Performance of various mathematical functions for the in-situ relative detector efficiency towards its applicability...

The in-situ relative detection efficiency strongly influences the characteristics of the k₀-based internal monostandard neutron activation analysis (IM-NAA). In the present work, various mathematical functions were explored for the establishment of in-situ relative detector efficiency calibration and compared their performance based on the reduced chi-square (χ²) values. Among the various mathematical functions, the polynomial logarithm with 6th order was found to be associated with the minimum mean standard deviation for the experimental data and the lowest value of reduced χ² after carrying out multiple iterations using Nelder-Mead algorithm. Quality assurance of the function was tested by carrying out elemental quantification of the NIST SRM 1633b coal fly ash. Gamma energies of the activation products, ^152mEu, ⁵⁹Fe, ¹⁴⁰La, ²⁴Na and ⁴⁶Sc of the irradiated NIST standard were used for the in-situ relative full energy peak efficiency calibration of 30% HPGe detector. The sample was counted for different time intervals for the complete profiling of the elements present in the NIST SRM. The deviations for most of the elements were found to be within ±5% with respect to the certified values and ξ-score values were within ±2, demonstrating its better accuracy. This method was also applied satisfactorily to profile the elemental concentrations of alloy materials used in a thermal sensor guide tube of the steam generator in a test reactor.