The Coulomb bridge function and the Pair-distribution functions of the 2-dimensional electron liquid in the quantum regime

The electron-electron pair distribution functions (PDF) of the 2-D electron fluid (2DEF) in the quantum regime (at T=0) are calculated using a classical-map-hyper-netted-chain (CHNC) scheme and compared with currently available Quantum Monte-Carlo (QMC) simulations in the coupling range r_s=1 to 50. We iteratively extract the bridge function of the "equivalent" classical 2-D liquid in the quantum regime. These bridge functions B(r) are relatively insensitive to spin-polarization effects. The structure of the bridge functions changes significantly for r_s>6, suggesting the onset of strongly correlated clusters. The new B(r), appropriate for the long-range Coulomb potential, can be used to replace the hard-sphere B(r) previously used in these calculations. They provide accurate classical representations of the QMC-PDFs even at very strong coupling, and probably at finite-T near T=0.