Methodology for the simultaneous determination of the parameters associated with the k0 method of neutron activation analysis and experimental determination of the k0 and Q0 parameters for the 158Gd(n, γ )159Gd reaction

Abstract

A nonlinear adjustment framework for the calculation of k`0`-NAA parameters is presented, integrating covariance analysis with the Levenberg–Marquardt optimization algorithm. This approach enables the simultaneous adjustment of multiple parameters, explicitly incorporating their uncertainties and correlations within a unified fitting procedure. Experimental validation was performed using data from irradiations conducted in 2010, 2015, and 2023, resulting in new values of k`0` and Q`0` for several radionuclides. In particular, the adjustment framework enabled the determination of k`0` values for radionuclides and energies previously absent from the reference database. The results were compared with reference data, demonstrating improved reliability and precision in neutron activation analysis. Furthermore, the framework presented here enables the inclusion of different combinations of targets, energies, and irradiation dates in a single adjustment, providing greater flexibility for future applications.