The on-top pair-correlation density in the homogeneous electron liquid

TL;DR

This paper uses the ladder theory and the Bethe-Goldstone equation to accurately compute the on-top pair-correlation density in the homogeneous electron liquid, confirming the theory's validity at zero distance.

Contribution

It provides exact solutions for the on-top pair-correlation density in 2D and 3D electron liquids and proves the ladder theory satisfies the cusp condition at zero distance.

Findings

Accurate calculation of g(0) in 2D and 3D electron liquids.

Validation that ladder theory satisfies the cusp condition.

Theoretical confirmation of short-range correlation descriptions.

Abstract

The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.