Electron densities for 146 planetary nebulae have been obtained for analyzing a large sample of forbidden lines by interpolating theoretical curves obtained from solutions of the five-level atoms using up-to-date collision strengths and transition probabilities. Electron temperatures were derived from forbidden N II and/or forbidden O III lines or were estimated from the He II 4686 A line strengths. The forbidden O II densities are generally lower than those from forbidden Cl III by an average factor of 0.65. For data sets in which forbidden O II and forbidden S II were observed in common, the forbidden O II values drop to 0.84 that of the forbidden S II, implying that the outermost parts of the nebulae might have elevated densities. The forbidden Cl II and forbidden Ar IV densities show the best correlation, especially where they have been obtained from common data sets. The data give results within 30 percent of one another, assuming homogeneous nebulae.
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Stanghellini et al. (1989) studied this question.