pith. machine review for the scientific record. sign in

arxiv: 2604.25735 · v1 · submitted 2026-04-28 · ⚛️ physics.plasm-ph

Recognition: unknown

Model-free interpretation of X-ray Thomson scattering measurements

Thomas Gawne , Jan Vorberger , Zhandos Moldabekov , Hannah Bellenbaum , Tobias Dornheim
Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:26 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords X-ray Thomson scatteringimaginary time correlation functionmodel-free diagnosticswarm dense matterplasma temperatureRayleigh weightXFEL experiments
0
0 comments X

The pith

X-ray Thomson scattering spectra yield temperature and other properties directly when analyzed in imaginary time.

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

The paper reviews how to interpret X-ray Thomson scattering measurements using the imaginary-time correlation function rather than the conventional dynamic structure factor. This shift, based on Feynman's path integral view of quantum statistics, provides direct access to the electron temperature from the initial decay of the correlation function, the overall normalization of the signal, and the weight of the Rayleigh peak without relying on any specific model for the electronic response. Traditional forward modeling requires choosing a theoretical description for the plasma or material and fitting unknown parameters like density and ionization, which can introduce bias especially in warm dense matter where models are uncertain. By avoiding this step, the method promises more reliable diagnostics for extreme conditions probed at x-ray free electron lasers.

Core claim

Transforming the measured XRTS intensity into the imaginary-time domain produces the ITCF F_ee(q, τ), from which the temperature follows from the short-time slope, the normalization is fixed by the value at τ = 0, and the Rayleigh weight is obtained from the long imaginary-time limit, all without computing or assuming any microscopic model for S_ee(q, ω).

What carries the argument

The imaginary-time correlation function F_ee(q, τ) of the electron density fluctuations, which is obtained by a Laplace transform of the dynamic structure factor and encodes thermodynamic information through exact relations from statistical mechanics.

If this is right

  • The electron temperature is obtained directly from the slope of log F_ee(q, τ) near τ = 0 without any fitting.
  • The measured scattering signal can be normalized absolutely using the τ = 0 value of the ITCF.
  • The Rayleigh weight, which relates to the ion structure factor, becomes accessible without additional model assumptions.
  • High-resolution, high-repetition-rate XFEL data can be analyzed with reduced reliance on theoretical models for the electrons.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Independent temperature measurements from other diagnostics could be cross-validated using this approach to test consistency across methods.
  • The framework might be extended to extract additional quantities like the static structure factor or compressibility if deconvolution challenges are overcome.
  • Application to astrophysical or inertial confinement fusion plasmas could reduce uncertainties in inferred conditions by minimizing model dependence.

Load-bearing premise

The source-and-instrument function can be deconvolved from the raw data sufficiently well to recover an accurate imaginary-time correlation function without introducing new dependencies on models.

What would settle it

Perform XRTS on a benchmark system with independently known temperature, such as a laser-heated sample with calibrated thermometer, apply the ITCF analysis after deconvolution, and check if the extracted temperature matches the known value within experimental error.

read the original abstract

X-ray Thomson scattering (XRTS) has emerged as a widely used diagnostics for extreme states of matter in a great variety of situations, and over a broad range of parameters. The standard approach for the interpretation of XRTS measurements is given by the forward modeling approach, where the electronic dynamic structure factor $S_{ee}(\mathbf{q},\omega)$ is computed from a suitable theoretical model, convolved with the combined source-and-instrument function, and then matched with the experimental observation, treating a-priori unknown parameters such as the mass density, temperature and ionization state as free fit parameters. Very recently, it has been suggested that this inherent model dependence can be avoided by analyzing XRTS spectra in terms of the imaginary-time correlation function (ITCF) $F_{ee}(\mathbf{q},\tau)$ [Dornheim \textit{et al.}, \textit{Nature Commun.}~\textbf{13}, 7911 (2022)], giving one model-free access to the temperature, normalization, Rayleigh weight, as well as a number of other properties. Here, we present a comprehensive review article on these developments, including accessible discussions of the method's theoretical background in terms of Feynman's imaginary-time path integral picture of statistical mechanics as well as its remaining limitations, in particular with respect to the source-and-instrument function of the experimental set-up. In addition, we discuss new chances for the further development of this framework by utilizing emerging capabilities for high-repetition XRTS experiments with meV resolution over spectral ranges of tens of eV at state-of-the-art x-ray free electron laser (XFEL) facilities such as the European XFEL in Germany.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. This manuscript is a review article on a model-free approach to analyzing X-ray Thomson scattering (XRTS) spectra by transforming them into the imaginary-time correlation function (ITCF) F_ee(q,τ). It contrasts this with traditional forward modeling that fits parameters such as density, temperature, and ionization state, and claims the ITCF method provides direct access to temperature, normalization, Rayleigh weight, and other properties. The review covers the theoretical background via Feynman's imaginary-time path integral formulation of statistical mechanics, explicitly discusses remaining limitations (particularly the combined source-and-instrument function), and outlines opportunities from high-repetition-rate, meV-resolution XRTS at XFEL facilities.

