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Excitation density, diffusion-drift, and proportionality in scintillators



Stopping of an energetic electron produces a track of high excitation density, especially near its end, and consequent high radial concentration gradient. The effect of high excitation density in promoting nonlinear quenching is generally understood to be a root cause of nonproportionality in scintillators. However, quantitative data on the kinetic rates of nonlinear quenching processes in scintillators are scarce. We report experimental measurements of second-order dipole–dipole rate constants governing the main nonlinear quenching channel in CsI, CsI:Tl, NaI, and NaI:Tl. We also show that the second of the extreme conditions in a track, i.e., radial concentration gradient, gives rise to fast (≤picoseconds) diffusion phenomena which act both as a competitor in reducing excitation density during the relevant time of nonlinear quenching, and as a determiner of branching between independent and paired carriers, where the branching ratio changes with dE/dx along the primary electron track. To investigate the interplay of these phenomena in determining nonproportionality of light yield, we use experimentally measured rate constants and mobilities in CsI and NaI to carry out quantitative modeling of diffusion, drift, and nonlinear quenching evaluated spatially and temporally within an electron track which is assumed cylindrical Gaussian in this version of the model.