Superlinearity revisited: A new analytical equation for the dose response of defects in solids, using the Lambert W function

In a recent paper we developed a new analytical equation for the dose response of dosimetric materials based on the Lambert W function, within the framework of the simplest model, the one trap one recombination center model (OTOR). In the present paper we extend this recent work to develop a new analytical equation describing the nonlinear trap filling process during irradiation of insulators. The new equations are developed within the framework of a more complex two trap and one recombination center model (2T1R). The model has been proposed previously to explain the nonlinear dose response function of luminescence signals in solids, and is based on competition between two traps during irradiation. The new analytical equation describes the superlinear behavior commonly exhibited by dosimetric materials and contains meaningful physical parameters. It is tested by fitting previously published dose response curves for dosimetric materials.