Cascades of energy among the vibrational levels of diatomic molecules trapped in a rare gas matrix: With application to 12C16O(ν) in Ar

Energy stored in vibrational level ν = 1 of several individual dipolar diatomic molecules AB which are trapped in a rare gas matrix M is automatically accumulated in a higher level ν > 1 of a single molecule AB. This remarkable cascade of energy upwards competes with a cascade of energy downwards. the radiative decay. The interplay of both cascades, first observed by Dubost and Charneau, is explained a simple model. The model incorporates three processes into a master equation for the relative populations P_ν(t) of levels ν: (a) migration of single quanta by resonance energy transfer, AB(1) + AB(0) ? AB(0) + AB(1); (b) phonon assisted excitation of upper levels, AB(1) + AB(ν) → AB(0) + AB(ν+1); and (c) radiative decay, AB(ν) → AB(ν-1). The model assumes that there is only one isotopic species AB which has a small but nonzero vibrational anharmonicity, that the temperature is low, T → 0 K, the concentration ratio ?_M/?_AB is large and that, initially, at time t = 0, a small fraction p₁ of molecules AB is excited to level ν = 1. The master equation has only two parameters, the radiative lifetime t_rad and k  2/?_AB?₁k(1,1 → 0,2)t_rad], where k(1,1 → 0,2) is the reference rate constant of process (b). The master equation is solved in closed form for the Pν(t). For t_rad = 14 ms and k = 0.2, very satisfactory qualitative agreement is found for the theoretical P_ν(t) and the experimental time evolution of the relative population of vibrational levels of ¹²C¹⁶O in an argon matrix, for ?_M/?_AB = 2000 at T = 9 K. In agreement with experimental results it is concluded that the risetime of the fluorescence signals decreases whereas population inversion increases for decreasing values of ?_M/?AB. At long times, t > t_rad, any population inversion should disappear.