# Atom-in-jellium equations of state in the high energy density regime

## TL;DR

This paper develops and compares atom-in-jellium equations of state for various elements, highlighting the importance of electronic shell effects in high energy density regimes and proposing a hierarchical approach for EOS construction.

## Contribution

It extends atom-in-jellium models to predict full equations of state for multiple elements, emphasizing shell effects and hierarchical modeling strategies.

## Key findings

- Atom-in-jellium EOS matches pseudo-atom MD results, with variable accuracy.
- Electronic shell effects significantly influence shock Hugoniot predictions.
- Hierarchical EOS construction combines efficiency with accuracy.

## Abstract

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudo-atom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous 3D multi-atom calculations to validate and adjust the EOS.