We report measurements of electron response of scintillators, including data on 29 halides, oxides, organics, and fluorides. We model the data based on combining the theories of: Onsager, to account for formation of excitons and excited activators; Birks, to allow for exciton-exciton annihilation; Bethe-Bloch, to relate electron stopping to its energy; and Landau, to describe how fluctuations in the linear energy deposited (dE/dx) lead to nonproportionality's contribution to resolution. In general there is satisfactory agreement with experiment, in terms of fitting the electron response data and reproducing the literature values of resolution. We find that the electron response curve shapes are more affected by the host lattice than by the activator or its concentration.

Analytical expressions for the local light yield as a function of the local deposited energy $\left(-dE/dx\right)$ 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.

Recent years have seen significant advances in both theoretically understanding and mathematically modeling the underlying causes of scintillator non-proportionality. The core cause is that the interaction of radiation with matter invariably leads to a non-uniform ionization density in the scintillator, coupled with the fact that the light yield depends on the ionization density. The mechanisms that lead to the luminescence dependence on ionization density are incompletely understood, but several important features have been identified, notably Auger-like processes (where two carriers of excitation interact with each other, causing one to de-excite non-radiatively), the inability of excitation carriers to recombine (caused either by trapping or physical separation), and the carrier mobility. This paper reviews the present understanding of the fundamental origins of scintillator non-proportionality, specifically the various theories that have been used to explain non-proportionality.

The scintillation yield and decay time of ${\mathrm{LaBr}}_3$ doped with 0.2%, 0.5%, and 5% cerium were studied between $80\mathrm{K}$ and $600\mathrm{K}$. ${\mathrm{LaBr}}_3:5\%{\mathrm{Ce}}^{3+}$ on a photomultiplier tube shows at $300\mathrm{K}$ a very high scintillation yield of $22800$ photoelectrons per MeV ($64000$ photons per MeV) with a decay time of $16\mathrm{ns}$. At $600\mathrm{K}$ the yield decreases by $\simeq 15\%$. The scintillation yield of ${\mathrm{LaBr}}_3:0.2\%{\mathrm{Ce}}^{3+}$ is $19800$ photoelectrons per MeV ($56000$ photons per MeV) at $300\mathrm{K}$ with a decrease by $\simeq 50\%$ at $600\mathrm{K}$ and a main scintillation decay time around $30\mathrm{ns}$. The appearance of slow components in the Ce emission indicates a relatively slow energy transfer from the host crystal to Ce. The presence or absence of slow components depends on both concentration and temperature. The results are analyzed and interpreted with a model that comprises prompt charge carrier trapping by Ce and delayed excitation of Ce by means of thermally activated transport of self-trapped exciton defects. The results of the study provide detailed information on the scintillation mechanism. Besides presenting experimental data, the different energy transfer processes are quantified.