Light scattering by Gaussian random particles: Rayleigh and Rayleigh-Gans approximations

We study absorption and scattering by Gaussian random particles in the Rayleigh and Rayleigh-Gans approximations. The random shape is characterized by the autocovariance function, usually parameterized by the standard deviation of radius and the correlation length of angular variations. As for the Rayleigh-Gans approximation, we outline a Monte Carlo algorithm that can be adjusted for almost arbitrary, mathematically star-like particles in random orientation. The algorithm is computationally constrained to particles with size parameters less than about five. We examine how the autocovariance function affects the scattering and absorption properties of Gaussian particles, and compare to the Rayleigh-Gans solution for spheres. By ensemble-averaging the volume of the Gaussian particle, we develop criteria for the validity of the Rayleigh and Rayleigh-Gans approximations. The results help us understand, in part, light scattering by small particles in planetary atmospheres and cometary comae.