We report on a theoretical study of the H₂–He and H₂–Ar pair trace-polarizability and the corresponding isotropic Raman spectra. The conventional quantum mechanical approach for calculations of interaction-induced spectra, which is based on an isotropic interaction potential, is employed. This is compared with a close-coupling approach, which allows for inclusion of the full, anisotropic potential. It is established that the anisotropy of the potential plays a minor role for these spectra. The computed isotropic collision-induced Raman intensity, which is due to dissimilar pairs in H₂–He and H₂–Ar gas mixtures, is comparable to the intensities due to similar pairs (H₂–H₂, He–He, and Ar–Ar), which have been studied previously.