Kramer-Heisenberg formula

The identity of the Kramers-Heisenberg formula obtained in the two gauges is a celebrated example [22], It should be noted, however, that the popular multipolar Hamiltonian ... 

Raman scattering is a two-photon process and must be described by second-order perturbation theory. The cross section for a transition from state ot(Et)> with energy Ei to state of(Ef)) with energy Ef (in the following the indices 0 and 1 will label the lower and the upper electronic state, respectively) is given by the Kramers-Heisenberg-Dirac formula (Kramers and Heisenberg 1925 Dirac 1927 for a sufficiently detailed derivation see, for example, Weissbluth 1978 ch.24)... 

The time-dependent formulation of Raman scattering has been introduced by Lee and Heller (1979), Heller, Sundberg, and Tannor (1982), Tannor and Heller (1982), and Myers, Mathies, Tannor, and Heller (1982). Its derivation is strikingly simple. We start from the Kramers-Heisenberg-Dirac formula (14.1) and (14.2) without the nonresonant term and transform it into an integral over time by using the identity... 

The polarisability tensor is given by a second-order perturbation expression known as the Kramers-Heisenberg dispersion formula (4)... 

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

Remarkably, the expansion (4.422) may be also obtained by requiring that the Kramers-Heisenberg dispersion relation reduce to the Thomas scattering formula at high energies indeed, through re-writing Eq. (4.422) in the form... 

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