A new analytical equation for the dose response of dosimetric materials, based on the Lambert W function

Abstract

The dose response of dosimetric materials is of fundamental importance in luminescence dosimetry and luminescence dating applications. In this paper we present a new analytical equation describing the trap filling process during irradiation of insulators, starting from the one trap and one recombination center model (OTOR). Even though this model has been studied extensively during the past 50 years, there are no published analytical solutions for the dose response n(D) in this model, where n is the concentration of filled traps and D is the irradiation dose. The new analytical equation contains the well-known Lambert function W, which has been used extensively during the past 20 years in diverse research areas. Under certain conditions, the new n(D) equation leads to the empirical saturating exponential function (SE). The new equation contains a smaller number of fitting parameters than two other commonly used fitting functions, the saturating exponential plus a linear function (SEL), and the double saturating exponential (DSE). In addition, the new equation contains physically meaningful parameters. Examples are shown of using the new equation to fit a variety of experimental signals, namely thermoluminescence (TL), optically simulated luminescence (OSL), isothermal TL (ITL) and electron spin resonance (ESR).