Pith. sign in

REVIEW 3 major objections 6 minor 53 references

Ion stopping from bound and free electrons in plasmas: A channel-mixed RPA approach with average-atom orbitals

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A channel-mixed RPA dielectric reproduces proton stopping near and above the Bragg peak in partially ionized plasmas.

desk verdict A solid, usable all-electron linear-response stopping model with a real but contained free-free weak spot; worth refereeing, conditional on reproducibility and f-f consistency checks. read the letter →

arxiv 2608.00797 v1 pith:SCFMQCIK submitted 2026-08-01 physics.plasm-ph physics.atom-ph

Zachary A Johnson , Patrick J Adrian , Joshua A Leveillee , Charles E. Starrett This is my paper · ORCID
classification physics.plasm-phphysics.atom-ph
keywords ionstoppingdielectricresponserandomphaseapproximationaverageatomboundelectronswarmdensematterinertialconfinementfusionlinear
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 paper builds a single dielectric response function for ion stopping in partly ionized plasmas by putting bound-electron transitions, computed from average-atom orbitals, on the same footing as the standard Lindhard free-electron response, and mixing them at the level of the random phase approximation rather than adding their stopping contributions separately. The aim is a predictive, all-electron, linear-response stopping tool cheap enough to sweep across the densities and temperatures relevant to inertial confinement fusion. Against ambient experiments and TD-DFT simulations, the resulting channel-mixed RPA stopping power agrees well for protons at and above the Bragg peak. The paper's main new claims are that bound and free channels interfere through the dielectric denominator, that bound-bound transitions contribute at low projectile velocity when bound states are partially occupied, and that bound electrons still matter for alpha stopping in highly compressed tungsten. Applied to a recent warm dense carbon stopping experiment, the model indicates that inadequate bound-state modeling is unlikely to explain the measured deficit within linear response.

What carries the argument

Equation (4), the channel-mixed energy loss function Im[ε⁻¹]_{cmRPA} = V_k Im[χ_bb + χ_bf + χ_ff] / |1 − V_k(χ_bb + χ_bf + χ_ff)|², is the central object. It is what distinguishes cmRPA from the Chihara-style unmixed form, Eq. (5), because taking the imaginary part of the inverse dielectric puts every channel's real and imaginary response into one denominator; that mixing is the mechanism by which bound-free transitions and the free-electron plasmon interfere. The bound channel polarizabilities come from radial matrix elements of average-atom orbitals, with a small width that smooths the continuum, and the free-free piece is the finite-temperature Lindhard function with exactly ⟨Z⟩ electrons

What would settle it

Measure proton stopping in warm dense carbon near 0.5 g/cm3 and 10 eV across the Bragg peak with enough precision to distinguish cmRPA's hybridized curve from the unmixed additive model; if the data trace the additive curve, the paper's channel-mixing claim is falsified.

Watch

Extended reading notes

Core claim

The paper claims that the electronic stopping of an ion in a partially ionized plasma can be captured by a dielectric function in which bound-bound, bound-free, and free-free transitions all enter a single random-phase-approximation denominator, with the bound transitions built from average-atom orbitals and the free-free piece taken as finite-temperature Lindhard response. The resulting energy-loss function, Eq. (4), is the channel-mixed RPA (cmRPA) form. It is distinguished from a Chihara-style unmixed decomposition, Eq. (5), because the real and imaginary parts of all channels screen each other in one denominator, so bound and free responses interfere. Against ambient-condition stopping d

Load-bearing premise

Everything rests on the assumption that the small inconsistency between how free electrons (plane waves) and bound electrons (average-atom orbitals) are treated does not materially change the stopping power the model predicts.

Editorial extensions

If this is right

  • Stopping curves for protons and alphas in warm dense and inertial-confinement fusion conditions can be generated orders of magnitude faster than TD-DFT, enabling parameter sweeps and diagnostic design.
  • At temperatures where bound states are partially occupied, bound-bound transitions give a low-velocity stopping contribution that a free-electron-only model misses.
  • A proper RPA treatment of bound-free transitions can either enhance or suppress stopping relative to additive channel models, depending on where the bound edge sits relative to the plasmon, so the bound correction is condition-dependent.
  • In double-shell inertial-confusion tungsten at 10–100 times compression, omitting bound electrons under-predicts stopping, and cold versus hot tungsten give noticeably different alpha ranges.
  • For the recent warm dense carbon measurement, the model implies that bound-state treatment cannot fix the measured deficit under linear response, directing attention to other physics or experimental effects.

