Lifetimes of n ${}_{}{}^2{}_{}{}^{}P$ states of thallium by analysis of cascade fluorescence following two-photon excitation

The lifetimes of the n ${\mathrm{}}^2$$P_{1/2}$ and n ${\mathrm{}}^2$$P_{3/2}$ states of thallium, n=7–11, have been determined through measurements of the fluorescence signal resulting from two-photon excitation in an atomic beam. The temporal dependence of the fluorescence signal is determined by solving the equations governing cascade spontaneous fluorescence from higher-lying initial states. It is shown that under conditions applicable to our experiments, the asymptotic decay of the fluorescence is a measure of the lifetime of the initial state. The possibility of self-absorption of the fluorescence within the atomic beam is investigated; it is found to be negligible over the range of thallium densities used in the experiment. Our lifetime measurements for these eight ${}_{}{}^2{}_{}{}^{}\mathrm{P}$ states are compared with other known experimental data and with the results of previous semiempirical calculations.