Pair-correlation function of the electron gas with long-range Coulomb interaction: Ladder theory

We present analytical and numerical results for the pair-correlation function g (r=0) of the electron gas with long-range Coulomb interaction obtained within the ladder theory, Analytical results obtained by perturbation calculation and a Pade approximation are derived and are found to be in good agreement with our numerical solution of the ladder equation. Finite-width effects in the two-dimensional electron gas (quantum well) are also described. For quasi-one-dimensional systems (quantum wires) numerical and analytical results are derived fur an oscillator confinement model.