Reading between the lines

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

  • Editorial inference: because the paper's local-field-correction test raises low-velocity stopping toward experiment, adding a consistent local-field correction to the mixed denominator is a natural next step that could push cmRPA's validity down across the Bragg peak.
  • Editorial inference: the same dielectric function governs inelastic x-ray scattering, so the predicted bound-free/plasmon hybridization should be visible as a redistribution of spectral weight in warm dense matter x-ray Thomson scattering or electron-energy-loss measurements; a direct spectral measurement would independently test the channel-mixing claim.
  • Editorial inference: the f-sum violation and the Appendix A low-velocity artifact both trace to using plane-wave Lindhard for continuum states that the average-atom model sees as quasibound; replacing the Lindhard free-free response with an average-atom-consistent continuum appears to be the highest-leverage fix and would likely recalibrate the tungsten predictions at extreme compression.
  • Editorial inference: at projectile charges beyond protons, nonlinear effects enter precisely in the low-velocity region where bound-bound features appear, so comparing cmRPA against all-electron TD-DFT for alpha or heavier ions in partially ionized targets would map where linear response breaks and where bound contributions must be folded into binary-collision models.
Share X Bluesky LinkedIn Reddit HN

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. The manuscript develops a channel-mixed RPA (cmRPA) dielectric function for electronic stopping in partially ionized plasmas, combining a finite-temperature Lindhard free-free response with average-atom (AA) bound-bound and bound-free polarizabilities in a single RPA denominator (Eq. 4). The model is validated against ambient IAEA data and TD-DFT for Al, Fe, Ne, and W, and applied to temperature-dependent Al stopping, HED tungsten, and the Malko et al. warm dense carbon experiment. The authors report good agreement above the Bragg peak, identify non-trivial channel-mixing and bound-bound contributions, and conclude that improved bound-state modeling is unlikely to explain the Malko discrepancy.

Significance. If the central claim holds, cmRPA is an efficient, physically transparent all-electron linear-response stopping model for partially ionized plasmas, with explicit bound-channel transitions and a natural mechanism for bound-free/free-free interference. The paper's strengths are the explicit orbital matrix elements, the broad ambient validation set, the direct comparison with TD-DFT, and the application to ICF-relevant conditions. The main limitation is the inconsistent treatment of the free-free response: the Lindhard assumption is not validated in regimes where AA continuum states deviate strongly from plane waves, and Appendix A shows that a sum-rule-preserving modification of the f-f kernel produces large, unphysical stopping changes. This makes the predictive claim for such regimes currently unsupported.

