Total dose (TD) formula for uranium saturation-uptake model for ESR and TL dating

Models of uranium-uptake at the early stage and at a constant rate (linear-uptake) were re-examined for ESR dating of fossil bones and teeth. An analytical equation for the total dose of natural radiation (DT) was obtained for uranium uptake in the form of a saturation function, Cυ(t) CUS (1 -e-if), where CUS is the saturation level of the uranium and λ is the uranium uptake rate, presumably associated with the decomposition rate of organic materials and the diffusion of uranium. The present uranium content Cυ(T) Cυ* at the unknown age T gives CUS Cυ*/(1 - ei./T) and so λ = -(1/T)In(1 -Cυ*/CUS). The DT calculated by taking 238U-series secular disequilibrium into account is reduced to that of an early uptake for λT >> 1 and to that of a linear uptake for λT << 1. The activity ratios of 234U/238U and 230Th/238U for the saturation-uptake model are also given. The model of linear uptake is applicable for Cυ* < CUS. The curves of DT as a function of T was calculated for CUS as a parameter. (author)