  Context. Level population inversion of hydrogen atoms in ionized gas may lead
to stimulated emission of hydrogen recombination lines, and the level
populations can in turn be affected by powerful stimulated emissions. Aims. In
this work the interaction of the radiation fields and the level population
inversion of hydrogen atoms is studied. The effect of the stimulated emissions
on the line profiles is also investigated. Methods. Our previous nl-model for
calculating level populations of hydrogen atoms and hydrogen recombination
lines is improved. The effects of line and continuum radiation fields on the
level populations are considered in the improved model. By using this method
the properties of simulated hydrogen recombination lines and level populations
are used in analyses. Results. The simulations show that hydrogen radio
recombination lines are often emitted from the energy level with an inverted
population. The widths of Hn$\alpha$ lines can be significantly narrowed by
strong stimulated emissions to be even less than 10 km s$^{-1}$. The
amplification of hydrogen recombination lines is more affected by the line
optical depth than by the total optical depth. The influence of stimulated
emission on the estimates of electron temperature and density of ionized gas is
evaluated. We find that comparing multiple line-to-continuum ratios is a
reliable method for estimating the electron temperature, while the
effectiveness of the estimation of electron density is determined by the
relative significance of stimulated emission.
