Effect of radiation physics on inherent statistics of glow curves from small samples or low doses

A theory is developed to predict statistical noise in the trap populations of small samples or single grains subjected to high-energy ionizing irradiation. Using a model of the radiation process and a one-trap one-center model of a thermoluminescent (TL) material, the statistical behavior of the number of occupied traps during irradiation is predicted. The model focuses on the inherent physics of the process. Experimental sources of error are not considered. The interaction of radiation with the TL material is modeled in a simple way using the Bethe equation. The trap and center populations in the TL material are modeled both with the conventional phenomenological equations and also the more general Master Equation approach. The theory predicts, as the irradiation process proceeds, the mean, standard deviation, dispersion, skewness, and kurtosis of the probability distribution of occupied traps in the TL material. For the same applied dose, the standard deviation and dispersion of the trap population depend strongly on the type of radiation as well as the shape and orientation of the material. High-energy radiation sources, such as alpha, beta, or gamma rays, are found to produce standard deviations and dispersion much larger than low-energy sources, such as UV radiation. The results are summarized in tables which enable, for useful limiting cases, easy calculation of not just standard deviation but also skewness and kurtosis for various radiation sources and geometries.