A semi-empirical model of the efficiency curve for extended sources in gamma-ray spectrometry

A semi-empirical formula for the full energy peak efficiency of extended sources in the range from 4 to 3000 keV is presented, taking into account self-absorption in the sample. The formula is based on physically sound premises and features a low number of free parameters, which exhibit physically viable values. Along with very good fits it furnishes, this makes the model suitable for extrapolation of the efficiency values towards the energies where measurements are not available. The model we use is based on the assumption of independence of the intrinsic peak-to-total ratio on the emission point of the gamma-ray. For extended sources, it features a term which takes into account the attenuation of gamma-rays in the sample. The proposed model was tested against a number of experimental efficiency curves measured with point and extended sources on n- and p-type HPGe detectors, as well as against data sets obtained from Monte Carlo calculations using the GEANT and MCNP codes.