Efficiency fitting for TDCR measurement data using polynomial approximation and the Newton–Raphson method

A tritium radioactivity source was measured by triple-to-double coincidence ratio (TDCR) equipment of the National Metrology Institute of Japan (NMIJ), and measured data were fitted using polynomial approximation and the Newton–Raphson method, a technique whereby equations are solved numerically by successive approximations. The method used to obtain the activity minimizes the difference between statistically calculated data and experimental data. In the fitting, since calculated statistical efficiency and TDCR values are discrete, the calculated efficiencies are approximated by quadratic functions around experimental values and the Newton–Raphson method is used for convergence at the minimal difference between experimental data and calculated data. In this way, the activity of tritium was successfully obtained.

► The TDCR data were fitted using polynomial approximation and the Newton–Raphson method. ► Activity was then successfully obtained by this fitting. ► The fitting procedure developed in this paper enables kB to be extracted for the scintilltor being used.