major comments (3)
  1. [Sec. II.A, Eqs. (4),(6); Appendix A, Fig. 12] The free-free Lindhard assumption is load-bearing. Because Eq. (4) mixes chi_ff nonlinearly with chi_bb and chi_bf in the denominator, an error in the f-f spectral distribution is not a small additive correction; it modifies the channel interference that is a central result (Sec. III.C). Appendix A shows that replacing the Lindhard DOS with the AA DOS in a sum-rule-preserving manner creates an unphysical low-velocity peak in stopping (Fig. 12b). This demonstrates that f-sum-rule conservation is insufficient to control the stopping-relevant spectrum. The full AA f-f polarizability, with both initial and final continuum states in Eq. (6), is not computed in this work. The ambient validations in Fig. 2 involve small Z_bar and nearly free-electron-like free states, so they do not constrain the problematic regime, e.g., Al at T=100 eV (Fig. 1c-d) or HED tungsten (Sec. III.D). Please provide a
  2. [Sec. II.A, Eq. (12)] The width parameter c_Gamma is set to 1 with the statement that varying it changes only computational expense and 'does not change the result,' but no convergence study is shown. Given the continuum sensitivity demonstrated in Appendix A, this insensitivity must be supported numerically. Please provide the stopping power as a function of c_Gamma (or, equivalently, continuum mesh spacing) for at least one representative case, and state the criterion used to choose c_Gamma in the production runs.
  3. [Appendix B, Fig. 13] The paper uses the ion-sphere-restricted radial integrals for all production results, explicitly sacrificing orthogonality between bound and free states. The authors show that the effect on stopping is small for carbon at T=10 eV, but this is a single, relatively low-Z case. For the high-Z, tightly compressed tungsten conditions of Sec. III.D, bound-state radii may be comparable to the ion-sphere radius, and the j0 -> j0-1 correction described in Appendix B is an ad hoc fix. Please provide a targeted check of the ion-sphere truncation error for at least one of the tungsten conditions, or state a criterion for when the truncation is valid.
minor comments (6)
  1. [Notation throughout] The angular frequency appears as w in Eqs. (6), (10)-(12), and (A1), but as omega elsewhere. Use \omega consistently.
  2. [Fig. 1 caption, panel b] The phrase 'the f-f part only (orange) versus ⟨Z⟩' is unclear; please say 'the free-free contribution normalized to ⟨Z⟩'.
  3. [Fig. 8] The initial proton beam energy distribution is shown 'in green,' but the RPA+CBC curve is also green; use different colors/linestyles to avoid ambiguity.
  4. [Appendix A] Define g_AA_DOS(E) and g_ideal_DOS(E) explicitly; currently only their ratio is used, which makes the construction hard to reproduce.
  5. [Reference [36]] The journal name 'Npj Comput. Mater.' should be 'npj Computational Materials'.
  6. [Sec. III.A] Typographical issue: 'we have a)aluminum...' lacks spaces after the panel labels in several places.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: cmRPA is self-contained; acknowledged f-f inconsistency is a limitation, not a circular step.

full rationale

The derivation is self-contained. Equation (1) is the standard linear-response stopping integral; Eq. (2) defines the RPA dielectric as a sum of independent-particle channel polarizabilities; Eqs. (6)-(11) give those polarizabilities from average-atom orbitals and matrix elements. No parameter is fitted to the stopping data used for validation. The only tunable coefficient, c_Gamma in Eq. (12), is set to unity with a stated insensitivity check, and the ion-sphere truncation is explicitly checked against the extended-sphere result (Appendix B). The f-f channel is approximated by finite-T Lindhard rather than by the fully consistent AA continuum response; this is an acknowledged approximation that produces a ~1% f-sum violation and a sensitivity demonstration in Appendix A. These are consistency/accuracy caveats, not circular reductions: Lindhard's Z_bar sum and AA orbitals are inputs, while the predicted ELF and stopping powers are compared to independent IAEA experiments and TD-DFT simulations. The tartarus code citation [28] is a tool citation, not a load-bearing argument that assumes the target result. No equation or prediction reduces by construction to its inputs.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard linear response and RPA framework, plus two ad hoc modeling choices (Lindhard f-f and ion-sphere truncation) that the authors acknowledge. No fitted parameters are used for the main results, and no new physical entities are introduced.

free parameters (1)
  • c_Gamma = 1
    Width coefficient in Eq. (12); set to 1. Authors claim varying it changes computational cost but not results, but this is not demonstrated with a convergence plot.
assumptions (6)
  • domain assumption Linear response approximation: projectile potential perturbs the plasma weakly, so stopping is given by Eq. (1) in terms of the dielectric function.
    Invoked in Section II; known to hold for fast ions above the Bragg peak, and the paper restricts its central validation to that regime.
  • domain assumption The irreducible polarizability is the independent-particle (RPA) susceptibility computed from average-atom Kohn-Sham orbitals with Fermi-Dirac occupations.
    Section II A, Eq. (6); ignores dynamic exchange-correlation and many-body effects beyond the static Kohn-Sham potential.
  • ad hoc to paper Free-free response is approximated by the finite-temperature Lindhard function with Z_bar electrons, not by AA continuum states.
    Section II A; necessary for tractability but inconsistent with the AA bound states, causing the acknowledged f-sum rule violation (Fig. 1).
  • domain assumption The average-atom model (tartarus) with spherical symmetry gives reliable orbitals and charge states for the conditions studied.
    Used throughout; the paper notes potential failure at low density and temperature where chemical bonding occurs (Section III E).
  • ad hoc to paper A finite width Gamma(omega) with c_Gamma=1 smooths the continuum without changing integrated stopping.
    Introduced in Eq. (12); the insensitivity claim is asserted, not shown with a convergence study.
  • ad hoc to paper Truncating bound-free radial integrals at the ion-sphere radius, and applying the j0-1 correction, preserves stopping accuracy.
    Appendix B; sacrifices orthogonality and sum rules but is shown to have small stopping impact for the tested cases.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ion stopping from bound and free electrons in plasmas: A channel-mixed RPA approach with average-atom orbitals." pith.science (2026). https://pith.science/paper/SCFMQCIK

