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 rs. Our approach is based on solving the Schrödinger equation for the two-electron wavefunction 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) (Bulutay and Tanatar 2002 Phys. Rev. B 65 195116). We also show that the spin-up spin-down correlation function at the origin, g↑↓(0), is mainly independent of the degree of spin polarization of the electronic system.
Publication Source (Journal or Book title)
Journal of Physics Condensed Matter
Moreno, J., & Marinescu, D. (2003). Pair distribution function in a two-dimensional electron gas. Journal of Physics Condensed Matter, 15 (37), 6321-6329. https://doi.org/10.1088/0953-8984/15/37/002