Abstract
We study the many-body exchange-correlation properties of electrons confined to the lowest subband of a quantum wire, including effects of impurity scattering. Without impurity scattering, virtual excitations of arbitrarily low-energy plasmons destroy the Fermi surface of the electrons, whereas the presence of impurity scattering damps out these plasmons and restores he Fermi surface. The electron inelastic scattering rate \ensuremath{\Gamma} in the absence of scattering is zero below ${\mathit{k}}_{\mathit{c}}$ corresponding to the plasmon emission threshold, above which \ensuremath{\Gamma} diverges as (k-${\mathit{k}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}1/2}$ as k\ensuremath{\rightarrow}${\mathit{k}}_{\mathit{c}}$. For typical wire widths and electron densities currently available, the band-gap renormalization is found to be 10--20 meV.
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