Superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals in luminescence materials: An analytical approach

The phenomenon of superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals has been reported for several important dosimetric materials. We develop new analytical equations for the filling of traps and centers during irradiation and for the read-out stage of annealed luminescence materials, within the context of a two-trap and two-center model. The equations are applicable for both TL and OSL signals in annealed dosimetric materials, and are derived under the assumptions of low irradiation doses and dominant strong retrapping (weak recombination) processes. For low doses all traps and centers display linear dose response, which leads to quadratic dose response of the integrated TL/OSL signals. A new analytical expression is presented for this well-known quadratic dose dependence, in terms of the kinetic parameters in the model. The effect of elevated irradiation temperature on the integrated TL/OSL signals is also considered, and analytical expressions are obtained for this situation as well. A new type of dose-rate effect is reported based on the modeling results, which is due to irradiation during elevated temperatures. The accuracy of the analytical expressions is verified by comparing with the results of numerical simulations.