@misc{pith2026260800797,
  author       = {Pith},
  title        = {Pith review of: Ion stopping from bound and free electrons in plasmas: A channel-mixed RPA approach with average-atom orbitals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SCFMQCIK}},
  note         = {Machine review of arXiv:2608.00797}
}
read the original abstract

Ion stopping in partially ionized plasmas often receives roughly equal contributions from bound and free electrons, yet bound electron contributions are usually treated at a very coarse level, with the exception of costly time-dependent density functional theory (TD-DFT) simulations. At energies above the Bragg peak, where linear response methods are a good approximation, more accurate treatment is both feasible and critical for predictive modeling. We develop a channel-mixed random phase approximation (cmRPA) dielectric response function that combines Lindhard free response with explicit average-atom bound state transitions. Validating against ambient condition experiments and TD-DFT simulations, we demonstrate excellent agreement for proton stopping near and above the Bragg peak. The computational efficiency of our approach enables systematic exploration of extreme conditions across a wide range of densities and temperatures. We find non-trivial stopping effects from channel mixing between bound and free transitions via RPA, bound-bound stopping contributions at low velocity, and predict significant bound electron contributions to stopping in tungsten at peak compression conditions relevant to inertial confinement fusion experiments. Applying our model to the warm dense matter stopping experiment of Malko et al. (2022), we evaluate whether improved bound-state modeling could resolve the reported theory-experiment discrepancy, finding that within the constraints of linear response theory, bound stopping mismodeling is unlikely to be the source of the observed deficit.

Figures

Figures reproduced from arXiv: 2608.00797 by the authors.

Figure 1
Figure 1. On the left in panel a) we have the T = 1 eV case where we can clearly see the sharp plasmon peak at ω = 0.58 a.u. with an upturn just before reaching the continuum of individual Fermi-sphere electron scattering losses[27]. We can see two distinct bound-free ionization thresholds which are roughly k independent except near the narrow impact approximation asymptote at ω = k 2/2 which appears as a sharp feature extend… view at source ↗
Figure 2
Figure 2. FIG. 2. We plot proton stopping near ambient conditions from the IAEA experimental database (purple circles) [ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Stopping power of our full model (solid) and RPA only [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4. We show the effect of hybridization of the plasmon [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. For HED tungsten at 3 conditions in the range of 10- [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Stopping power for points evenly spaced in [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. We show our time dependent energy loss prediction [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. For Al at [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. We show carbon at [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. In a more detailed version of Fig. [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. We show again the result in Fig. [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 52 canonical work pages

  1. [1]

    Bethe, Theory of the Passage of Fast Corpuscular Rays Through Matter, Annalen Phys.5, 325 (1930)

    H. Bethe, Theory of the Passage of Fast Corpuscular Rays Through Matter, Annalen Phys.5, 325 (1930)

    work page 1930

  2. [2]

    Bohr, Ii

    N. Bohr, Ii. on the theory of the decrease of velocity of moving electrified particles on passing through matter, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science25, 10 (1913)

    work page 1913

  3. [3]

    T. W. Hentschel, A. Kononov, A. Olmstead, A. Cangi, A. D. Baczewski, and S. B. Hansen, Improving dynamic collision frequencies: Impacts on dynamic structure fac- tors and stopping powers in warm dense matter, Physics of Plasmas30(2023)

    work page 2023

  4. [4]

    A. J. White, L. A. Collins, K. Nichols, and S. X. Hu, Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense car- bon, Journal of Physics: Condensed Matter34, 174001 (2022)

    work page 2022

  5. [5]

    Schleife, Y

    A. Schleife, Y. Kanai, and A. A. Correa, Accurate atomistic first-principles calculations of electronic stopping, Phys. Rev. B91, 014306 (2015)

    work page 2015

  6. [6]

