One-dimensional electron gas with short-range interaction: Local-field correction and critical exponents

We study the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using the ladder theory we obtain analytical results for the ground-state energy and the compressibility which are in agreement with exact results for weak and strong coupling. We calculate the short- and the long-distance behaviour of the pair-correlation function g(z) and derive critical exponents from g(z --> infinity). We evaluate the connection between the local-field correction and critical exponents.