\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional(2D)electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering schr?dinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our result for the correlation energy show a quantum phase transition occurring at coupling strength $r_{s}\approx24$ from the paramagnetic to the fully spin-polarized fluid.
\end{document}