Abstract
We present a model for the statistical equilibrium of the levels of H, considering recombinations to excited levels, collisional excitations up from the ground state and spontaneous radiative transitions. This problem has a simple "cascade matrix" solution, describing a cascade of downwards spontaneous transitions fed by both recombinations and collisional excitations. The resulting predicted Balmer line ratios show a transition between a low temperature and a high temperature regime (dominated by recombinations and by collisional excitations, respectively), both with only a weak line ratio vs. temperature dependence. This clear characteristic allows a direct observational identification of regions in which the Balmer lines are either recombination or collisionally excited transitions. We find that for a gas in coronal ionization equilibrium the Halpha and Hbeta lines are collisionally excited for all temperatures. In order to have recombination Halpha and Hbeta it is necessary to have higher ionization fractions of H than the ones obtained from coronal equilibrium (e.g., such as the ones found in a photoionized gas).
