2789–2795, 1984

    1984

  134. [143]

    F . Perrot. Model for atomic species in a dense plasma: Description and applications. Phys. Rev. A, 35:1235–1244, 1987

    1987

  135. [144]

    Blenski and B

    T. Blenski and B. Cichocki. Density-functional approach to the absorption bands in a dense, partially ionized plasma. Phys. Rev. A, 41(12):6973–6981, June 1990

    1990

  136. [145]

    S. B. Hansen. Self-consistent and detailed opacities from a non-equilibrium average-atom model. Phil. Trans. R. Soc. A, 381:20220212, 2023

    2023

  137. [146]

    J. M. Green. The statistical mechanics of the interdependent electrons in the screening constant model of the many-electron-atom. J. Quant. Spectrosc. Radiat. Transf., 4:639–662, 1964

    1964

  138. [147]

    G. Bekefi. Radiation Processes in Plasmas. Wiley, 1966

    1966

  139. [148]

    Stein, D

    J. Stein, D. Shalitin, and Akiva Ron. Average-atom models of line broadening in hot dense plasmas. Phys. Rev. A, 31:446–450, 1985

    1985

  140. [149]

    M. Y . Kuchiev and W. R. Johnson. Low-frequency plasma conductivity in the average-atom approximation. Phys. Rev. E, 78:026401, 2008

    2008

  141. [150]

    H. G. Wei, J. R. Shi, G. Zhao, Yi Zhang, Quan-Li Dong, Yu-Tong Li, Shou-Jun Wang, Jie Zhang, Zuotang Liang, Ji-Y an Zhang, Tian-Shu Wen, Wen-Hai Zhang, Xin Hu, Shen-Y e Liu, Y ong-Kun Ding, Lin Zhang, Y ong-Jian Tang, Bao-Han Zhang, Zhi-Jian Zheng, Hiroaki Nishimura, Shinsuke ...

    2008

  142. [151]

    Ionization competition effects on population distribution and radiative opacity of mixture plasmas

    Y ongjun Li, Cheng Gao, Qinyun Tian, Jiaolong Zeng, and Jianmin Yuan. Ionization competition effects on population distribution and radiative opacity of mixture plasmas. Phys. of Plasmas, 22:113302, 2015. 90 / 102 7. REFERENCES

    2015

  143. [152]

    F . Bloch. Bremsvermögen von Atomen mit mehreren Elektronen. Z. Phys., 81:363–376, 1933

    1933

  144. [153]

    W. R. Johnson, C. Guet, and G. F . Bertsch. Optical properties of plasmas based on an average- atom model. J. Quant. Spectrosc. Radiat. Transf., 99(1-3):327–340, 2006

    2006

  145. [154]

    Ishikawa, B

    K. Ishikawa, B. U. Felderhof, T. Blenski, and B. Cichocki. Photoabsorption by an ion immersed in a plasma at any temperature. J. Plasma Physics, 60:787–810, 1998

    1998

  146. [155]

    W.R. Johnson. Low-frequency conductivity in the average-atom approximation. High Energy Density Physics, 5:61 – 67, 2009

    2009

  147. [156]

    B. L. Henke, J. C. Davis, E. M. Gullikson, and R. C. C. Perera. A Preliminary Report on X-Ray Photoabsorption Coefficients and Atomic Scattering Factors for 92 Elements in the 10-10,000 eV Region. Technical Report LBL–26259 UC–411, Lawrence Berkeley Laboratory, 1988

    1988

  148. [157]

    M. J. Seaton. Quantum defect theory. Reports on Progress in Physics , 46:167–257, 1983. doi:10.1088/0034-4885/46/2/002

    1983 doi

  149. [158]

    Ishikawa

    K. Ishikawa. Photoabsorption by an ion immersed in a plasma. PhD thesis, 1998

    1998

  150. [159]

    G. D. Mahan and K. R. Subbaswamy. Local Density Theory of Polarizability. Springer, New Y ork, 1990

    1990

  151. [160]

    T. Blenski. On the linear dynamic response of average atom in plasma. J. Quant. Spectrosc. Radiat. Transf., 99(1-3):84–101, 2006

    2006

  152. [161]

    M. J. Seaton. Quantum defect theory I. General formulation.Proceedings of the Physical Society, 88:801–814, 1966. doi:10.1088/0370-1328/88/4/302

    1966 doi

  153. [162]

    G. D. Doolen and D. A Liberman. Calculations of photoabsorption by atoms using a linear re- sponse method. Physica Scripta, 36:77, 1987

    1987

  154. [163]

    Zangwill and D.A

    A. Zangwill and D.A. Liberman. A nonrelativistic program for optical response in atoms using a time-dependent local density approximation. Computer Physics Communications, 32:63–73, 1984