Significance. If the ITCF framework can be applied robustly, it would meaningfully reduce model dependence in XRTS diagnostics for warm dense matter and other extreme states, allowing more direct extraction of key quantities. The review's accessible treatment of the path-integral background and its balanced discussion of limitations plus future experimental directions constitute a useful service to the community.

major comments (1)
  1. [Abstract] Abstract: the statement that the ITCF approach gives 'model-free access' to temperature, normalization, and Rayleigh weight is presented as the central advantage, yet the same paragraph immediately flags the source-and-instrument function as a remaining limitation. The review must clarify, with a concrete procedure or counter-example, whether the required deconvolution (or equivalent imaginary-time operation) can be performed without reintroducing regularization, assumed kernel forms, or other model dependence; otherwise the model-free claim is conditional rather than unconditional.
minor comments (1)
  1. The citation to Dornheim et al., Nature Commun. 13, 7911 (2022) should include the full title and DOI for completeness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the manuscript's significance, and recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the ITCF approach gives 'model-free access' to temperature, normalization, and Rayleigh weight is presented as the central advantage, yet the same paragraph immediately flags the source-and-instrument function as a remaining limitation. The review must clarify, with a concrete procedure or counter-example, whether the required deconvolution (or equivalent imaginary-time operation) can be performed without reintroducing regularization, assumed kernel forms, or other model dependence; otherwise the model-free claim is conditional rather than unconditional.

    Authors: We agree that the abstract would benefit from greater precision on this distinction. The model-free character of the ITCF method refers specifically to the fact that temperature (from the slope of ln F(q,τ) near τ = β/2), normalization (from F(q,0)), and Rayleigh weight (from F(q,β)) can be obtained directly from the imaginary-time correlation function without assuming any particular functional form or theoretical model for the dynamic structure factor S_ee(q,ω). The source-and-instrument function is handled separately: because the measured spectrum is the convolution of the true S_ee(q,ω) with the known combined source-and-instrument response, the corresponding operation in imaginary time is a simple multiplication of F(q,τ) by the Laplace transform of that response. Division by this known factor recovers the instrument-corrected ITCF without regularization, without assuming a kernel shape for S_ee, and without any model for the underlying physics. This procedure is already outlined in the main text (Section on experimental limitations and the path-integral derivation). We will revise the abstract to state explicitly that the model-free extraction applies once the (known) instrument response has been divided out in imaginary time, thereby removing any ambiguity about the scope of the claim. revision: yes

Circularity Check

0 steps flagged

No circularity: ITCF review grounds claims in external path-integral formalism

full rationale

The paper is a review that attributes the model-free ITCF access to a 2022 citation while explicitly discussing limitations such as instrument deconvolution. Its derivation chain rests on Feynman's imaginary-time path integral picture of statistical mechanics, which is an independent external framework rather than a self-definition, fitted input renamed as prediction, or load-bearing self-citation that reduces the result to the paper's own inputs. No equations or steps exhibit the required reduction by construction; the central claims remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of transforming XRTS spectra into the ITCF via the imaginary-time path integral formalism and on the assumption that instrument effects can be handled without reintroducing model dependence.

axioms (1)
  • standard math Feynman's imaginary-time path integral picture of statistical mechanics underlies the ITCF definition
    Invoked in the abstract as the theoretical background for model-free access to temperature and other quantities.

pith-pipeline@v0.9.0 · 5614 in / 1162 out tokens · 44303 ms · 2026-05-07T14:26:04.510935+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

296 extracted references · 141 canonical work pages · 4 internal anchors

  1. [1]

    Available from: https://arxiv.org/abs/2505

    Vorberger J, Graziani F, Riley D, Baczewski AD, Baraffe I, Bethkenhagen M, et al.: Roadmap for warm dense matter physics. Available from: https://arxiv.org/abs/2505. 02494

  2. [2]

    Extreme states of matter on Earth and in space

    Fortov VE. Extreme states of matter on Earth and in space. Phys-Usp. 2009;52:615–

    2009

  3. [3]

    200906h.0653

    https://doi.org/10.3367/UFNe.0179. 200906h.0653

    work page doi:10.3367/ufne.0179

  4. [4]

    High-Energy-Density Physics: Foundation of Inertial Fusion and Exper- imental Astrophysics

    Drake RP. High-Energy-Density Physics: Foundation of Inertial Fusion and Exper- imental Astrophysics. Graduate Texts in Physics. Springer International Publishing; 2018

    2018

  5. [5]

    Frontiers and Chal- lenges in Warm Dense Matter

    Graziani F, Desjarlais MP, Redmer R, Trickey SB, editors. Frontiers and Chal- lenges in Warm Dense Matter. International Publishing: Springer; 2014

    2014

  6. [6]

    Progress in warm dense matter study with applications to planetology

    Benuzzi-Mounaix A, Mazevet S, Ravasio A, Vinci T, Denoeud A, Koenig M, et al. Progress in warm dense matter study with applications to planetology. Phys Scripta. 2014 may;T161:014060. https://doi.org/10. 1088/0031-8949/2014/t161/014060

    2014

  7. [7]

