A kinetic model incorporating both localized and delocalized recombination: Application to the dependence of the TL dose response on photon energy

A conduction band/valence band kinetic model for thermoluminescence (TL) dose response is described which incorporates both localized and delocalized recombination mechanisms. The model is capable of simulating the linear/supralinear behaviour of TL dose response and, as well, the experimentally observed decrease of the supralinearity with decreasing photon energy. These characteristics are observed in the dose response of the various peaks in the glow curve of LiF:Mg,Ti and in other TL materials. In the irradiation stage, the model uses nanodosimetric considerations to describe the electron-hole concentration, ne-h and e-only concentration, ne, filling rates with dose of a spatially correlated trapping center/luminescent center (TC/LC) complex. The linear dose response arises from the dominant role of the geminate/localized recombination at low dose. The supralinearity arises due to the increased relative intensity of delocalized recombination at high dose coupled with a decrease in the efficiency of the competitive processes with increasing dose. The dependence of the supralinearity on photon energy is obtained by adopting different dose-filling-rates of ne-h and ne as a function of photon energy. Specifically, for low dose-levels below ~1-10 Gy, ne-h/ne is assumed to increase slowly/linearly with dose and to increase slightly with decreasing photon energy below ~100 keV due to the increasing average ionization density of the electron tracks. For levels of dose above ~10 Gy, the ratio increases more rapidly in an exponential manner with later entry to maximum values with decreasing photon energy. The demarcation dose of ~1-10 Gy separating the linear from the exponentially increasing behaviour of ne-h/ne corresponds to the approximate onset of supralinearity observed for composite peak 5 in LiF:Mg,Ti. This assumed behaviour for ne-h/ne is consistent with the structure/size of electron tracks and the onset and relative importance of intra-track versus inter-track recombination.