In describing the excitation of atomic and molecular species with lasers in spectroscopic applications, only the density matrix formulation is exactly correct. Many workers, however, have used the conventional rate equation formulation. The range of application of the conventional rate equations is examined and, for flames, shown to be valid for sufficiently slow laser pulse rise times under single-mode excitation and for certain special cases of multimode excitation.
John W. Daily, "Use of rate equations to describe laser excitation in flames," Appl. Opt. 16, 2322-2327 (1977)