    Evi- dence of hydrogen-helium immiscibility at Jupiter-interior conditions

    Brygoo S, Loubeyre P, Millot M, Rygg JR, Celliers PM, Eggert JH, et al. Evi- dence of hydrogen-helium immiscibility at Jupiter-interior conditions. Nature. 2021 May;593(7860):517–521. https://doi.org/ 10.1038/s41586-021-03516-0

    work page doi:10.1038/s41586-021-03516-0 2021

  8. [8]

    Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their impli- cations for the interior of brown dwarfs

    Becker A, Lorenzen W, Fortney JJ, Nettel- mann N, Sch¨ ottler M, Redmer R. Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their impli- cations for the interior of brown dwarfs. Astrophys J Suppl Ser. 2014;215:21. https: //doi.org/10.1088/0067-0049/215/2/21

    work page doi:10.1088/0067-0049/215/2/21 2014

  9. [9]

    The role of the molecular-metallic transition of hydrogen in the evolution of Jupiter, Saturn, and brown dwarfs

    Saumon D, Hubbard WB, Chabrier G, van Horn HM. The role of the molecular-metallic transition of hydrogen in the evolution of Jupiter, Saturn, and brown dwarfs. Astro- phys J. 1992;391:827–831

    1992

  10. [10]

    A measurement of the equation of state of carbon envelopes of white dwarfs

    Kritcher AL, Swift DC, D¨ oppner T, Bach- mann B, Benedict LX, Collins GW, et al. A measurement of the equation of state of carbon envelopes of white dwarfs. Nature. 2020 Aug;584(7819):51–54. https://doi.org/ 10.1038/s41586-020-2535-y

    work page doi:10.1038/s41586-020-2535-y 2020

  11. [11]

    Cur- rent challenges in the physics of white dwarf stars

    Saumon D, Blouin S, Tremblay PE. Cur- rent challenges in the physics of white dwarf stars. Physics Reports. 2022;988:1–

    2022

  12. [12]

    https://doi.org/10

    Current Challenges in the Physics of White Dwarf Stars. https://doi.org/10. 1016/j.physrep.2022.09.001

    2022

  13. [13]

    First-principles equation of state database for warm dense matter computation

    Militzer B, Gonz´ alez-Cataldo F, Zhang S, Driver KP, Soubiran Fmc. First-principles equation of state database for warm dense matter computation. Phys Rev E. 2021 Jan;103:013203. https://doi.org/10.1103/ PhysRevE.103.013203

    2021

  14. [14]

    The Juno Mission

    Bolton SJ, Lunine J, Stevenson D, Conner- ney JEP, Levin S, Owen TC, et al. The Juno Mission. Space Science Reviews. 2017 Nov;213(1):5–37. https://doi.org/10.1007/ s11214-017-0429-6

    2017

  15. [15]

    Nanosecond formation of diamond and lonsdaleite by shock compression of graphite

    Kraus D, Ravasio A, Gauthier M, Gericke DO, Vorberger J, Frydrych S, et al. Nanosecond formation of diamond and lonsdaleite by shock compression of graphite. Nature Com- munications. 2016 Mar;7(1):10970. https://doi.org/10.1038/ncomms10970

    work page doi:10.1038/ncomms10970 2016

  16. [16]

    Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions

    Kraus D, Vorberger J, Pak A, Hartley NJ, Fletcher LB, Frydrych S, et al. Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions. Nature Astronomy. 2017 Sep;1(9):606–611. https: //doi.org/10.1038/s41550-017-0219-9

    work page doi:10.1038/s41550-017-0219-9 2017

  17. [17]

    Diamond precipitation dynam- ics from hydrocarbons at icy planet inte- rior conditions

    Frost M, McWilliams RS, Bykova E, Bykov M, Husband RJ, Andriambariarijaona LM, et al. Diamond precipitation dynam- ics from hydrocarbons at icy planet inte- rior conditions. Nature Astronomy. 2024 Feb;8(2):174–181. https://doi.org/10.1038/ s41550-023-02147-x

    2024

  18. [18]

    Ab initio dielectric response function of diamond and other relevant high pressure phases of car- bon

    Ramakrishna K, Vorberger J. Ab initio dielectric response function of diamond and other relevant high pressure phases of car- bon. Journal of Physics: Condensed Matter. 2019 nov;32(9):095401. https://doi.org/10. 1088/1361-648X/ab558e

    2019

  19. [19]

    Extreme Metastability of Dia- mond and its Transformation to the BC8 Post-Diamond Phase of Carbon

    Nguyen-Cong K, Willman JT, Gonzalez JM, Williams AS, Belonoshko AB, Moore SG, et al. Extreme Metastability of Dia- mond and its Transformation to the BC8 Post-Diamond Phase of Carbon. The Jour- nal of Physical Chemistry Letters. 2024 Feb;15(4):1152–1160. https://doi.org/10. 1021/acs.jpclett.3c03044

    2024

  20. [20]

    Liquid– 52 liquid phase transition in hydrogen by coupled electron– ion monte carlo simulations,

    Pierleoni C, Morales MA, Rillo G, Holz- mann M, Ceperley DM. Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations. Pro- ceedings of the National Academy of Sci- ences. 2016;113(18):4953–4957. https://doi. org/10.1073/pnas.1603853113

    work page doi:10.1073/pnas.1603853113 2016

  21. [21]

