Shape effects in scattering and absorption by randomly oriented particles small compared to the wavelength

We study the effects of particle shape on the absorption and scattering cross sections of randomly oriented particles in the Rayleigh domain, i.e. particles that are very small compared to the wavelength of radiation both inside and outside the particle. In particular, we investigate the validity of the so-called statistical approach. In this approach it is assumed that the scattering and absorption properties of irregularly shaped particles can be simulated by the average properties of a distribution of simple shapes. We depart from the assumption of homogeneous spherical particles in two ways: 1) by using various distributions of elongated and flattened homogeneous ellipsoids and spheroids, 2) by using a distribution of hollow spherical particles. We derive explicit formulas for the shape averaged scattering and absorption cross sections as functions of the refractive index for various distributions of particle shapes in the Rayleigh limit. We compare the absorption cross sections as functions of the refractive index of the various distributions with each other and with those of homogeneous spheres. We also study the effects of the distributions on the shapes of absorption spectra. We find that there is a strong similarity between the absorption spectra of distributions of various non-spherical homogeneous particles and a distribution of hollow spheres. We show that the positions of features in the shape averaged mass absorption coefficient as a function of wavelength of small ellipsoidal, spheroidal or hollow spherical crystalline forsterite particles coincide with those deduced from the spectral energy distributions of various astronomical sources and with measurements of the mass absorption coefficients of small particles. This is not the case when we use homogeneous spherical particles.