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A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]