    1984

  155. [164]

    F . J. Dyson and A. Lenard. Stability of Matter. I. Journal of Mathematical Physics , 8:423–434, 1967

    1967

  156. [165]

    N. M. Gill, C. J. Fontes, and C. E. Starrett. Time-dependent density functional theory applied to average atom opacity. Phys. Rev. E, 103:043206, Apr 2021. URL: https://link.aps.org/ doi/10.1103/PhysRevE.103.043206, doi:10.1103/PhysRevE.103.043206

    2021 doi

  157. [166]

    Haensel, G

    R. Haensel, G. Keitel, P . Schreiber, and C. Kunz. Optical Absorption of Solid Krypton and Xenon in the Far Ultraviolet. Phys. Rev., 188:1375–1380, 1969

    1969

  158. [167]

    E. H. Lieb and J. L. Lebowitz. The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Advances in Mathematics, 9:316–398, 1972

    1972

  159. [168]

    J. K. Percus. The equilibrium theory of classical fluids , chapter The pair distribution function in classical statistical mechanics, page II–33 – II–170. W. A. Benjamin, Inc., New Y ork, 1964

    1964

  160. [169]

    J. K. Percus. At the boundary between reduced density-matrix and density-functional theories. J. Chem. Phys., 122:234103, 2005

    2005

  161. [170]

    F . J. Dyson and A. Lenard. Stability of Matter. II. Journal of Mathematical Physics, 9:698–711, 1968

    1968

  162. [171]

    J. L. Lebowitz and E. H. Lieb. Existence of Thermodynamics for Real Matter with Coulomb Forces. Phys. Rev. Lett., 22:631–634, 1969

    1969

  163. [172]

    Perrot and M

    F . Perrot and M. W. C. Dharma-wardana. Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions. Phys. Rev. B, 62:16536–16548, 2000

    2000

  164. [173]

    E. H. Lieb. The stability of matter. Rev. Mod. Phys., 48:553–569, 1976

    1976

  165. [174]

    Sandipan Dutta and J. W. Dufty. Classical representation of a quantum system at equilibrium: Applications. Phys. Rev. E, 87:032102, 2013

    2013

  166. [175]

    F . Lado. Effective Potential Description of the Quantum Ideal Gases. The Journal of Chemical Physics, 47:5369–5375, 1967

    1967

  167. [176]

    M. W. C. Dharma-wardana and F . Perrot. Simple Classical Mapping of the Spin-Polarized Quantum Electron Gas: Distribution Functions and Local-Field Corrections. Phys. Rev. Lett., 84:959–962, 2000

    2000

  168. [177]

    J. P . Hansen and I. R. MacDonald.Theory of simple liquids. Academic Press, 1976

    1976

  169. [178]

    J. W. Dufty and Sandipan Dutta. Classical representation of a quantum system at equilibrium: Theory. Phys. Rev. E, 87:032101, 2013

    2013

  170. [179]

    Starrett and D

    C.E. Starrett and D. Saumon. A simple method for determining the ionic structure of warm dense matter. High Energy Density Physics, 10:35–42, 2014

    2014

  171. [180]

    J. Chihara. Derivation of Quantal Hyper-Netted Chain Equation from the Kohn-Sham Theory. Progress of Theoretical Physics, 59:76–86, 1978

    1978

  172. [181]

    J. Chihara. Unified description of metallic and neutral liquids and plasmas. J. Phys.: Condens. Matter, 3:8715, 1991

    1991

  173. [182]

    Morita and K

    T. Morita and K. Hiroike. A New Approach to the Theory of Classical Fluids. I. Prog. Theor. Phys., 23:1003–1027, 1960

    1960

  174. [183]

    J. A. Anta and A. A. Louis. Probing ion-ion and electron-ion correlations in liquid metals within the quantum hypernetted chain approximation. Phys. Rev. B, 61:11400–11410, 2000

    2000

  175. [184]

    F . Lado. Perturbation Correction for the Free Energy and Structure of Simple Fluid Mixtures. J. Chem. Phys., 59:4830–4835, 1973

    1973

  176. [185]

    J. Chihara. Average Atom Model based on Quantum Hyper-Netted Chain Method. High Energy Density Physics, 19:38–47, 2016

    2016

  177. [186]

    Iyetomi and S

    H. Iyetomi and S. Ichimaru. Free energies of electron-screened ion plasmas in the hypernetted- chain approximation. Phys. Rev. A, 34(1):433–439, 1986

    1986

  178. [187]

    R. Abe. Giant Cluster Expansion Theory and Its Application to High Temperature Plasma. Prog. Theor. Phys., 22:213–226, 1959

