Theoretical Approach to the Correlations of a Hard-Sphere Crystal

TL;DR

This paper introduces a novel theoretical method to calculate the angular-averaged two-body correlation function in simple solids, specifically applied to FCC hard-sphere crystals, showing excellent agreement with simulations.

Contribution

It presents the first theoretical framework based on sum rules for calculating the correlation function in simple solids, advancing perturbation theories.

Findings

Excellent agreement with simulation data across densities

Applicable to FCC hard-sphere solids and potentially other simple systems

Provides a new route for perturbation theories in solid-state physics

Abstract

We present the first theoretical approach to the angular-average of the two-body correlation function $\tilde g(r)$ for simple solids. It is based on three sum rules for $\tilde g(r)$: the compressibility and virial equations and the normalization. We apply the theory to determine this correlation function for the case of the FCC solid phase of hard spheres. The agreement with simulation data is excellent over all the density range. The application to other simple systems is discussed. The approach opens a new route to perturbation theories for simple solids.