Difference Between Stokes and Anti-Stokes Raman Shiftsand Time-reversal Symmetry

The anti-Stokes scattering was defined as the corresponding time-reversed process of the Stokes scattering. Based on the time-reversal symmetry the differences between one Stokes and its corresponding antiStokes Raman shifts have been theoretically demonstrated for the systems with Kramers-degenerate ground or final states. In the former cases the Stokes and its corresponding anti-Stokes Raman lines should display on the same side of the excited line. In the latter cases, they show major differences on two sides of the excited line. However, the whole normal Stokes Raman spectrum of a system may be still symmetric to the whole anti-Stokes spectrum, except in the cases of resonant, or laser, or circularly polarized excitation Raman scattering. This is a preliminary theoretical predication which needs more experimental and theoretical investigations.