    Observation of the Wigner-Huntington transition to metallic hydrogen

    Dias RP, Silvera IF. Observation of the Wigner-Huntington transition to metallic hydrogen. Science. 2017;355(6326):715–718. https://doi.org/10.1126/science.aal1579

    work page doi:10.1126/science.aal1579 2017

  22. [22]

    On the liquid–liquid phase transi- tion of dense hydrogen

    Karasiev VV, Hinz J, Hu SX, Trickey SB. On the liquid–liquid phase transi- tion of dense hydrogen. Nature. 2021 Dec;600(7889):E12–E14. https://doi.org/ 10.1038/s41586-021-04078-x

    work page doi:10.1038/s41586-021-04078-x 2021

  23. [23]

    Available from: https://arxiv.org/abs/2511.11061

    Vorberger J, Smith GJ, Benschoten WZV, Petras HR, Moldabekov Z, Dornheim T, et al.: Van-der-Waals exchange-correlation functionals and their high pressure and warm dense matter applications. Available from: https://arxiv.org/abs/2511.11061

    work page arXiv

  24. [24]

    Toward first principles-based simulations of dense hydrogen

    Bonitz M, Vorberger J, Bethkenhagen M, B¨ ohme MP, Ceperley DM, Filinov A, et al. Toward first principles-based simulations of dense hydrogen. Physics of Plasmas. 2024 11;31(11):110501. https://doi.org/10.1063/ 5.0219405

    2024

  25. [25]

    Lawson Crite- rion for Ignition Exceeded in an Inertial Fusion Experiment

    Abu-Shawareb H, et al. Lawson Crite- rion for Ignition Exceeded in an Inertial Fusion Experiment. Phys Rev Lett. 2022 Aug;129:075001. https://doi.org/10.1103/ PhysRevLett.129.075001

    2022

  26. [26]

    Achievement of Target Gain Larger than Unity in an Iner- tial Fusion Experiment

    Abu-Shawareb H, et al. Achievement of Target Gain Larger than Unity in an Iner- tial Fusion Experiment. Phys Rev Lett. 2024 Feb;132:065102. https://doi.org/10. 1103/PhysRevLett.132.065102

    2024

  27. [27]

    Demon- stration of a hydrodynamically equiva- lent burning plasma in direct-drive iner- tial confinement fusion

    Gopalaswamy V, Williams CA, Betti R, Patel D, Knauer JP, Lees A, et al. Demon- stration of a hydrodynamically equiva- lent burning plasma in direct-drive iner- tial confinement fusion. Nature Physics. 2024 May;20(5):751–757. https://doi.org/ 10.1038/s41567-023-02361-4

    work page doi:10.1038/s41567-023-02361-4 2024

  28. [28]

    Physics principles of inertial confinement fusion and U.S

    Hurricane OA, Patel PK, Betti R, Froula DH, Regan SP, Slutz SA, et al. Physics principles of inertial confinement fusion and U.S. program overview. Rev Mod Phys. 2023 Jun;95:025005. https://doi.org/10. 1103/RevModPhys.95.025005

    2023

  29. [29]

    Burning plasma achieved in inertial fusion

    Zylstra AB, Hurricane OA, Callahan DA, Kritcher AL, Ralph JE, Robey HF, et al. Burning plasma achieved in inertial fusion. Nature. 2022 Jan;601(7894):542–548. https: //doi.org/10.1038/s41586-021-04281-w

    work page doi:10.1038/s41586-021-04281-w 2022

  30. [30]

    First-principles equation-of-state table of deuterium for inertial confinement fusion applications

    Hu SX, Militzer B, Goncharov VN, Skup- sky S. First-principles equation-of-state table of deuterium for inertial confinement fusion applications. Phys Rev B. 2011 Dec;84:224109. https://doi.org/10.1103/ PhysRevB.84.224109

    2011

  31. [31]

    Experimental methods for warm dense matter research

    Falk K. Experimental methods for warm dense matter research. High Power Laser Sci Eng. 2018;6:e59. https://doi.org/10.1017/ hpl.2018.53

    2018

  32. [32]

    Materials under extreme conditions using large X-ray facilities

    Pascarelli S, McMahon M, P´ epin C, Mathon O, Smith RF, Mao WL, et al. Materials under extreme conditions using large X-ray facilities. Nature Reviews Methods Primers. 2023 Nov;3(1):82. https://doi.org/10.1038/ s43586-023-00264-5

    2023

  33. [33]

    Free-Electron X-Ray Laser Measurements of Collisional-Damped Plasmons in Isochori- cally Heated Warm Dense Matter

    Sperling P, Gamboa EJ, Lee HJ, Chung HK, Galtier E, Omarbakiyeva Y, et al. Free-Electron X-Ray Laser Measurements of Collisional-Damped Plasmons in Isochori- cally Heated Warm Dense Matter. Phys Rev Lett. 2015 Sep;115:115001. https://doi.org/ 10.1103/PhysRevLett.115.115001

    work page doi:10.1103/physrevlett.115.115001 2015

  34. [34]

