Critical densities for the RPA approach in quasi-one-dimensional electronic systems

The intrasubband pair-correlation function, g(x), for a quasi-one-dimensional electron gas confined in a GaAs-AlxGa1-xAs rectangular quantum wire within the random-phase approximation (RPA) is calculated for several values of the potential barrier height and wire width. We have studied the dependence of the pair-correlation function on the electronic density, and delimited the region where the RPA approach gives physically acceptable results, i.e. the electronic density value where g(x) possesses positive values for small interparticle separations. The critical density in creases with increasing potential barrier height or decreasing wire width.