Due to the spin-orbit interaction in ${A}_{3}{B}_{5}$ semiconductor quantum wells, the resonant Raman scattering amplitude from the charge density excitations (CDE) interferes with that from the spin density excitations (SDE). This spin-charge coupling manifests itself in an asymmetry of the non-spin-flip Raman spectrum with respect to directions of circular polarizations of incident and scattered photons. Consequently, the difference spectrum obtained by subtracting the spectra taken at reversed polarizations has a band in the region of single-particle spin conserving transitions. Since CDE are involved, Coulomb screening effects are expected to have strong influence on the intensity of this band. We have calculated the difference spectrum, taking into account the long range Coulomb interaction in the random phase approximation. We have found that this interaction does not destroy the spin-charge coupling. Our calculations suggest that the experimentally observed non-spin-flip band in the Raman difference spectrum of a GaAs/AlGaAs heterostructure serves as an evidence of the CDE-SDE interference.