Knowledge Bank

The theory of Rayleigh and Raman intensities far from resonance has been reinvestigated. A closely related problem, the effect of nuclear motion on the optical second-order properties, has been considered as well. The correct simplification of the Kramers-Heisenberg dispersion equation is that proposed, though not justified, by Pleaczek, in which diagonal and transition matrix elements of the electric polarizability tensor are computed. Higher-order terms are formally shown here to be small and various correction terms leading to the exact dispersion equation, within the Born-Oppenheimer approximation, have been evaluated. Representative calculations on $H2+$, which is both exactly soluble and for which the parallel and perpendicular components represent highly and less polarizable molecules, respectively, are given for transitions between all bound vibrational states. A complete test of the approximate theory is thus made, including Herzberg-Teller expansions.