New best practices for efficiency fitting for accurate gamma-ray spectroscopy with semi-conductor detectors

Gamma spectroscopy of high energy photons is a commonly applied technique in fundamental en applied research. In such studies one of the goals is to determine an a-priori unknown source activity or intensity of a transition. In order to do so, one needs to evaluate the efficiency response function. This process involves the measurement of count rates of lines emitted in the decay of calibration sources, followed by an empirical fitting procedure. Such calibration sources have known activity, yet the uncertainty on this activity and the positioning of the source are often the biggest contributions to the total error budget. While investigations of such an efficiency response function are often performed, reports in literature neglect the correlation between efficiencies determined from different lines. Consequently, the fitted efficiency will have both an unreliable central value and uncertainty. Furthermore, in such cases, the relative efficiency between two energies becomes unreliable as well. In this work, we start by showing some common issues that occur in the conventional fitting methods. This is followed by several suggestions for best practices with increasing levels of complexity: (1) Scaling the energy to a reference value in order to reduce correlation; (2) Using Bayesian methods to treat the activities as fit parameters; (3) Increasing the robustness by including hyperpriors on the activity uncertainties.