Molecular Motion and the Moment Analysis of Molecular Spectra. II. The Rotational Raman Effect

Abstract

The rotational Raman effect is analyzed in terms of moments of its intensity distribution. Each moment may be expressed as an equilibrium property of the molecular distribution in a scattering substance. The first and second moments of rotational Raman spectra are shown to obey the simple proportionality M(1)/M(2)=ℏ/2kT in the high-temperature, or classical limit. This relation is necessary in order that a classical system remain in equilibrium with its black-body radiation. It is the analog for two-photon scattering processes of the Einstein relation for the single photon processes of absorption and emission. The third and higher moments are found to depend on statistical averages of angular derivatives of the intermolecular potential energy, the angular correlation between molecules, and the molecular rotational kinetic energy. The analysis may be applied to the experimental determination of the nonspherical part of intermolecular forces from the rotational Raman effect in compressed gases.