Atom-in-jellium predictions of the shear modulus at high pressure

TL;DR

This paper introduces a novel atom-in-jellium method to predict the shear modulus of elements across an extremely wide pressure range relevant to astrophysical objects, demonstrating good accuracy and extending electronic structure calculations.

Contribution

First application of atom-in-jellium theory to calculate shear modulus, covering pressures from ambient to relativistic regimes, with validation against experimental data.

Findings

Predicted shear modulus variation over 10 orders of magnitude in pressure.

Achieved ~10% accuracy compared to experimental and detailed calculations.

Extended the electronic structure approach to extreme conditions in astrophysics.

Abstract

Atom-in-jellium calculations of the Einstein frequency in condensed matter and of the equation of state were used to predict the variation of shear modulus from zero pressure to ~$10^7$ g/cm$^3$, for several elements relevant to white dwarf (WD) stars and other self-gravitating systems. This is by far the widest range reported electronic structure calculation of shear modulus, spanning from ambient through the one-component plasma to extreme relativistic conditions. The predictions were based on a relationship between Debye temperature and shear modulus which we assess to be accurate at the o(10%) level, and is the first known use of atom-in-jellium theory to calculate a shear modulus. We assessed the overall accuracy of the method by comparing with experimental measurements and more detailed electronic structure calculations at lower pressures.