Pair densities at contact in the quantum electron gas

TL;DR

This paper investigates the value of the pair distribution function at contact in a quantum electron gas, comparing theoretical scattering-based results with many-body calculations and quantum Monte Carlo data across different dimensions.

Contribution

It introduces a detailed comparison of scattering-based theoretical predictions for g(0) with many-body and Monte Carlo results in 2D and 3D electron gases.

Findings

Theoretical g(0) values align well with quantum Monte Carlo data.

Effective scattering potentials capture many-body effects.

Results vary with coupling strength r_s and dimensionality D.

Abstract

The value of the pair distribution function g(r) at contact (r = 0) in a quantum electron gas is determined by the scattering events between pairs of electrons with antiparallel spins. The theoretical results for g(0) as a function of the coupling strength r_s in the paramagnetic electron gas in dimensionality D=2 and 3, that have been obtained from the solution of the two-body scattering problem with a variety of effective scattering potentials embodying many-body effects, are compared with the results of many-body calculations in the ladder approximation and with quantum Monte Carlo data.