Continuum resonance Raman scattering of light by diatomic molecules. I. The role of radiative crossings between the potentials of the dressed molecule

摘要

Usual scattering theory only provides a formal result for continuum resonance Raman scattering amplitudes, leaving the task of evaluating numerically these amplitudes. We look instead, in the case of a diatomic molecule, for a system of coupled equations patterned after those of molecular collision theory which can provide them directly (i.e., numerically). These equations emphasize the role of radiative crossings between the potential curves of the dressed molecule (molecule in its initial electronic state with the incoming photon, in its intermediate state with no photon, in its final state with the outgoing photon). The channels involve the potentials of the dressed molecule plus two artificial entrance and exit channels coupled in such a way as to yield the Raman scattering amplitudes through the analysis of one of the elements of the scattering matrix. Electronic transition moments depending on the internuclear distance are easily introduced into the formalism. In order to test the numerical accuracy of this method it is possible to use an analytically exact formula valid for harmonic and linear potentials. It is shown that a threehyphen;figure accuracy is easily achieved. Comparisons are also made with the results of a semiclassical procedure based on an Airy representation of the Franckndash;Condon amplitudes. This method, which is used abundantly in the next paper, has the advantage of providing a very fast way of reaching the scattering amplitudes and gives an error which generally does not exceed a few percent.