  The bosonisation technique is used to calculate the resonant Raman spectrum
of a quantum wire with two electronic sub-bands occupied. Close to resonance,
the cross section at frequencies in the region of the inter sub-band
transitions shows distinct peaks in parallel polarisation of the incident and
scattered light that are signature of collective higher order spin density
excitations. This is in striking contrast to the conventional selection rule
for non-resonant Raman scattering according to which spin modes can appear only
in perpendicular polarisation. We predict a new selection rule for the
excitations observed near resonance, namely that, apart from charge density
excitations, only spin modes with positive group velocities can appear as peaks
in the spectra in parallel configuration close to resonance. The results are
consistent with all of the presently available experimental data.
