  We present a self-consistent analytic theory of the intra-layer and
inter-layer pair correlation functions in electron-electron and electron-hole
fluid bilayer systems. Our approach involves the solution of a zero-energy
scattering Schroedinger equation with an effective potential which includes a
Bose-like term from Jastrow-Feenberg correlations and a Fermi term from kinetic
energy and exchange, tailored to yield the Hartree-Fock limit at high carrier
density. The theory is also shown to satisfy the plasmon sum rule and the
charge neutrality condition. We obtain good agreement with the available
Quantum Diffusion Monte Carlo (DMC) data in symmetric bilayers over a wide
range of carrier density and layer spacing, and stress the role of three-body
correlation terms in yielding fully quantitative agreement at strong coupling.
Signals of impending transitions to density-modulated states at strong coupling
and low layer spacing appear in the calculated pair correlations through
inter-layer in-phase oscillations for electron-hole bilayers and out-of-phase
oscillations for electron-electron bilayers, in agreement with the DMC
findings.
