Quasi-particle properties of a one-dimensional electron system interactingwith a short-range potential

We study the quasi-particle properties of a one-dimensional electron gas in teracting via a short-range electron-electron interaction. The electron sel f-energy is calculated using the leading-order dynamical-screening approxim ation with (GWT approximation) and without the vertex corrections (GW appro ximation). We test the reliability of the plasmon-pole approximation agains t the full self-energy calculations. Energy relaxation rate via longitudina l optical (LO)-phonon emission is also examined to explore the effects of s hort-range potential. Our results for the quasi-particle properties indicat e that an effective short-range interaction can be used as a qualitative mo del to understand various quantities in a realistic quantum wire with long- range Coulomb interactions.