Energy Rayleigh transitions

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.

Figure 14. Tunneling to the alternative state at energy can be accompanied by a distortion of the domain boundary and thus populating the ripplon states. All transitions exemplified by solid lines involve tunneling between the intrinsic states and are coupled linearly to the lattice distortion and contribute the strongest to the phonon scattering. The vertical transitions, denoted by the dashed lines, are coupled to the higher order strain (see Appendix A) and contribute only to Rayleigh-type scattering, which is much lower in strength than that due to the resonant transitions.

Figure 3. Energy schemata of transitions involving vibrational states (a excitation of 1st vibrational state - mid-IR absorption b excitation of overtone vibrations - near-IR absorptions c elastic scattering - Rayleigh lines d Raman scattering - Stokes lines e Raman scattering - Anti-Stokes lines f fluorescence).

In either case, the information on the vibrational transition is contained in the energy difference between the excitation radiation and the inelastically scattered Raman photons. Consequently, the parameters of interest are the intensities of the lines and their position relative to the Rayleigh line, usually expressed in wavenumbers (cm 1). As the actually recorded emissions all are in the spectral range determined by the excitation radiation, Raman spectroscopy facilitates the acquisition of vibrational spectra through standard VIS and/or NIR spectroscopy. 

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.

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

The concentrations of the CH and CN radicals were determined to have maximum values of (1.3 0.5) x 10 cm and (3.9 1.5) x 10 ° cm respectively. CH and CN-LIF measurements were carried out under linear excitation conditions. This was verified for the strongest optical transitions of both radicals by plotting the LIF signal intensity versus laser energy, as shown in Part (a) of Fig. 8. For each data point the laser was scanned over the complete spectral line to account for possible background signals. N2 Rayleigh calibration curves are shown in Part (b) of Fig. 8. 

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