Kramers-Heisenberg-Dirac expression

Here X(, i(g) denotes a vibrational wavefunction for level 6, of mode i in the ground electronic state. As we discussed in connection with absorption spectra in Chap. 11, Eq. (12.18) makes the wavepacket formalism much more manageable than the Kramers-Heisenberg-Dirac expression for calculating Raman excitation spectra. It is not necessary to sum over all possible combinations of quantum numbers for the different modes. 

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

The theory discussed until now is based on the Kramers-Heisenberg-Dirac dispersion relation for the transition polarizability tensor as given in Eq. (6.1-1). The expression shown in this equation describes a steady state scattering process and contains no explicit reference to time. Therefore, the resonance Raman theory which is based on the KHD dispersion relation is sometimes also termed as time-independent theory (Ganz et al., 1990). 

The tfaeoiy of intensities of re onantly>enhanced Raman lines is based on the Kramers-Heisenberg-Dirac dispersion equation [266,267], The problem is analyzed in teims of vibronic interactions in die molecule. The JK matrix component of the molecular polarizability for the gi gf transition in die Raman spectrum can be expressed as follows [256,257]... 

---