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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 Schr�odinger 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 threebody 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 electronhole bilayers and out-of-phase oscillations for electron-electron bilayers, in agreement with the
DMC findings.
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