    1959

  179. [188]

    F . Lado. Perturbation Correction for the Free Energy and Structure of Simple Fluids. Phys. Rev. A, 8:2548–2552, 1973

    1973

  180. [189]

    R. E. Kidder and H. E. DeWitt. Application of a modified Debye-Hückel theory to fully ionized gases. J. Nucl. Energy, Part C: Plasma Physics, 2:218–223, 1961. 92 / 102 7. REFERENCES

    1961

  181. [190]

    Enciso, F

    E. Enciso, F . Lado, M. Lombardero, J. L. F . Abascal, and S. Lago. Extension of the optimized RHNC equation to multicomponent liquids. J. Chem. Phys., 87:2249–2255, 1987

    1987

  182. [191]

    Olivares and D

    W. Olivares and D. A. McQuarrie. A variational approach to the theory of ionic solutions. The Journal of Chemical Physics, 65(9):3604–3610, 1976

    1976

  183. [192]

    Penfold, S

    R. Penfold, S. Nordholm, B. Jönsson, and C. E. Woodward. A simple analysis of ion-ion correla- tion in polyelectrolyte solutions. J. Chem. Phys., 92:1915–1922, 1990

    1915

  184. [193]

    H. E. DeWitt. Classical Theory of the Pair Distribution Function of Plasmas. Phys. Rev., 140:A466–A470, 1965

    1965

  185. [194]

    Classical

    R. W. Zwanzig. Transition from Quantum to “Classical” Partition Function.Phys. Rev., 106:13–15, 1957

    1957

  186. [195]

    Vieillefosse

    P . Vieillefosse. Improved Debye Hückel theory for one- and multicomponent plasmas. J. Physique, 42:723–733, 1981

    1981

  187. [196]

    Nordholm

    S. Nordholm. Simple Analysis of the thermodynamic properties of the one-component plasma. Chem. Phys. Lett., 105:302–306, 1984

    1984

  188. [197]

    Martinez, M

    B. Martinez, M. Lobet, R. Duclous, E. d’Humières, and L. Gremillet. High-energy radiation and pair production by Coulomb processes in particle-in-cell simulations. Physics of Plasmas, 26:103109, 2019. doi:10.1063/1.5118339

    2019 doi

  189. [198]

    J. G. Kirkwood. Quantum Statistics of Almost Classical Assemblies. Phys. Rev., 44:31–37, 1933

    1933

  190. [199]

    Hubeny and D

    I. Hubeny and D. Mihalas. Theory of Stellar Atmospheres: An Introduction to Astrophysical Non-equilibrium Quantitative Spectroscopic Analysis. Princeton University Press, 2014

    2014

  191. [200]

    van Kampen

    N. van Kampen. Stochastic Processes In Physics And Chemistry . North Holland Publishing, 2007

    2007

  192. [201]

    Le, Mark Sherlock, and Howard A

    Hai P . Le, Mark Sherlock, and Howard A. Scott. Influence of atomic kinetics on in- verse bremsstrahlung heating and nonlocal thermal transport. Phys. Rev. E , 100:013202,

  193. [202]

    URL: https://link.aps.org/doi/10.1103/PhysRevE.100.013202, doi:10.1103/ PhysRevE.100.013202

    doi

  194. [203]

    Peyrusse

    O. Peyrusse. A superconfiguration model for broadband spectroscopy of non-LTE plasmas. J. Phys. B, 33:4303–4321, 2000

    2000

  195. [204]

    Kalkofen, editor

    W. Kalkofen, editor. Methods in radiative transfer. Cambridge University Press, 1984

    1984

  196. [205]

    Einstein

    A. Einstein. Phys. Z., 18:121, 1917

    1917

  197. [206]

    D. H. Sampson, Hong Lin Zhang, and C. J. Fontes. A fully relativistic approach for calculating atomic data for highly charged ions. Phys. Rep., 477:111–214, 2009

    2009

  198. [207]

    C. J. Fontes, H. L. Zhang, J. Abdallah, R. E. H. Clark, D. P . Kilcrease, J. Colgan, R. T. Cun- ningham, P . Hakel, N. H. Magee, and M. E. Sherrill. The Los Alamos suite of relativistic atomic physics codes. J. Phys. B, 48:144014, 2015

    2015

  199. [208]

    Peyrusse

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

    1999

  200. [209]

    Busquet, M

    M. Busquet, M. Klapisch, and A. Bar-Shalom. Absorption and emission profiles of unresolved arrays near local thermodynamic equilibrium. J. Quant. Spectrosc. Radiat. Transf., 81:255, 2003

    2003

  201. [210]

