Many-body effects in the interacting quasi-one-dimensional electron gas: Oscillator confinement

Many-body effects described by the local-field correction are calculated for the quasi-one-dimensional electron gas with an oscillator confinement of width parameter $b.$ The self-consistent theory of Singwi, Tosi, Land, and Sj\"olander is used with an analytical form for the local-field correction. We use a three-sum-rule approach in order to parametrize the local-field correction by three coefficients. The coefficients are determined self-consistently and depend on the width parameter b and on the Wigner-Seitz parameter rₛ. Numerical results for the exchange energy and the correlation energy for 0<rₛ<1000 are presented. The exchange energy and the correlation energy in the low-density regime are described by εₑₓ(rₛ→∞)∝-ln(rₛ)/rₛ and εcor(rₛ→∞)∝-ln(rₛ)/rₛ with ${{ε}}cor{(r}ₛ{→}{∞})/{{ε}}ₑₓ{(r}ₛ{→}{∞}){≈}0.8.$ We derive analytical and numerical results for the compressibility, the chemical potential, screening properties, and bound-state energies of positively and negatively charged impurities. The long-distance behavior of the pair-correlation function is calculated. The compressibility sum rule and the long-wavelength behavior of the dielectric function are discussed in detail. The Hartree energy is calculated.