Calculations of hydrogen departure coefficients using a model with the angular momentum quantum levels resolved that includes the effects of external radiation fields are presented. The stimulating processes are important at radio frequencies and can influence level populations. New numerical techniques with a solid mathematical basis have been incorporated into the model to ensure convergence of the solution. Our results differ from previous results by up to 20 per cent. A direct solver with a similar accuracy but more efficient than the iterative method is used to evaluate the influence of continuum radiation on the hydrogen population structure. The effects on departure coefficients of continuum radiation from dust, the cosmic microwave background, the stellar ionising radiation, and free-free radiation are quantified. Tables of emission and absorption coefficients for interpreting observed radio recombination lines are provided.

Atomic hydrogen masers occur in recombination plasmas in sufficiently dense H ii regions. These hydrogen recombination line (HRL) masers have been observed in a handful of objects to date and the analysis of the atomic physics involved has been rudimentary. In this work a new model of HRL masers is presented which uses an nlmodel to describe the atomic populations interacting with free-free radiation from the plasma, and an escape probability framework to deal with radiative transfer effects. The importance of including the collisions between angular momentum quantum states and the free-free emission in models of HRL masers is demonstrated. The model is used to describe the general behaviour of radiative transfer of HRLs and to investigate the conditions under which HRL masers form. The model results show good agreement with observations collected over a broad range of frequencies. Theoretical predictions are made regarding the ratio of recombination lines from the same upper quantum level for these objects.