    Peyrusse

    O. Peyrusse. On the superconfiguration approach to model NLTE plasma emission. J. Quant. Spectrosc. Radiat. Transfer, 71:571–579, 2001

    2001

  202. [211]

    Fowler and L

    R. Fowler and L. Nordheim. Electron emission in intense electric fields. Proc. R. Soc. London Ser. A, 119(781):173, 1928

    1928

  203. [212]

    W. E. Milne. Statistical equilibrium in relation to the photo-electric effect, and its application to the determination of absorption coefficients. Philos. Mag., 47:209, 1924

    1924

  204. [213]

    V. A. Makhrov, A. Yu. Sechin, and A. N. Starostin. Theory of nonstationary transfer of resonance radiation under conditions of partial frequency redistribution. JETP, 70:623, 1990

    1990

  205. [214]

    Yu. K. Zemtsov and A. N. Starostin. Does the probability for spontaneous emission depend on the density and the temperature? JETP, 76:186, 1993

    1993

  206. [215]

    J. G. Rubiano, R. Florido, C. Bowen, R. W. Lee, and Yu. V. Ralchenko. Review of the 4th NLTE Code Comparison Workshop. High Energ. Dens. Phys., 3:225–232, 2007

    2007

  207. [216]

    Klein and S

    O. Klein and S. Rosseland. Über zusammenstöße zwischen atomen und freien elektronen. Z. Phys., 4:46, 1921

    1921

  208. [217]

    Chung, C

    H.-K. Chung, C. Bowen, C. J. Fontes, S. B. Hansen, and Yu. Ralchenko. Comparison and analy- sis of collisional-radiative models at the NLTE-7 workshop.High Energ. Dens. Phys., 9:645–652, 2013

    2013

  209. [218]

    R. W. Lee, J. K. Nash, and Yu. Ralchenko. Review of the NLTE kinetics code workshop.J. Quant. Spectrosc. Radiat. Transfer, 58:737–742, 1997

    1997

  210. [219]

    Bowen, A

    C. Bowen, A. Decoster, C. J. Fontes, K. B. Fournier, O. Peyrusse, and Yu. V. Ralchenko. Re- view of the NLTE emissivities code comparison virtual workshop. J. Quant. Spectrosc. Radiat. Transfer, 81:71—84, 2003

    2003

  211. [220]

    Bowen, R

    C. Bowen, R. W. Lee, and Yu. V. Ralchenko. Comparing plasma population kinetics codes: Review of the NLTE-3 Kinetics Workshop. J. Quant. Spectrosc. Radiat. Transfer, 99:102–119, 2006

    2006

  212. [221]

    S. B. Hansen, J. Bauche, C. Bauche-Arnoult, and M. F . Gu. Hybrid atomic models for spectro- scopic plasma diagnostics. High Energ. Dens. Phys., 3:109–114, 2007

    2007

  213. [222]

    C. J. Fontes, J. Abdallah Jr, C. Bowen, R. W. Lee, and Yu. Ralchenko. Review of the NLTE-5 kinetics workshop. High Energ. Dens. Phys., 5:15–22, 2009

    2009

  214. [223]

    S. B. Hansen, J. Bauche, and C. Bauche-Arnoult. Superconfiguration widths and their effects on atomic models. High Energ. Dens. Phys., 7:27, 2011

    2011

  215. [224]

    S. B. Hansen, G. S. J. Armstrong, S. Bastiani-Ceccotti, C. Bowen, H.-K. Chung, J. Colgan, F . de Dortan, C. J. Fontes, F . Gilleron, J.-R. Marquès, R. Piron, O. Peyrusse, M. Poirier, Yu. Ralchenko, A. Sasaki, E. Stambulchik, and F . Thais. Testing the reliability of non-LTE sp...

    2013 doi

  216. [225]

    Piron, F

    R. Piron, F . Gilleron, Y . Aglitskiy, H.-K. Chung, C. J. Fontes, S. B. Hansen, O. Marchuk, H. A. Scott, E. Stambulchik, and Yu. Ralchenko. Review of the 9th NLTE code comparison workshop. High Energy Density Physics, 23:38–47, 2017. doi:10.1016/j.hedp.2017.02.009

    2017 doi

  217. [226]

    Hansen, H.-K

    S.B. Hansen, H.-K. Chung, C.J. Fontes, Yu Ralchenko, H.A. Scott, and E. Stambulchik. Review of the 10th Non-LTE code comparison workshop. High Energy Density Physics , 35:100693,

  218. [227]

    Ralchenko and Y

    Yu. Ralchenko and Y . Maron. Accelerated recombination due to resonant deexcitation of metastable states. J. Quant. Spectrosc. Radiat. Transfer, 71:609–621, 2001. 94 / 102 7. REFERENCES

