Theoretical derivation of a simplified form of the OTOR/GOT differential equation

• Published in: Radiation measurements 2013-12, Vol.59, p.160-164
• Main Authors: Lovedy Singh, L., Gartia, R.K.
• Format: Article
• Language: English
• Subjects: Derivation; Differential equations; Earth sciences; Earth, ocean, space; Empirical analysis; Exact sciences and technology; Formalism; General order kinetics; Geochronology; Isotope geochemistry. Geochronology; Mathematical analysis; Persistent luminescence; Radiation measurement; Scintillator; Simulation; Sound; Thermoluminescence
• ISSN: 1350-4487; 1879-0925
• DOI: 10.1016/j.radmeas.2013.04.022

A simplified form of the OTOR/GOT differential equation has been derived, which may be employed in the evaluation of TL curves for saturated (N = no) and non-saturated cases (N > no). The present eqn. is found to be theoretically correct and physically sound in comparison with empirical general order kinetics. It has been found that the TL curve evaluated using the present eqn. matches the TL curves evaluated using differential eqn. formalism, and spans the region from α = no/(100N) to α = 0.999 (where α is the ratio of the retrapping probability to the recombination probability). The simulated curve resembles a first order kinetics curve when α = no/(100N) and a second order kinetics curve when α = 0.999. However, comparison with general order kinetics for the intermediate range is not possible as a one- to-one correspondence between α and b cannot be made. Also, calculation in the saturated case is made simpler since only three unknown parameters (E, s and α) are required. •Theoretically and physically sound general order equation has been derived.•Can be employed in the calculation of saturated and non-saturated cases.•It is found to match with those evaluated using differential equation formalism.•Calculation in the saturated case requires only three unknown parameter.