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

Many-body effects described by the local-held 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 Sjolander is used with an analytical form for the local-field correction. Wt-use a three-sum-rule approach in order to parametrize the local-held correction by three coefficients. The coefficients are determined self-consistently and depend on the width parameter b and on the Wigner-Seitz parameter,,. Numerical results for the exchange energy and the correlation energy for 0<r(s)<1000 are presented. The exchange energy and the correlation energy in the low-density regime are described by epsilon(ex)(r(s)-->infinity)proportional to - ln(r(s))/r(s) and epsilon(cor)(r(s)-->infinity)proportional to - ln(r(s))/r(s) with epsilon(cor)(r(s)-->infinity)/epsilon(ex)(r(s)-->infinity) approximate to 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.