An analytical model of nonproportional scintillator light yield in terms of recombination rates

Analytical expressions for the local light yield as a function of the local deposited energy (-dE/dx) and total scintillation yield integrated over the track of an electron of initial energy E are derived from radiative and/or nonradiative rates of first through third order in density of electronic excitations. The model is formulated in terms of rate constants, some of which can be determined independently from time-resolved spectroscopy and others estimated from measured light yield efficiency as a constraint assumed to apply in each kinetic order. The rates and parameters are used in the theory to calculate scintillation yield versus primary electron energy for comparison to published experimental results on four scintillators. Influence of the track radius on the yield is also discussed. Results are found to be qualitatively consistent with the observed scintillation light yield. The theory can be applied to any scintillator if the rates of the radiative and nonradiative processes are known.