Derivation of the reflection principle in continuum resonance Raman scattering

Abstract

We prove the reflection principle in continuum resonance Raman scattering as stated recently by Kolba, Manz, Schreier and Trisca. For a Stokes (or anti-Stokes) transition, the nodal pattern of the coordinate or momentum representation of the initial wavefunction |i> (or final wavefunction |f>) is mapped on the time-dependent overlap |<f;|i(t)>|. An interesting aspect of the proof is the use of all three approaches to Raman scattering: the Kramers-Heisenberg-Dirac sum-over-states approach, the Lee-Heller time-dependent approach, and the Hizhnyakov-Tehver transform method. We also derive new expressions for the resonance Raman scattering amplitude and associated correlation function in terms of the Rayleigh scattering amplitude and associated autocorrelation function. A new algorithm using a fast Fourier transform to implement the Hizhnyakov-Tehver transform method for fundamental Raman excitation profiles is also discussed. © 1993.