Experiment reveals how electrons actually behave in warm dense matter

Researchers at European XFEL, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Rostock University and other collaborating institutions have used high-precision experiments to demonstrate that the most widely used models for the behaviour of electrons in warm dense matter are inaccurate. Warm dense matter is challenging to study but also of key importance for a plethora of research, including the investigation of planetary interiors, material science, and laser fusion experiments. The study has been published in Physical Review Letters. (DOI: 10.1103/86cw-8wm5)

In warm dense matter, electron density oscillates. The collective oscillations are called plasmons. They carry important information and can be observed using X-rays, resulting in scattering spectra – abstract images captured by a detector. In many experiments, these spectra are interpreted using simplified uniform electron gas models. However, the new measurements show that, for warm dense aluminium, these models consistently overestimate the plasmon energy by up to about 25 per cent (about 8 electronvolts) and fail to reproduce the full measured shape of the signal.

“Our measurements are precise enough to clearly distinguish between competing models,” says Dr. Thomas Preston of European XFEL. “That is important because these models are widely used to diagnose extreme states of matter. If the model is incorrect, that leads to inaccurately inferred properties.” The electron behaviour affects predictions of opacity, optical properties, electrical conductivity, and energy transport, for instance.

“Capturing the complex physics of warm dense matter requires a more sophisticated treatment of the underlying microphysics,” explains Dr. Zhandos Moldabekov from HZDR, who led the simulation part of the analysis. The team demonstrated that – as opposed to the simpler models – state-of-the-art time-dependent density functional theory simulations do reliably reproduce the experimental observations. This method precisely calculates how electrons respond in the disordered atomic structure of the compressed liquid. It does require more computational resources, but has become more feasible in recent years. The researchers argue that these more detailed simulations are necessary when quantitative accuracy is required, because the positions of the atoms in the liquid and the interactions between electrons and ions directly affect the electron response.

“Even for aluminium, often treated as a simple metal, the electron response is not described well by overly uniform models once the material is driven into this extreme regime,” says Dmitrii Bespalov, first author of the study. “Only when we account for the real disordered structure do theory and experiment agree.” The same experimental approach can be extended to other materials and to higher temperatures, including conditions relevant to planetary interiors and fuel targets used for laser fusion.

The experiment was conducted at the high energy density instrument (HED-HIBEF) at European XFEL, using the powerful nanosecond DiPOLE laser. The laser compressed a thin aluminium foil to a pressure of around 50 gigapascals (500,000 times atmospheric pressure) and a temperature of approximately 7,000 Kelvin (about 6,700 degrees Celsius). Before the shock wave broke out of the rear surface of the aluminium, ultrashort X-ray pulses from the European XFEL probed the sample and recorded the plasmon signal. Using multiple methods simultaneously – X-ray Thomson scattering, X-ray diffraction, and independent shock diagnostics – enabled the researchers to benchmark theory against a well-constrained experimental state. Scientists from more than a dozen international institutions contributed to the study.

Publication:
D. S. Bespalov et al.: Momentum-Resolved X-Ray Thomson Scattering Benchmark of Electronic-Response Models in Warm Dense Aluminium, in Physical Review Letters, 2026 (DOI: 10.1103/86cw-8wm5).

Additional information:
Dr. Thomas Preston | Dmitrii Bespalov
European XFEL
Email: thomas.preston@xfel.eu | dmitrii.bespalov@xfel.eu
Phone: +49 40 8998-6718 |

Dr. Zhandos Moldabekov
Institut für Strahlenphysik am HZDR
Phone: +49 351 260 3657 | Email: z.moldabekov@hzdr.de

Media contact:
Thomas Reintjes | Communication Officer
European XFEL
Phone: +49 40 8998-6596 | Email: thomas.reintjes@xfel.eu

Simon Schmitt | Head
Communications and Media Relations at HZDR
Phone: +49 351 260 3400 | Mobile: +49 175 874 2865 | Email: s.schmitt@hzdr.de

The Helmholtz-Zentrum Dresden-Rossendorf (HZDR) performs – as an independent German research center – research in the fields of energy, health, and matter. We focus on answering the following questions:

• How can energy and resources be utilized in an efficient, safe, and sustainable way?
• How can malignant tumors be more precisely visualized, characterized, and more effectively treated?
• How do matter and materials behave under the influence of strong fields and in smallest dimensions?

To help answer these research questions, HZDR operates large-scale facilities, which are also used by visiting researchers: the Ion Beam Center, the Dresden High Magnetic Field Laboratory and the ELBE Center for High-Power Radiation Sources.
HZDR is a member of the Helmholtz Association and has six sites (Dresden, Freiberg, Görlitz, Grenoble, Leipzig, Schenefeld near Hamburg) with almost 1,500 members of staff, of whom about 700 are scientists, including 200 Ph.D. candidates.