    2001

  219. [228]

    Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermody- namic equilibrium

    Cheng Gao, Jiaolong Zeng, Y ongqiang Li, Fengtao Jin, and Jianmin Yuan. Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermody- namic equilibrium. High Energ. Dens. Phys., 9:583–593, 2013

    2013

  220. [229]

    S. B. Hansen. Configuration interaction in statistically complete hybrid-structure atomic models. Can. J. Phys., 89:633, 2011

    2011

  221. [230]

    E. V. Marley, D. A. Liedahl, M. B. Schneider, R. F . Heeter, L. C. Jarrott, C. W. Mauche, G. E. Kemp, M. E. Foord, Y . Frank, K. Widmann, and J. Emig. Using L-shell x-ray spectra to determine conditions of non-local thermal dynamic equilibrium plasmas. Review of Scientific Ins...

    2018 doi

  222. [231]

    H. A. Scott and S. B. Hansen. Advances in NLTE modeling for integrated simulations. High Energ. Dens. Phys., 6:39–47, 2010

    2010

  223. [232]

    Chung, M

    H.-K. Chung, M. H. Chen, W. L. Morgan, Yu. Ralchenko, and R. W. Lee. FL YCHK: Generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements. High Energ. Dens. Phys., 1:3–12, 2005

    2005

  224. [233]

    A. F . Nikiforov, V. G. Novikov, and V. B. Uvarov.Quantum-Statistical Models of Hot Dense Matter. Birkhauser, 2005

    2005

  225. [234]

    M. F . Gu. The flexible atomic code. Can. J. Phys., 86:675–689, 2008

    2008

  226. [235]

    URL: https://github.com/ fnevgeny/cfac

    CFAC is a fork of the Flexible Atomic Code of Ming-Feng Gu, partially rewritten, and main- tained by Evgeny Stambulchik (Weizmann Institute of Science). URL: https://github.com/ fnevgeny/cfac

  227. [236]

    Bastiani-Ceccotti, A.-C

    S. Bastiani-Ceccotti, A.-C. Bourgaux, C. Bowen, F . Dorchies, F . Gilleron, J.-R. Marquès, J.-C. Pain, V. Silvert, and T. Vinci. Analysis of X-ray and Thomson scattering data from non-LTE Nb and Ta plasmas. High Energy Density Physics, 16:41–52, 2015. doi:10.1016/j.hedp.2015. 05.003

    2015 doi

  228. [237]

    Ralchenko and A

    Yu. Ralchenko and A. Kramida. Development of NIST Atomic Databases and Online Tools. Atoms, 8, 2020. doi:10.3390/atoms8030056

    2020 doi

  229. [238]

    Bishel, E

    David T. Bishel, E. V. Marley, M. B. Schneider, D. A. Liedahl, R. F . Heeter, M. E. Foord, G. E. Kemp, Y . Frank, J. A. Emig, G. Pérez-Callejo, P . M. Nilson, J. R. Rygg, and G. W. Collins. Ionization diequilibrium in K- and L-shell ions. Phys. of Plasmas , 30:073303, 2023. do...

    2023 doi

  230. [239]

    E. V. Marley, C. M. Krauland, D. A. Liedahl, G. E. Kemp, R. F . Heeter, M. B. Schneider, and M. E. Foord. Contribution to the conference Atomic Processes in Plasmas : Comparing the sensitivities of Au and Zn ionization in buried layer targets

  231. [240]

    A. Morana. Caractérisation hydrodynamique et spectroscopique de plasmas de carbone, alu- minium et germanium produits par impulsion laser picoseconde . PhD thesis, Institut Polytech- nique de Paris, 2021. URL: https://theses.hal.science/tel-03371355

    2021

  232. [241]

    R. Mewe. Interpolation Formulae for the Electron Impact Excitation of Ions in the H-, He-, Li-, and Ne- Sequences. Astronomy and Astrophysics, 20:215, 1972

    1972

  233. [242]

    An empirical formula for the electron-impact ionization cross-section

    Wolfgang Lotz. An empirical formula for the electron-impact ionization cross-section. Zeitschrift fur Physik, 206:205–211, 1967. doi:10.1007/BF01325928

    1967 doi

  234. [243]

    Kramida, Yu Ralchenko, J

    A. Kramida, Yu Ralchenko, J. Reader, and NIST ASD Team (2023). NIST Atomic Spectra Database (version 5.11). URL: https://physics.nist.gov/asd, doi:10.18434/T4W30F

    2023 doi

  235. [244]

    M. S. Dimitrijevic and N. Konjevic. Stark widths of doubly-and triply-ionized atom lines. J. Quant. Spectrosc. Radiat. Transf., 24:451, 1980

