Recombination line intensities for hydrogenic ions – III. Effects of finite optical depth and dust

We explore systematically the effect on the recombination spectrum of hydrogen arising from: (i) finite optical thickness in the Lyman lines; (ii) the overlapping of Lyman lines near the series limit; (iii) the absorption of Lyman lines by dust or photoionization, and (iv) the long-wave radiation emitted by dust. Full account is taken of electron and heavy particle collisions in redistributing energy and angular momentum. We find that each of these deviations from the classical Case B leads to observable effects, and that dust influences the recombination spectrum in characteristic ways that may make possible new observational constraints on dust properties in nebulosities. On the basis of these calculations we believe the uncertainty in the determination of the helium-to-hydrogen abundance ratio in the Universe may be larger than currently claimed.