Non-empirical peak shape methods based on the physical model of the one trap one recombination center model

Any experimental Thermoluminescent (TL) glow-peak contains the activation energy information of its corresponding energy level within the band gap in insulating materials. The theory of peak shape methods (PSM) correlates the macroscopic geometrical characteristics of a single TL peak with activation energy of the level responsible for the TL peak by assuming that the area under a TL peak can be approximated by the area of a triangle. In this way the geometrical characteristics becomes the measure of the activation energy. In the present work new PSM expressions are derived, which are not empirical as the existing ones but are based of the physical model of one trap one recombination (OTOR) center. Three cases are considered. (I) Delocalized OTOR for re-trapping probability smaller than the recombination probability. (II) Delocalized OTOR for re-trapping probability greater than recombination probability. (III) Localized transitions OTOR model. The system of differential equations of each case model were solved analytically using the Lambert $W$ function (or equivalently the Wright $\omega$ function). Then the resulted analytical expressions of TL intensity as a function of temperature were used to derive new PSM. The new PSM from all cases are formally exactly the same, having, however, strong differentiation in their coefficients. The functionality of the new expressions is tested and its comparison with pre-existing PSM is performed.