Rate equation solution for the temporal behavior of a three-level system

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Abstract
The time behavior of a three-level system has been solved with general assumptions using the rate equation approach and under a pulsed spectral irradiance with rectangular shape. Three different specific cases, corresponding to possible conditions for inorganic atom seeds in atmospheric flame, have been investigated making use of literature values for the collisional and radiative rate constants. Results of these calculations are presented for Tl and Ga atoms when excited via the transitions 1 → 3, 2 → 3, and 1 → 2 under different source spectral irradiances, flame conditions, and the most significant collisional coupling constants between the various levels.