In this work we have studied the electron LO phonon interaction on the pair-correlation function g(x) and its dependence on the electronic density for a GaAs-AlGaAs rectangular quantum wire within the random-phase approximation (RPA). We assumed two different values of the wire width. As negative non-physical results are found for lower electronic densities and small interparticle separations in the RPA approach, we have delimited the regions where the RPA approach cannot be used for the calculation of the Q1D electron gas collective excitation.

The ground state intrasubband pair-correlation function for a quasi-one-dimensional electron gas confined in a GaAs-Al xGa1-xAs parabolic quantum well wire within the Random-Phase Approximation (RPA) is calculated. We have considered two wires with subband energies separation homega = 2:0 meV and homega = 2:5 meV. The dependence of the pair-correlation function on the electronic density was studied and the regions where the RPA approach cannot be used were precisely determined.