Thermoluminescence glow curve deconvolution functions by continued fractions for different orders of kinetics

Abstract

The shape of the peaks in thermoluminescence (TL) dosimetry can be represented by the so-called temperature integral. In this paper, we present a very efficient method, based on a continued fraction approach to the incomplete gamma function, intended to calculate the overall temperature integral which includes the frequency factor ∝ T a . The single glow-peak algorithm for linear and exponential heating rates is derived. In the first case, the method provides a good approximation with a maximum relative error of 1.1×10−5 within the 0.1≤E/kT≤90 range in the case of a=0. It is shown that, in general, the method is efficient, converges quickly and can be adopted in the numerical fitting of glow lines in order to obtain the parameters relevant to TL. The utility of this approach is exemplified by adjusting the standard lithium flouride doped with magnesium and titanium (LiF): Mg, Ti (TLD-100) using five and six thermoluminescent peaks, determining that peak 6 is present and observable in the analysed spectrum. Finally, methods such as asymptotic expansion of the temperature integral by the asymptotic series approximation, the convergent series approximation, the Lagrange continued fraction approximation and a new obtained continued fraction approximation are compared with the method proposed here in the case of linear heating.