General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert W-function

Thermoluminescence (TL), linear modulated-optically stimulated luminescence (LM-OSL) and continuous-wave optically stimulated luminescence (CW-OSL) are very well-established techniques for dosimetry of ionizing radiation as well as archaeological and geological dating. The simplest phenomenological model describing all these techniques is the one-trap-one recombination center model (OTOR). The differential equations describing the OTOR model can-not be solved analytically; therefore, the TL, LM-OSL and CW-OSL experimental results are treated through various analytical expressions, with the most general expression being empirical. In the present study, computational mathematics provides the tools to find a semi-analytical solution for the OTOR model thus deriving a general equation, which can provide elementary model peaks for any luminescence stimulation mode described by the OTOR model. The new general, semi-analytical expression was tested using reference curves derived using the numerical solution of the OTOR model. In the case of TL and LM-OSL, new conditions for the maximum were obtained and compared with the results of general order kinetics. Finally, an initial trial to convert the semi-analytical general expression into a purely analytical solution is also discussed.

► The Lambert W-function is introduced in the TL and OSL kinetic theory.
► The differential equations of OTOR model were semi-analytically solved using Lambert W-function.
► New single peak equations were derived for TL, LM-OSL and CW-OSL.
► New conditions for the maximum were obtained for TL and LM-OSL.