    1980

  236. [245]

    R. M. More. Electronic energy-levels in dense plasmas. J. Quant. Spectrosc. Radiat. Transf. , 27:345–357, 1982

    1982

  237. [246]

    R. M. More. Atomic Physics in Inertial Confinement Fusion. Technical Report UCRL-84991, 1991

    1991

  238. [247]

    van Regemorter

    H. van Regemorter. Rate of collisional excitation in stellar atmospheres. Ap. J., 136:906–915, 1962

    1962

  239. [248]

    H. W. Drawin and F . Emard. Optical Escape Factors for Bound-bound and Free-bound Radiation from Plasmas I. Constant Source Function. Beiträge aus der Plasmaphysik, 11:143–168, 1973

    1973

  240. [249]

    F . E. Irons. The Escape Factor In Plasma Spectroscopy – I. The Escape Factor Defined And Evaluated. J. Quant. Spectrosc. Radiat. Transf., 22:1–20, 1979

    1979

  241. [250]

    A. Burgess. A general formula for the estimation of dielectronic recombination coefficients in low-density plasmas. Ap. J., 141:1588–1590, 1965

    1965

  242. [251]

    M. Busquet. Radiation-dependent ionization model for laser-created plasmas. Phys. of Fluids B, 5:4191–4206, 1993

    1993

  243. [252]

    O. Marchuk. Modeling of He-like spectra measured at the tokamaks TEXTOR and TORE SUPRA. PhD thesis, 2004

    2004

  244. [253]

    Marchuk, G

    O. Marchuk, G. Bertschinger, C. Fenzi-Bonizec, B. Schunke, M. Mattioli, A. Whiteford, and N. R. Badnell. Impurity transport studies in TORE SUPRA with He-like spectroscopy. 32nd EPS conference on Plasma Phys. ECA, 29C:P–2.025, 2005

    2005

  245. [254]

    A. H. Gabriel. Dielectronic satellite spectra for highly-charged helium-like ion lines. Mon. Not. R. astr. Soc., 160:99–119, 1972

    1972

  246. [255]

    R. M. More. Dielectronic Recombination in the Average-Atom Model. Technical Report UCRL- 96522, 1987

    1987

  247. [256]

    R. M. More, G. B. Zimmerman, and Z. Zinamon. Dielectronic recombination in the average-atom model. AIP Conference Proceedings, 168:33–41, 1988. doi:10.1063/1.37182

    1988 doi

  248. [257]

    G. B. Rybicki. Escape probability methods. In W. Kalkofen, editor, Methods in radiative transfer. Cambridge University Press, 1984

    1984

  249. [258]

    Dallot, G

    P . Dallot, G. Faussurier, A. Decoster, and A. Mirone. Average-ion level-population correlations in off-equilibrium plasmas. Phys. Rev. E, 57:1017–1028, 1998

    1998

  250. [259]

    W. A. Lokke and W. H. Grasberger. XSNQ-U A Non-LTE Emission And Absorption Coefficient Subroutine. Technical Report UCRL-52276, 1977

    1977

  251. [260]

    B. F . Rozsnyai. Collisional-radiative average-atom model for hot plasmas . Phys. Rev. E , 55:7507–7521, 1997

    1997

  252. [261]

    V. P . Zhdanov. Dielectronic recombination of electrons in collisions with ions.JETP, 48:611–615, 1978

    1978

  253. [262]

    Kluth, K

    G. Kluth, K. D. Humbird, B. K. Spears, J. L. Peterson, H. A. Scott, M. V. Patel, J. Koning, M. Mari- nak, L. Divol, and C. V. Y oung. Deep learning for NLTE spectral opacities. Physics of Plasmas, 27:052707, 2020. doi:10.1063/5.0006784

    2020 doi

  254. [263]

    Kluth, B.-J

    G. Kluth, B.-J. Grea, F . Gilleron, R. Piron, O. Soulard, S. Thevenin, L. Lepareur, and O. Morice. to be published (in french). Chocs

  255. [264]

    J. R. Albritton and B. G. Wilson. Non-LTE Ionization and Energy Balance in High-Z Laser Plas- mas Including Two-Electron Transitions.Phys. Rev. Lett., 83:1594–1597, 1999

    1999

  256. [265]

    Q. Y . van den Berg, E. V. Fernandez-Tello, T. Burian, J. Chalupský, H.-K. Chung, O. Ciricosta, G. L. Dakovski, V. Hájková, P . Hollebon, L. Juha, J. Krzywinski, R. W. Lee, M. P . Minitti, T. R. Preston, A. G. de la Varga, V. Vozda, U. Zastrau, J. S. Wark, P . Velarde, and S. ...