    Kononov, T

    A. Kononov, T. W. Hentschel, S. B. Hansen, and A. D. Baczewski, Nonlinear effects in light-ion stopping powers within real-time time-dependent density functional theory, 12 Physics of Plasmas33, 032704 (2026)

    work page 2026

  7. [7]

    N. D. Mermin, Lindhard dielectric function in the relaxation-time approximation, Phys. Rev. B1, 2362 (1970)

    1970

  8. [8]

    Faussurier, Finite-temperature static local-field- correction factor in warm-dense-matter stopping-power calculation, Physics of Plasmas32, 032704 (2025)

    G. Faussurier, Finite-temperature static local-field- correction factor in warm-dense-matter stopping-power calculation, Physics of Plasmas32, 032704 (2025)

    work page 2025

Show all 53 references
  1. [9]

    Z. H. Levine and S. G. Louie, New model dielectric function and exchange-correlation potential for semiconductors and insulators, Phys. Rev. B25, 6310 (1982)

    1982

  2. [10]

    A. H. Søndersted, M. Kuisma, J. K. Svaneborg, M. K. Svendsen, and K. S. Thygesen, Improved dielectric response of solids: Combining the bethe-salpeter equation with the random phase approximation, Phys. Rev. Lett.133, 026403 (2024)

    2024

  3. [11]

    Onida, L

    G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional versus many-body green’s-function ap- proaches, Rev. Mod. Phys.74, 601 (2002)

    2002

  4. [12]

    Salvat, Bethe stopping-power formula and its correc- tions, Phys

    F. Salvat, Bethe stopping-power formula and its correc- tions, Phys. Rev. A106, 032809 (2022)

    2022

  5. [13]

    J. F. Ziegler, M. Ziegler, and J. Biersack, Srim – the stop- ping and range of ions in matter (2010), Nuclear Instru- ments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms268, 1818 (2010), 19th International Conference on Ion Beam Analysis

    2010

  6. [14]

    This database is available from the iaea web site,https: //nds.iaea.org/stopping, accessed: March, 2026

    2026

  7. [15]

    K. Wittmaack, Misconceptions impairing the validity of the stopping power tables in the srim library and suggestions for doing better in the future, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms380, 57 (2016)

    2016

  8. [16]

    Montanari, P

    C. Montanari, P. Dimitriou, L. Marian, A. Mendez, J. Per- alta, and F. Bivort-Haiek, The iaea electronic stopping power database: Modernization, review, and analysis of the existing experimental data, Nuclear Instruments and Methods in Physics Research Section B: Beam Interact...

    2024

  9. [17]

    Malko, W

    S. Malko, W. Fox, L. Volpe, R. Fedosejevs, W. Cayzac, X. Vaisseau, V. Ospina-Bohorques, P. Grabowski, A. Cor- rea, C. Walsh, A. White, L. Collins, S. Hu, K. Nichols, S. Hansen, A. Baczewski, T. Hentschel, A. Kononov, M. Bailly-Grandvaux, K. Bhutwala, F. Beg, C. McGuffey, D. Ba...

    2022

  10. [18]

    J. A. Frenje, R. Florido, R. Mancini, T. Nagayama, P. Grabowski, H. Rinderknecht, H. Sio, A. Zylstra, M. Gatu Johnson, C. Li,et al., Experimental valida- tion of low-z ion-stopping formalisms around the bragg peak in high-energy-density plasmas, Physical review let- ters (2019)

    2019

  11. [19]

    Malko, W

    S. Malko, W. Cayzac, V. Ospina-Boh´ orquez, K. Bhutwala, M. Bailly-Grandvaux, C. McGuffey, R. Fedosejevs, X. Vais- seau, A. Tauschwitz, J. I. Api˜ naniz, D. De Luis Blanco, G. Gatti, M. Huault, J. A. P. Hernandez, S. X. Hu, A. J. White, L. A. Collins, K. Nichols, P. Neumayer, ...

