This paper discusses the Rayleigh approximation and solves the corresponding electrostatic problem for a nonspherical particle of virtually arbitrary (starlike) shape, using an analog of the expanded-boundary-condition method. The essence of the recently proposed uniform-internal-field approximation, which gives approximating relationships for the Rayleigh approximation, is explained. Simple analytical expressions for the polarizability and other optical characteristics of small rectangular parallelepipeds are given in terms of the uniform-internal-field approximation. The results of numerical calculations of the absorption and scattering cross sections of light by such particles obtained from these approximate formulas and by the exact discrete-dipole method showed good agreement, especially for averaged cross sections in the case of unpolarized light or ensembles of randomly oriented parallelepipeds.
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