A TUTORIAL REVIEW OF THE RATE-EQUATION AND DENSITY-MATRIX FORMALISMS FOR 2-AND 3-LEVEL ATOMIC AND MOLECULAR-SYSTEMS IN HIGH COLLISIONAL MEDIA EXPOSED TO PULSED-LASER LIGHT WITH ARBITRARY LASER BANDWIDTHS

This work gives a thorough description and comparison of excitations o f two- and three-level atomic and molecular systems by pulsed one- or two-step excitations described by the Rate-Equation formalism as well as by the Density-Matrix formalism (i.e., the Block equations in a sem i-classical description). The atomic (molecular) systems are exposed t o a high collisional environment (GHz). The laser frequency spectrum i s described as a single mode with an arbitrary bandwidth, given by pha se fluctuations (in the GHz-range). The systems of equations are solve d analytically both for steady-state conditions as well as for partly or full temporal conditions under various simplifying conditions. Emph asis has been given to the situation when the laser bandwidths are com parable to or larger than the collisional rates. Of special interest a re the results obtained for three-level systems exposed to two nearly resonant light fields in the Density-Matrix formalism. It is found tha t the Density-Matrix treatment of three-level systems predicts signifi cantly different behaviours of the atomic (molecular) systems as compa red to what the commonly used Rate-Equation formalism does, even thoug h the laser bandwidths are larger than the collisional rates. Phenomen a such as dynamic Stark-splittings, dynamic Stark shifts and two-photo n excitations appear which in turn lead to anomalous line shapes and n on-monotonous saturation curves. New manageable analytical expressions for excited state populations, Stark-splittings and Stark shifts in c ollision-exposed three-level atomic (molecular) systems exposed to two nearly resonant light fields are given. In addition, an analytical de scription of excitations of degenerate three-level systems by two-step excitations, reduced from ordinary N2 equations (N being the total de generacy of the system) to only 3 generalized time-dependent equations for the populations, is also given.