    2022

  12. [20]

    Zylstra, J

    A. Zylstra, J. Frenje, P. Grabowski, C. Li, G. Collins, P. Fitzsimmons, S. Glenzer, F. Graziani, S. Hansen, S. Hu, et al., Measurement of charged-particle stopping in warm dense plasma, Physical review letters114, 215002 (2015)

    2015

  13. [21]

    L. J. Stanek, A. Kononov, S. B. Hansen, B. M. Haines, S. X. Hu, P. F. Knapp, M. S. Murillo, L. G. Stanton, H. D. Whitley, S. D. Baalrud, L. J. Babati, A. D. Baczewski, M. Bethkenhagen, A. Blanchet, I. Clay, Raymond C., K. R. Cochrane, L. A. Collins, A. Dumi, G. Faussurier, M. ...

    2024

  14. [22]

    The CBC model has also been extended to use AA input, however it was found to typically overestimate stopping [4]

    which uses a simple Bethe-like stopping term derived from Hartree-Fock bound states. The CBC model has also been extended to use AA input, however it was found to typically overestimate stopping [4]. Other models for bound stopping based on the AA use the known free electron l...

  15. [23]

    Faussurier, C

    G. Faussurier, C. Blancard, P. Coss´ e, and P. Renaudin, Equation of state, transport coefficients, and stopping power of dense plasmas from the average-atom model self- consistent approach for astrophysical and laboratory plas- mas, Physics of Plasmas17(2010)

    2010

  16. [24]

    M. D. Barriga-Carrasco and D. Casas, Electronic stopping of protons in xenon plasmas due to free and bound elec- trons, Laser and Particle Beams31, 105–111 (2013)

    2013

  17. [25]

    T. A. Mehlhorn, M. F. Gu, and I. Golovkin, An enhanced rpa-lda model for ion stopping power from cold matter to high-energy density plasmas: A unified, open-source frame- work (2026), arXiv:2606.30978 [physics.plasm-ph]

    2026 arXiv

  18. [26]

    P. Wang, T. Mehlhorn, and J. MacFarlane, A unified self- consistent model for calculating ion stopping power in icf plasma, Physics of Plasmas5, 2977 (1998)

    1998

  19. [27]

    Kremp, M

    D. Kremp, M. Schlanges, and K. Wolf-Dietrich,Quantum Statistics of Nonideal Plasmas, 2005th ed., Springer Series on Atomic, Optical, and Plasma Physics (Springer, Berlin, Germany, 2004)

    2004

  20. [28]

    M. D. Barriga-Carrasco, F. Chac´ on-Rubio, and C. C. Mon- tanari, Stopping power of plasma free and bound electrons using dielectric formalism, The European Physical Journal Plus137, 375 (2022)

    2022

  21. [29]

    Johnson, J

    W. Johnson, J. Nilsen, and K. Cheng, Thomson scatter- ing in the average-atom approximation, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics86, 036410 (2012)

    2012

  22. [30]

    N. M. Gill and C. E. Starrett, Tartarus: A relativistic green’s function quantum average atom code, High Energy Density Physics24, 33 (2017)

    2017

  23. [31]

    Blenski and K

    T. Blenski and K. Ishikawa, Pressure ionization in the spherical ion-cell model of dense plasmas and a pressure formula in the relativistic pauli approximation, Phys. Rev. E51, 4869 (1995)

    1995

  24. [32]

    B le´ nski and B

    T. B le´ nski and B. Cichocki, Linear response of partially ionized, dense plasmas, Laser and Particle Beams10, 299 (1992)

    1992

  25. [33]

    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 Physics18, 7 (2016)

    2016

  26. [34]

    G. B. Arfken, H. J. Weber, and F. E. Harris, Mathemat- ical preliminaries, inMathematical Methods for Physicists (Elsevier, 2013) pp. 1–82

    2013

  27. [35]

    G. D. Mahan,Many-particle physics, Physics of Solids and Liquids (Springer, New York, NY, 2010)

    2010

  28. [36]

    sum rule violations since the states are mutually orthogo- nal only when integrated over all space

    for a 3e pseudopotential (pink circles) and an 11e pseudopotential (turquoise triangles),b)iron at ambient density,ρ= 7.87 g/cm3 andT= 0.026 eV,c)neon gas atρ= 0.125 g/cm 3 andT= 0.026 eV,d)tungsten at ambient conditions,T= 0.026 eV and ρ= 19.3 g/cm 3. sum rule violations sinc...

