Pair distribution function in a two-dimensional electron gas

TL;DR

This paper derives an analytical expression for the pair distribution function at the origin in a two-dimensional electron gas, aligning well with numerical data and revealing spin polarization independence.

Contribution

It introduces a simple analytical formula for $g(0)$ in 2D electron gases, validated against quantum Monte Carlo results and recent numerical calculations.

Findings

Analytical expression for $g(0)$ as a function of $r_s$

Good agreement with Quantum Monte Carlo data

Spin-up spin-down correlation at the origin is spin polarization independent

Abstract

We calculate the pair distribution function, $g(r)$, in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of $r_s$. Our approach is based on solving the Schr\"{o}dinger equation for the two-electron wave function in an appropriate effective potential, leading to results that are in good agreement with Quantum Monte Carlo data and with the most recent numerical calculations of $g(0)$. [C. Bulutay and B. Tanatar, Phys. Rev. B {\bf 65}, 195116 (2002)] We also show that the spin-up spin-down correlation function at the origin, $g_{\uparrow \downarrow}(0)$, is mainly independent of the degree of spin polarization of the electronic system.