Approximation of effective lifetimes for spatially nonuniform excitation of atoms

This paper analyzes the error of the Biberman approximation and interprets results obtained when the zone of primary excitation of atoms is localized inside gaseous media. This occurs during the contraction of a discharge column or during the excitation of atoms by a narrow beam of high-speed particles (electrons, protons, photons). The authors consider a volume of gas in the form of an infinitely long cylinder with radius 'R'. This model is a good approximation of the experimental conditions for a variety of laboratory set-ups. The results of this study illustrate the error of the Biberman approximation in calculating the density of excited atoms in optically dense media