Electron scattering off simple gaseous molecules such as N-2 (E-1(g)+) is calculated within a quantum treatment of the collision process that is in turn formulated 9 in the laboratory frame of reference. The corresponding partial cross sections, integral and differential, elastic and vibrationally inelastic, are obtained at collision energies very close to the thresholds and are satisfactorily compared with existing experiments, which are, for the first time, well reproduced by computational methods at such low energies.