Rayleigh transitions, energy level

Fig. 2 Jablonski energy level diagram illustrating possible transitions, where solid lines represent absorption processes and dotted lines represent scattering processes. Key A, IR absorption B, near-IR absorption of an overtone C, Rayleigh scattering D, Stokes Raman transition and E, anti-Stokes Raman transition. S0 is the singlet ground state, S, the lowest singlet excited state, and v represents vibrational energy levels within each electronic state.

In Fig. 1.30 the lines designated v = 0 and v = 1 represent vibrational energy levels of a molecule such as HCl. The energy difference between these levels is given by Eq. (1.39) as AE = hv. A transition directly between these two levels causes the absorption of an infrared photon whose frequency is the same as the molecular frequency. In Rayleigh and Raman scattering. 

Figure 7.2 Transitions between vibrational energy levels involved in the processes of infrared absorption, Rayleigh and Raman scattering.

Although each Stokes line and its anti-Stokes counterpart are equally separated from the Rayleigh line, they are not of equal intensity. This is because the intensity of each transition is proportional to the population of the energy level from which the transition originates under equilibrium conditions the ratio of populations is given by the Boltzmann distribution. With the fourth-power dependence on the scattering frequency, the ratio of intensities of the Stokes line and its anti-Stokes partner in a Raman spectrum is given by... 

Thus each allowed Raman coupling generally produces two frequencies in the spectrum of scattered light, shifted to the negative and positive sides of the dominant Rayleigh line by the same amount, Av = AE/h, For this reason Raman spectroscopy is concerned with measurements of frequency shifts, rather than absolute frequencies. In most cases a number of Raman transitions can take place, involving various molecular energy levels, and the... 

Figure 4.61 The process of Rayleigh and Raman scattering. Two virtual states are shown, one of higher energy. Rayleigh and Raman scattering are shown from each state. Normal IR absorption is shown by the small arrow on the far right marked AE, indicating a transition from the ground state vibrational level to the first excited vibrational level within the ground electronic state.

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