    2018

  257. [266]

    Mirone, F

    A. Mirone, F . Gilleron, J.-C. Gauthier, and G. Faussurier. Statistical Mechanics Of Average Ions In Non-Local Thermodynamic Equilibrium Plasmas. J. Quant. Spectrosc. Radiat. Transf., 60:551–558, 1998

    1998

  258. [267]

    Lefebvre, S

    E. Lefebvre, S. Bernard, C. Esnault, P . Gauthier, A. Grisollet, P . Hoch, L. Jacquet, G. Kluth, S. Laffite, S. Liberatore, I. Marmajou, P .-E. Masson-Laborde, O. Morice, and J.-L. Willien. Devel- opment and validation of the TROLL radiation-hydrodynamics code for 3D hohlraum ...

    2018 doi

  259. [268]

    Jacquet, L

    L. Jacquet, L. Lecherbourg, M. Primout, P . Kaiser, F . Gilleron, R. Piron, B. Villette, C. Blancard, G. Soullie, C. Reverdin, B. Vauzour, and G. Legay. Investigation of multi-keV silver x-ray sources at OMEGA. Phys. of Plasmas, 30:123302, 2023. doi:10.1063/5.0173483

    2023 doi

  260. [269]

    J. E. Bailey, G. A. Rochau, C. A. Iglesias, J. Abdallah, J. J. MacFarlane, I. Golovkin, P . Wang, R. C. Mancini, P . W. Lake, T. C. Moore, M. Bump, O. Garcia, and S. Mazevet. Iron-Plasma Transmission Measurements at Temperatures Above 150 eV.Phys. Rev. Lett., 99:265002, 2007

    2007

  261. [270]

    Blenski, G

    T. Blenski, G. Loisel, M. Poirier, F . Thais, P . Arnault, T. Caillaud, J. Fariaut, F . Gilleron, J.-C. Pain, Q. Porcherot, C. Reverdin, V. Silvert, B. Villette, S. Bastiani-Ceccotti, S. Turck-Chièze, W. Foelsner, and F . de Gaufridy de Dortan. Opacity of iron, nickel, and cop...

    2011 doi

  262. [271]

    The Strong Enhancement of Electron-Impact Ionization Processes in Dense Plasma by Transient Spatial Localization

    Jiaolong Zeng, Chen Y e, Pengfei Liu, Cheng Gao, Y ongjun Li, and Jianmin Yuan. The Strong Enhancement of Electron-Impact Ionization Processes in Dense Plasma by Transient Spatial Localization. International Journal of Molecular Sciences, 23:6033, 2022. 96 / 102 7. REFERENCES

    2022

  263. [272]

    Renaudin, C

    P . Renaudin, C. Blancard, G. Faussurier, and P . Noiret. Combined Pressure and Electrical- Resistivity Measurements of Warm Dense Aluminum and Titanium Plasmas. Phys. Rev. Lett., 88:215001, 2002

    2002

  264. [273]

    S. J. Davidson, J. M. Foster, C. C. Smith, K. A. Warburton, and S. J. Rose. Investigation of the opacity of hot, dense aluminum in the region of its K edge.Applied Physics Letters, 52:847–849, 1988

    1988

  265. [274]

    Bruneau, C

    J. Bruneau, C. Chenais-Popovics, D. Desenne, J.-C. Gauthier, J.-P . Geindre, M. Klapisch, J.-P . Le Breton, M. Louis-Jacquet, D. Naccache, and J.-P . Perrine. Time-resolved L-shell absorption spectroscopy: A direct measurement of density and temperature in a germanium laser-pr...

    1990

  266. [275]

    L. B. Da Silva, B. J. MacGowan, D. R. Kania, B. A. Hammel, C. A. Back, E. Hsieh, R. Doyas, C. A. Iglesias, F . J. Rogers, and R. W. Lee. Absorption measurements demonstrating the importance of ∆n=0 transitions in the opacity of iron. Phys. Rev. Lett., 69:438–441, 1992

    1992

  267. [276]

    Kraus, D

    D. Kraus, D. A. Chapman, A. L. Kritcher, R. A. Baggott, B. Bachmann, G. W. Collins, S. H. Glenzer, J. A. Hawreliak, D. H. Kalantar, O. L. Landen, T. Ma, S. Le Pape, J. Nilsen, D. C. Swift, P . Neumayer, R. W. Falcone, D. O. Gericke, and T. Döppner. X-ray scattering measurement...

