RAYLEIGH-BRILLOUIN LIGHT-SCATTERING - SPECTRAL MOMENTS AND SUM-RULES

We present experimental and theoretical results concerning the spectra l moments of Rayleigh-Brillouin light scattering spectra of pure liqui ds and gas mixtures. First we derive a general equation for the second and fourth moment of the dynamic structure factor. Second, we derive explicit expressions for these moments for the Gaussian limit and mode ls that predict Lorentzian line shapes. Our experimental results for t he normalized second moment agree with the theoretical expressions. Th e n = 3 sum rule seems to be satisfied. The results for the normalized fourth moment do not agree with theory, but this can be shown to be c aused by frequency cutoff effects in the spectrum. The contribution of the instrumental function to the spectral moments is also investigate d. Our results indicate that in the analysis of Rayleigh-Brillouin lig ht scattering spectra use can be made of higher order sum rules (at le ast up to n = 3), provided that the free spectral range of the interfe rometer is chosen large enough. This would allow for a significant red uction in the number of fitting parameters needed to analyze such a li ght scattering spectrum.