  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.