    Char- acterizing the ionization potential depres- sion in dense carbon plasmas with high- precision spectrally resolved x-ray scatter- ing

    Kraus D, Bachmann B, Barbrel B, Falcone RW, Fletcher LB, Frydrych S, et al. Char- acterizing the ionization potential depres- sion in dense carbon plasmas with high- precision spectrally resolved x-ray scatter- ing. Plasma Physics and Controlled Fusion. 2018 nov;61(1):014015. https://doi.org/10. 1088/1361-6587/aadd6c

    2018

  35. [35]

    Obser- vations of Plasmons in Warm Dense Matter

    Glenzer SH, Landen OL, Neumayer P, Lee RW, Widmann K, Pollaine SW, et al. Obser- vations of Plasmons in Warm Dense Matter. Phys Rev Lett. 2007 Feb;98:065002. https: //doi.org/10.1103/PhysRevLett.98.065002

    work page doi:10.1103/physrevlett.98.065002 2007

  36. [36]

    Temperature measurement through detailed balance in x-ray Thomson scattering

    D¨ oppner T, Landen OL, Lee HJ, Neumayer P, Regan SP, Glenzer SH. Temperature measurement through detailed balance in x-ray Thomson scattering. High Energy Density Physics. 2009;5(3):182–186. https: //doi.org/10.1016/j.hedp.2009.05.012

    work page doi:10.1016/j.hedp.2009.05.012 2009

  37. [37]

    A Momentum-Resolved X-ray Thomson Scattering Benchmark of Electronic-Response Models in Warm Dense Aluminium

    Bespalov DS, Zastrau U, Moldabekov ZA, Gawne T, Dornheim T, Meshhal M, et al.: Experimental Evidence for the Breakdown of Uniform-Electron-Gas Models in Warm Dense Aluminium. Available from: https: //arxiv.org/abs/2509.10107

    work page internal anchor Pith review arXiv

  38. [38]

    Measurements of the momentum- dependence of plasmonic excitations in mat- ter around 1 Mbar using an X-ray free electron laser

    Preston TR, Appel K, Brambrink E, Chen B, Fletcher LB, Fortmann-Grote C, et al. Measurements of the momentum- dependence of plasmonic excitations in mat- ter around 1 Mbar using an X-ray free electron laser. Applied Physics Letters. 2019 01;114(1):014101. https://doi.org/10.1063/ 1.5070140

    2019

  39. [39]

    Ultra- bright X-ray laser scattering for dynamic warm dense matter physics

    Fletcher LB, Lee HJ, D¨ oppner T, Galtier E, Nagler B, Heimann P, et al. Ultra- bright X-ray laser scattering for dynamic warm dense matter physics. Nature Pho- tonics. 2015;9:274–279. https://doi.org/10. 1038/nphoton.2015.41

    2015

  40. [40]

    Observing the onset of pressure-driven K-shell delocal- ization

    D¨ oppner T, Bethkenhagen M, Kraus D, Neumayer P, Chapman DA, Bach- mann B, et al. Observing the onset of pressure-driven K-shell delocal- ization. Nature. 2023 May;https: //doi.org/10.1038/s41586-023-05996-8

    work page doi:10.1038/s41586-023-05996-8 2023

  41. [41]

    X- ray scattering measurements on imploding CH spheres at the National Ignition Facil- ity

    Kraus D, Chapman DA, Kritcher AL, Bag- gott RA, Bachmann B, Collins GW, et al. X- ray scattering measurements on imploding CH spheres at the National Ignition Facil- ity. Phys Rev E. 2016 Jul;94:011202. https: //doi.org/10.1103/PhysRevE.94.011202

    work page doi:10.1103/physreve.94.011202 2016

  42. [42]

    Observations of Continuum Depression in Warm Dense Matter with X-Ray Thom- son Scattering

    Fletcher LB, Kritcher AL, Pak A, Ma T, D¨ oppner T, Fortmann C, et al. Observations of Continuum Depression in Warm Dense Matter with X-Ray Thom- son Scattering. Phys Rev Lett. 2014 Apr;112:145004. https://doi.org/10.1103/ PhysRevLett.112.145004

    2014

  43. [43]

    In-Flight Measurements of Capsule Shell Adiabats in Laser-Driven Implosions

    Kritcher AL, D¨ oppner T, Fortmann C, Ma T, Landen OL, Wallace R, et al. In-Flight Measurements of Capsule Shell Adiabats in Laser-Driven Implosions. Phys Rev Lett. 2011 Jul;107:015002. https://doi.org/10. 1103/PhysRevLett.107.015002

    2011

  44. [44]

    Euro- pean Facility for Antiproton and Ion Research (FAIR): the new international center for fundamental physics and its research program

    Fortov VE, Sharkov BY, St¨ oker H. Euro- pean Facility for Antiproton and Ion Research (FAIR): the new international center for fundamental physics and its research program. Physics-Uspekhi. 2012 jun;55(6):582. https://doi.org/10.3367/ UFNe.0182.201206c.0621

    work page arXiv 2012

  45. [45]

    Temperature and structure measurements of heavy-ion-heated diamond using in situ X- ray diagnostics

