A universal solution method for the radiation transport equation in plane parallel geometry in the case of Lorentzian line shape is presented. As an example the plasma of an rf discharge in argon is considered. Spatial profiles and line densities of the four lowest excited argon atoms calculated by means of self-consistent models including and neglecting the radiation transport equation
are compared with experimental data. It is found that the correct treatment of the radiation transport in gas discharge modelling significantly improves the agreement with measured densities and spatial profiles of the excited atoms.