2005ApJ...633..309D

The 2s_1/2state of hydrogen is metastable and overpopulated in H II regions. In addition, the 2p states may be pumped by ambient Lyα radiation. Fine-structure transitions between these states may be observable in H II regions at 1.1 GHz (2s_1/2-2p_1/2) and/or 9.9 GHz (2s_1/2-2p_3/2), although the details of absorption versus emission are determined by the relative populations of the 2s and 2p states. The n=2 level populations are solved with a parameterization that allows for Lyα pumping of the 2p states. The Lyα pumping rate has long been considered uncertain, as it involves solution of the difficult Lyα transfer problem. The density of Lyα photons is set by their creation rate, easily determined from the recombination rate, and their removal rate. Here we suggest that the dominant removal mechanism of Lyα radiation in H II regions is absorption by dust. This circumvents the need to solve the Lyα transfer problem and provides an upper limit to the rate at which the 2p states are populated by Lyα photons. In virtually all cases of interest, the 2p states are predominantly populated by recombination, rather than Lyα pumping. We then solve the radiative transfer problem for the fine-structure lines in the presence of free-free radiation. In the likely absence of Lyα pumping, the 2s_1/2⟶2p_1/2 lines will appear in stimulated emission, and the 2s_1/2⟶2p_3/2lines in absorption. Because the final 2p states are short lived, these lines are dominated by intrinsic line width (99.8 MHz). In addition, each fine-structure line is a multiplet of three blended hyperfine transitions. Searching for the 9.9 GHz lines in high emission measure H II regions offers the best prospects for detection. The lines are predicted to be weak; in the best cases, line-to-continuum ratios of several tenths of a percent might be expected with line strengths of tens to a hundred mK with the Green Bank Telescope. Predicted line strengths, at both 1.1 and 9.9 GHz, are given for a number of H II regions, high emission measure components, and planetary nebulae, based on somewhat uncertain emission measures, sizes, and structures. The extraordinary width of these lines and their blended structure will complicate detection.