The mean path length of photons undergoing repeated scatterings in media of large optical thickness is calculated from accurate numerical solutions of the transfer equation including the effect of frequency redistribution characteristic of combined Doppler and natural broadening. Energy loss by continuous absorption processes, such as ionization or dust absorption, is discussed, and asymptotic scaling laws for the energy loss, the mean path length, and the mean number of scatterings are inferred from the numerical data.
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Hummer et al. (1980) studied this question.