The article discusses certain theoretical problems of the diffusion charging of aerosol particles in a bipolar ion environment. The ratio of polar conductivities, induced by cluster ions of either polarity, may vary in a wide range. New results are obtained for the calculation algorithm of the ion-aerosol equivalent attachment coefficient in a steady state. Applying the Poisson sum formula, an analytical approximation equation is derived for the ion-aerosol equivalent attachment coefficient as a function of the ratio of polar conductivities and of the particle diameter. This equation could simplify calculations of ion-aerosol interaction characteristics in the range of sufficiently large particle diameters. A possibility for the creation of a related approximation equation for the range of smaller particle diameters is briefly outlined.