    2016

  268. [277]

    D. C. Swift, A. L. Kritcher, J. A. Hawreliak, A. Lazicki, A. MacPhee, B. Bachmann, T. Döppner, J. Nilsen, G. W. Collins, S. Glenzer, S. D. Rothman, D. Kraus, and R. W. Falcone. Absolute Hugoniot measurements from a spherically convergent shock using x-ray radiography. Review o...

    2018

  269. [278]

    J. E. Bailey, T. Nagayama, G. P . Loisel, G. A. Rochau, C. Blancard, J. Colgan, Ph. Cosse, G. Faussurier, C. J. Fontes, F . Gilleron, I. Golovkin, S. B. Hansen, C. A. Iglesias, D. P . Kilcrease, J. J. MacFarlane, R. C. Mancini, S. N. Nahar, C. Orban, J.-C. Pain, A. K. Pradhan,...

    2015

  270. [279]

    D. J. Hoarty, P . Allan, S. F . James, C. R. D. Brown, L. M. R. Hobbs, M. P . Hill, J. W. O. Harris, J. Morton, M. G. Brookes, R. Shepherd, J. Dunn, H. Chen, E. Von Marley, P . Beiersdorfer, H. K. Chung, R. W. Lee, G. Brown, and J. Emig. Observations of the Effect of Ionizatio...

    2013

  271. [280]

    V. N. Korobenko and A. D. Rakhel. Electrical resistivity and equation of state measurements on hot expanded aluminum in the metal-nonmetal transition range. Phys. Rev. B, 75:064208, 2007

    2007

  272. [281]

    Gregori, S

    G. Gregori, S. H. Glenzer, F . J. Rogers, S. M. Pollaine, O. L. Landen, C. Blancard, G. Faus- surier, P . Renaudin, S. Kuhlbrodt, and R. Redmer. Electronic structure measurements of dense plasmas. Physics of Plasmas, 11:2754–2762, 2004

    2004

  273. [282]

    Electrical conductivity calculations in isochorically heated warm dense aluminum

    P Sperling, S Rosmej, R Bredow, L B Fletcher, E Galtier, E J Gamboa, H J Lee, H Reinholz, G Röpke, U Zastrau, and S H Glenzer. Electrical conductivity calculations in isochorically heated warm dense aluminum. Journal of Physics B: Atomic, Molecular and Optical Physics , 50(13)...

    2017

  274. [285]

    S. X. Hu, David T. Bishel, David A. Chin, Philip M. Nilson, Valentin V. Karasiev, Igor E. Golovkin, Ming Gu, Stephanie B. Hansen, Deyan I. Mihaylov, Nathaniel R. Shaffer, Shuai Zhang, and Timothy Walton. Probing atomic physics at ultrahigh pressure using laser-driven implosion...

    2022

  275. [287]

    Ciricosta, S

    O. Ciricosta, S. M. Vinko, H.-K. Chung, B.-I. Cho, C. R. D. Brown, T. Burian, J. Chalupský, K. Engelhorn, R. W. Falcone, C. Graves, V. Hájková, A. Higginbotham, L. Juha, J. Krzywinski, H. J. Lee, M. Messerschmidt, C. D. Murphy, Y . Ping, D. S. Rackstraw, A. Scherz, W. Schlotte...

    2012

  276. [288]

    G. P . Loisel, J. E. Bailey, D. A. Liedahl, C. J. Fontes, T. R. Kallman, T. Nagayama, S. B. Hansen, G. A. Rochau, R. C. Mancini, and R. W. Lee. Benchmark Experiment for Photoionized Plasma Emission from Accretion-Powered X-Ray Sources. Phys. Rev. Lett., 119:075001, 2017. doi: ...

    2017 doi

  277. [289]

    Pérez-Callejo, L

    G. Pérez-Callejo, L. C. Jarrott, D. A. Liedahl, E. V. Marley, G. E. Kemp, R. F . Heeter, J. A. Emig, M. E. Foord, K. Widmann, J. Jaquez, H. Huang, S. J. Rose, J. S. Wark, and M. B. Schneider. Laboratory measurements of geometrical effects in the x-ray emission of optically thi...

    2019 doi

  278. [290]

    Symbols may play a slightly different role in the various chapter, in particular when the same symbol is used in the description of different models (e.g

    Symbols and Notations This table gives systematic rules of notation rather than an exhaustive list of symbols. Symbols may play a slightly different role in the various chapter, in particular when the same symbol is used in the description of different models (e.g. ne). Tildas...

  279. [2018]

    doi:10.1002/ctpp.201700095

    doi

  280. [2019]

    doi:10.1103/PhysRevE.99.052134

    doi

  281. [2020]

    URL: https://www.sciencedirect.com/science/article/pii/S1574181819300357, doi:10.1016/j.hedp.2019.06.001

    2019 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.