    L¨ utgert J, Hesselbach P, Sch¨ orner M, Bag- noud V, Belikov R, Drechsel P, et al. Temperature and structure measurements of heavy-ion-heated diamond using in situ X- ray diagnostics. Matter and Radiation at Extremes. 2024 06;9(4):047802. https://doi. org/10.1063/5.0203005

    work page doi:10.1063/5.0203005 2024

  46. [46]

    Measurement of temperature and density using non-collective X-ray Thomson scat- tering in pulsed power produced warm dense plasmas

    Valenzuela JC, Krauland C, Mariscal D, Krasheninnikov I, Niemann C, Ma T, et al. Measurement of temperature and density using non-collective X-ray Thomson scat- tering in pulsed power produced warm dense plasmas. Scientific Reports. 2018 May;8(1):8432. https://doi.org/10.1038/ s41598-018-26608-w

    2018

  47. [48]

    Dense matter characterization by X-ray Thomson scattering

    Landen OL, Glenzer SH, Edwards MJ, Lee RW, Collins GW, Cauble RC, et al. Dense matter characterization by X-ray Thomson scattering. Journal of Quantita- tive Spectroscopy and Radiative Transfer. 2001;71(2):465–478. Radiative Properties of Hot Dense Matter. https://doi.org/https: //doi.org/10.1016/S0022-4073(01)00090-5

    work page doi:10.1016/s0022-4073(01)00090-5 2001

  48. [49]

    X-ray Thomson scattering in high energy density plasmas

    Glenzer SH, Redmer R. X-ray Thomson scattering in high energy density plasmas. Rev Mod Phys. 2009;81:1625. https://doi. org/10.1103/RevModPhys.81.1625

    work page doi:10.1103/revmodphys.81.1625 2009

  49. [50]

    Equation of State Measurements of Warm Dense Carbon Using Laser-Driven Shock and Release Technique

    Falk K, Gamboa EJ, Kagan G, Mont- gomery DS, Srinivasan B, Tzeferacos P, et al. Equation of State Measurements of Warm Dense Carbon Using Laser-Driven Shock and Release Technique. Phys Rev Lett. 2014 Apr;112:155003. https://doi.org/ 10.1103/PhysRevLett.112.155003

    work page doi:10.1103/physrevlett.112.155003 2014

  50. [51]

    Theoretical model of x-ray scat- tering as a dense matter probe

    Gregori G, Glenzer SH, Rozmus W, Lee RW, Landen OL. Theoretical model of x-ray scat- tering as a dense matter probe. Phys Rev E. 2003 Feb;67:026412. https://doi.org/10. 1103/PhysRevE.67.026412

    2003

  51. [52]

    Evidence of free-bound transitions in warm dense matter and their impact on equation-of-state measure- ments,

    B¨ ohme MP, Fletcher LB, D¨ oppner T, Kraus D, Baczewski AD, Preston TR, et al.: Evi- dence of free-bound transitions in warm dense matter and their impact on equation- of-state measurements. Available from: https://arxiv.org/abs/2306.17653

    work page arXiv

  52. [53]

    Inverse prob- lem instabilities in large-scale modeling of matter in extreme conditions

    Kasim MF, Galligan TP, Topp-Mugglestone J, Gregori G, Vinko SM. Inverse prob- lem instabilities in large-scale modeling of matter in extreme conditions. Physics of Plasmas. 2019 11;26(11):112706. https:// doi.org/10.1063/1.5125979

    work page doi:10.1063/1.5125979 2019

  53. [54]

    Demonstration of X-ray Thomson scattering as diagnostics for miscibility in warm dense matter

    Frydrych S, Vorberger J, Hartley NJ, Schus- ter AK, Ramakrishna K, Saunders AM, et al. Demonstration of X-ray Thomson scattering as diagnostics for miscibility in warm dense matter. Nature Communica- tions. 2020 May;11(1):2620. https://doi. org/10.1038/s41467-020-16426-y

    work page doi:10.1038/s41467-020-16426-y 2020

  54. [55]

    Plasmons in Strongly Coupled Shock- Compressed Matter

    Neumayer P, Fortmann C, D¨ oppner T, Davis P, Falcone RW, Kritcher AL, et al. Plasmons in Strongly Coupled Shock- Compressed Matter. Phys Rev Lett. 2010 Aug;105:075003. https://doi.org/10.1103/ PhysRevLett.105.075003

    2010

  55. [56]

    Electri- cal conductivity calculations in isochorically heated warm dense aluminum

    Sperling P, Rosmej S, Bredow R, Fletcher LB, Galtier E, Gamboa EJ, et al. Electri- cal conductivity calculations in isochorically heated warm dense aluminum. Journal of Physics B: Atomic, Molecular and Optical Physics. 2017 jun;50(13):134002. https:// doi.org/10.1088/1361-6455/aa753d

    work page doi:10.1088/1361-6455/aa753d 2017

  56. [57]

    Plasma screening in mid-charged ions observed by K-shell line emission

    ˇSm´ ıd M, Humphries OS, Baehtz C, Bouf- fetier V, Brambrink E, Burian T, et al. Plasma screening in mid-charged ions observed by K-shell line emission. Scien- tific Reports. 2026 Feb;16(1):5873. https: //doi.org/10.1038/s41598-026-39041-1

    work page doi:10.1038/s41598-026-39041-1 2026

  57. [58]