    2022

  29. [37]

    Johnson, Low-frequency conductivity in the average- atom approximation, High Energy Density Physics5, 61 (2009)

    W. Johnson, Low-frequency conductivity in the average- atom approximation, High Energy Density Physics5, 61 (2009)

    2009

  30. [38]

    Kononov, T

    A. Kononov, T. W. Hentschel, S. B. Hansen, and A. D. Baczewski, Trajectory sampling and finite-size effects in first-principles stopping power calculations, Npj Comput. 13 Mater.9(2023)

    2023

  31. [39]

    Gericke, M

    D. Gericke, M. Schlanges, and W. Kraeft, Stopping power of a quantum plasma—t-matrix approximation and dynam- ical screening, Physics Letters A222, 241 (1996)

    1996

  32. [40]

    L. J. Babati, S. Rightley, N. R. Shaffer, and S. D. Baalrud, Collisional stopping power of ions in warm dense matter, Phys. Rev. E113, 015201 (2026)

    2026

  33. [41]

    Kononov, T

    A. Kononov, T. W. Hentschel, S. B. Hansen, and A. D. Baczewski, Nonlinear effects in light-ion stopping powers within real-time time-dependent density functional theory (2025), arXiv:2511.00759 [physics.plasm-ph]

    2025

  34. [42]

    Kononov, T

    A. Kononov, T. W. Hentschel, S. B. Hansen, and A. D. Baczewski, Core contributions to stopping powers in warm dense matter (2023)

    2023

  35. [43]

    D. S. Montgomery, W. S. Daughton, B. J. Albright, A. N. Simakov, D. C. Wilson, E. S. Dodd, R. C. Kirkpatrick, R. G. Watt, M. A. Gunderson, E. N. Loomis, E. C. Mer- ritt, T. Cardenas, P. Amendt, J. L. Milovich, H. F. Robey, R. E. Tipton, and M. D. Rosen, Design considerations f...

    2018

  36. [44]

    Kramida, Yu

    A. Kramida, Yu. Ralchenko, J. Reader, and and NIST ASD Team, NIST Atomic Spectra Database (ver. 5.12), [On- line]. Available:https://physics.nist.gov/asd[2026, April 17]. National Institute of Standards and Technology, Gaithersburg, MD. (2024)

    2026

  37. [45]

    Hayes, J

    A. Hayes, J. D. Martin, G. Jungman, D. Montgomery, J. Colgan, C. J. Fontes, G. Rusev, H. Geppert-Kleinrath, J. B. Wilhelmy, E. Loomis,et al., Reaction-in-flight neu- trons as a diagnostic for hydrodynamical mixing in double shell inertial confinement fusion capsules, Physics o...

    2025

  38. [46]

    G. B. Zimmerman, Recent developments in monte carlo techniques (Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States), 1990)

    1990

  39. [47]

    C. C. Montanari, J. E. Miraglia, and N. R. Arista, Dynam- ics of solid inner-shell electrons in collisions with bare and dressed swift ions, Phys. Rev. A66, 042902 (2002)

    2002

  40. [48]

    L. S. Brown, D. L. Preston, and R. L. Singleton Jr., Charged particle motion in a highly ionized plasma, Physics Reports410, 237 (2005)

    2005

  41. [49]

    Maynard and C

    G. Maynard and C. Deutsch, Born random phase approx- imation for ion stopping in an arbitrarily degenerate elec- tron fluid, Journal de Physique46, 1113 (1985)

    1985

  42. [50]

    C. C. Montanari and J. E. Miraglia, Low- and intermediate- energy stopping power of protons and antiprotons in solid targets, Phys. Rev. A96, 012707 (2017)

    2017

  43. [51]

    J. P. Peralta, M. Fiori, A. M. P. Mendez, and C. C. Monta- nari, Stopping-power calculations and the levine-mermin dielectric function for inner shells, Phys. Rev. A105, 062814 (2022)

    2022

  44. [52]

    N. M. Gill, C. J. Fontes, and C. E. Starrett, Time- dependent density functional theory applied to average atom opacity, Physical Review E103, 043206 (2021)

    2021

  45. [53]

    Dornheim, Z

    T. Dornheim, Z. A. Moldabekov, and P. Tolias, Analytical representation of the local field correction of the uniform electron gas within the effective static approximationana- lytical representation of the local field correction of the uni- form electron gas within the effecti...

    2021

Pith tools

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