Uncertainty in HPGe detector calibrations for in situ gamma-ray spectrometry

Semi-empirical methods are often used for efficiency calibrations of in situ gamma-ray spectrometry measurements with high-purity germanium detectors. The intrinsic detector efficiency is experimentally determined for different photon energies and angles of incidence, and a suitable expression for the efficiency is fitted to empirical data. In this work, the combined standard uncertainty of such an efficiency function for two detectors was assessed. The uncertainties in individual efficiency measurements were found to be about 1.9 and 3.1% (with a coverage factor k = 1, i.e. with a confidence interval of about 68%) for the two detectors. The main contributions to these uncertainties were found to originate from uncertainties in source-to-detector distance, source activity and full-energy peak count rate. The standard uncertainties of the fitted functions were found to be somewhat higher than the uncertainty of individual data points, i.e. 5.2 and 8.1% (k = 1). With the introduction of a new expression for the detector efficiency, these uncertainties were reduced to 3.7 and 4.2%, i.e. with up to a factor of two. Note that this work only addresses the uncertainty in the determination of intrinsic detector efficiency.