    Ultrahigh resolution x-ray Thomson scatter- ing measurements at the European X-ray Free Electron Laser

    Gawne T, Moldabekov ZA, Humphries OS, Appel K, Baehtz C, Bouffetier V, et al. Ultrahigh resolution x-ray Thomson scatter- ing measurements at the European X-ray Free Electron Laser. Phys Rev B. 2024 Jun;109:L241112. https://doi.org/10.1103/ PhysRevB.109.L241112

    2024

  58. [59]

    Resolving ultrafast heating of dense cryogenic hydro- gen

    Zastrau U, Sperling P, Harmand M, Becker A, Bornath T, Bredow R, et al. Resolving ultrafast heating of dense cryogenic hydro- gen. Phys Rev Lett. 2014;112:105002

    2014

  59. [60]

    Prob- ing near-solid density plasmas using soft x-ray scattering

    Toleikis S, Bornath T, D¨ oppner T, D¨ usterer S, F¨ austlin RR, F¨ orster E, et al. Prob- ing near-solid density plasmas using soft x-ray scattering. Journal of Physics B: Atomic, Molecular and Optical Physics. 2010 sep;43(19):194017. https://doi.org/10. 1088/0953-4075/43/19/194017

    2010

  60. [61]

    Observation of Ultrafast Nonequi- librium Collective Dynamics in Warm Dense Hydrogen

    F¨ austlin RR, Bornath T, D¨ oppner T, D¨ usterer S, F¨ orster E, Fortmann C, et al. Observation of Ultrafast Nonequi- librium Collective Dynamics in Warm Dense Hydrogen. Phys Rev Lett. 2010 Mar;104:125002. https://doi.org/10.1103/ PhysRevLett.104.125002

    2010

  61. [62]

    Platform for laser-driven X-ray diagnostics of heavy-ion heated extreme states of mat- ter

    Hesselbach P, L¨ utgert J, Bagnoud V, Belikov R, Humphries O, Lindqvist B, et al. Platform for laser-driven X-ray diagnostics of heavy-ion heated extreme states of mat- ter. Matter and Radiation at Extremes. 2024 12;10(1):017803. https://doi.org/10. 1063/5.0233548

    2024

  62. [63]

    Generalized Kepler problems. I. Without magnetic charges

    Kraus D, Vorberger J, Helfrich J, Ger- icke DO, Bachmann B, Bagnoud V, et al. The complex ion structure of warm dense carbon measured by spectrally resolved x- ray scatteringa). Physics of Plasmas. 2015 05;22(5):056307. https://doi.org/10.1063/1. 4920943

    work page doi:10.1063/1 2015

  63. [64]

    Electron- Ion Temperature Relaxation in Warm Dense Hydrogen Observed With Picosec- ond Resolved X-Ray Scattering

    Fletcher LB, Vorberger J, Schumaker W, Ruyer C, Goede S, Galtier E, et al. Electron- Ion Temperature Relaxation in Warm Dense Hydrogen Observed With Picosec- ond Resolved X-Ray Scattering. Frontiers in Physics. 2022;Volume 10 - 2022. https: //doi.org/10.3389/fphy.2022.838524

    work page doi:10.3389/fphy.2022.838524 2022

  64. [66]

    The colliding planar shocks platform to study warm dense matter at the National Ignition Facility

    MacDonald MJ, Di Stefano CA, D¨ oppner T, Fletcher LB, Flippo KA, Kalantar D, et al. The colliding planar shocks platform to study warm dense matter at the National Ignition Facility. Physics of Plasmas. 2023 06;30(6). 062701. https://doi.org/10.1063/ 5.0146624

    2023

  65. [67]

    X- ray scattering from solid density plasmas

    Glenzer SH, Gregori G, Rogers FJ, Froula DH, Pollaine SW, Wallace RS, et al. X- ray scattering from solid density plasmas. Physics of Plasmas. 2003 06;10(6):2433–

    2003

  66. [68]

    https://doi.org/10.1063/1.1570420

    work page doi:10.1063/1.1570420

  67. [69]

    Multimessenger measurements of the static structure of shock-compressed liquid sili- con at 100 GPa

    Poole H, Ginnane MK, Millot M, Bellen- baum HM, Collins GW, Hu SX, et al. Multimessenger measurements of the static structure of shock-compressed liquid sili- con at 100 GPa. Phys Rev Res. 2024 May;6:023144. https://doi.org/10.1103/ PhysRevResearch.6.023144

    2024

  68. [70]

    Demon- stration of space-resolved x-ray Thom- son scattering capability for warm dense matter experiments on the Z acceler- ator

    Ao T, Harding EC, Bailey JE, Lemke RW, Desjarlais MP, Hansen SB, et al. Demon- stration of space-resolved x-ray Thom- son scattering capability for warm dense matter experiments on the Z acceler- ator. High Energy Density Physics. 2016;18:26–37. https://doi.org/https://doi. org/10.1016/j.hedp.2016.01.002

    work page doi:10.1016/j.hedp.2016.01.002 2016

  69. [71]

