  We develop the plasmon-pole approximation for an interacting electron gas
confined in a semiconductor quantum wire. We argue that the plasmon-pole
approximation becomes a more accurate approach in quantum wire systems than in
higher dimensional systems because of severe phase-space restrictions on
particle-hole excitations in one dimension. As examples, we use the
plasmon-pole approximation to calculate the electron self-energy due to the
Coulomb interaction and the hot-electron energy relaxation rate due to
LO-phonon emission in GaAs quantum wires. We find that the plasmon-pole
approximation works extremely well as compared with more complete many-body
calculations.
