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

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.