Scaling relations for two-component charged systems: Application to metallic hydrogen

Abstract

We derive exact scaling relations for the energy and pair-correlation functions of a neutral two-component system of charged nonrelativistic particles in its ground state. These are obtained under general conditions through the use of the virial theorem, and the use of the Hellmann-Feynman theorem with respect to masses and charges, and they are independent of symmetry. For a dense system of charged fermions of disparate masses, where Born-Oppenheimer separation is valid, these results are used to obtain the ground-state energy by scaling from known electron-gas results and evaluating terms from cross interactions by response and effective-mass theory. The results, which require very little numerical work, agree well with the quantum Monte Carlo simulations for metallic hydrogen.