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Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Hannah M. Bellenbaum1,2,3,*, Maximilian P. Böhme4, Michael Bonitz5, Tilo Döppner4, Luke B. Fletcher6, Thomas Gawne1,2, Dominik Kraus2,3, Zhandos A. Moldabekov1,2, Sebastian Schwalbe1,2 et al.

Jan Vorberger2 and Tobias Dornheim1,2,†

  • *Contact author: h.bellenbaum@hzdr.de
  • †Contact author: t.dornheim@hzdr.de
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Phys. Rev. Research 7, 033016 – Published 7 July, 2025

DOI: https://doi.org/10.1103/9d7r-1xbm

Abstract

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high-quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on ab initio simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree—quantities which are otherwise not directly accessible from the physical model—from first-principles path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and nonequilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high-density and high-temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from first-principles quantum Monte Carlo simulations.

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Phys. Rev. Research 7, 033016– Published 7 July, 2025
  • Received 17 March 2025
  • Accepted 30 May 2025
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