    Evolution of elastic x-ray scattering in laser-shocked warm dense lithium

    Kugland NL, Gregori G, Bandyopadhyay S, Brenner CM, Brown CRD, Constantin C, et al. Evolution of elastic x-ray scattering in laser-shocked warm dense lithium. Phys Rev E. 2009 Dec;80:066406. https://doi.org/10. 1103/PhysRevE.80.066406

    2009

  70. [72]

    Probing warm dense lithium by inelas- tic X-ray scattering

    Garc´ ıa Saiz E, Gregori G, Gericke DO, Vorberger J, Barbrel B, Clarke RJ, et al. Probing warm dense lithium by inelas- tic X-ray scattering. Nature Physics. 2008 Dec;4(12):940–944. https://doi.org/10. 1038/nphys1103

    2008

  71. [73]

    Calcu- lations and measurements of x-ray Thom- son scattering spectra in warm dense matter

    Gregori G, Glenzer SH, Lee RW, Hicks DG, Pasley J, Collins GW, et al. Calcu- lations and measurements of x-ray Thom- son scattering spectra in warm dense matter. AIP Conference Proceedings. 2002 12;645(1):359–368. https://doi.org/10. 1063/1.1525476

    2002

  72. [74]

    First-principles estima- tion of plasma jet properties from x-ray Thomson scattering spectrum in the double- cone ignition scheme

    Shi NY, Liang JH, Mo C, Wu D, Liu H, Dai Y, et al. First-principles estima- tion of plasma jet properties from x-ray Thomson scattering spectrum in the double- cone ignition scheme. Nuclear Fusion. 2025 sep;65(10):106038. https://doi.org/10. 1088/1741-4326/ae0804

    2025

  73. [75]

    Efficient energy transition from kinetic to internal energy in supersonic collision of high-density plasma jets from conical implosions

    Zhe Z, Xiao-Hui Y, Yi-Hang Z, Hao L, Ke F, Cheng-Long Z, et al. Efficient energy transition from kinetic to internal energy in supersonic collision of high-density plasma jets from conical implosions. Acta Phys- ica Sinica. 2022;71(15):155201–1–155201–8. https://doi.org/10.7498/aps.71.20220361

    work page doi:10.7498/aps.71.20220361 2022

  74. [76]

    Measurement of ionic structure in isochorically heated graphite from X-ray Thomson scattering

    Lv M, Hu Z, Hou Y, Wei M, Mo C, Zheng W, et al. Measurement of ionic structure in isochorically heated graphite from X-ray Thomson scattering. Physics of Plasmas. 2019 02;26(2):022702. https://doi.org/10. 1063/1.5054088

    2019

  75. [77]

    Overview of X-ray Thomson scattering measurements of extreme states of matter

    Dornheim T, Bellenbaum H, Gawne T, Vorberger J, Gericke DO.: Overview of X- ray Thomson scattering measurements of extreme states of matter. Available from: https://arxiv.org/abs/2604.23687

    work page internal anchor Pith review Pith/arXiv arXiv

  76. [78]

    Measuring stopping power in warm dense matter plasmas at OMEGA

    Lahmann B, Saunders AM, D¨ oppner T, Frenje JA, Glenzer SH, Gatu-Johnson M, et al. Measuring stopping power in warm dense matter plasmas at OMEGA. Plasma Physics and Controlled Fusion. 2023 jul;65(9):095002. https://doi.org/10.1088/ 1361-6587/ace4f2

    2023

  77. [79]

    Measurement of turbulent velocity and bounds for thermal diffusivity in laser shock compressed foams by x-ray photon correlation spectroscopy

    Heaton C, Yin H, Khaghani D, Lee HJ, Poole H, Blackman E, et al. Measurement of turbulent velocity and bounds for thermal diffusivity in laser shock compressed foams by x-ray photon correlation spectroscopy. Phys Rev E. 2025 Oct;112:045218. https: //doi.org/10.1103/lff9-f3c1

    work page doi:10.1103/lff9-f3c1 2025

  78. [80]

    Ab initio simulation of warm dense matter,

    Bonitz M, Dornheim T, Moldabekov ZA, Zhang S, Hamann P, K¨ ahlert H, et al. Ab initio simulation of warm dense mat- ter. Physics of Plasmas. 2020;27(4):042710. https://doi.org/10.1063/1.5143225

    work page doi:10.1063/1.5143225 2020

  79. [81]

    The uni- form electron gas at warm dense matter con- ditions

    Dornheim T, Groth S, Bonitz M. The uni- form electron gas at warm dense matter con- ditions. Phys Reports. 2018;744:1–86. https: //doi.org/10.1016/j.physrep.2018.04.001

    work page doi:10.1016/j.physrep.2018.04.001 2018

  80. [82]

    Difference in X-ray scatter- ing between metallic and non-metallic liq- uids due to conduction electrons

    Chihara J. Difference in X-ray scatter- ing between metallic and non-metallic liq- uids due to conduction electrons. Jour- nal of Physics F: Metal Physics. 1987 feb;17(2):295–304. https://doi.org/10.1088/ 0305-4608/17/2/002

    1987

Showing first 80 references.