The profile of Lyman-alpha radiation in an expanding gas cloud is calculated in detail in order to determine the color temperature of the radiation scattered by an H I atom within the cloud. Scattering of Lyα is likely to dominate in the excitation of the 21 cm transition of H I in astronomical gas clouds with very low densities. The spin temperature will then become equal to this color temperature. The method involves a Sobolov-like treatment and the application of a redistribution function for the scattering that preserves detailed balance when the recoil of the atom is included. Analogous color temperatures are calculated that are relevant for the excitation of the hyperfine transitions of atomic deuterium and ionized 3He.
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Deguchi et al. (1985) studied this question.