  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\"odinger 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 results for the correlation energy show a quantum phase
transition occurring at coupling strength $r_s\approx 24$ from the paramagnetic
to the fully spin-polarized fluid.
