An analytical calculation of the peak efficiency for cylindrical sources perpendicular to the detector axis in gamma-ray spectrometry

An analytical expression for the so-called full-energy peak efficiency ε(E) for cylindrical source with perpendicular axis to an HPGe detector is derived, using point-source measurements. The formula covers different measuring distances, matrix compositions, densities and gamma-ray energies; the only assumption is that the radioactivity is homogeneously distributed within the source. The term for the photon self-attenuation is included in the calculation. Measurements were made using three different sized cylindrical sources of 241Am, 57Co, 137Cs, 54Mn, and 60Co with corresponding peaks of 59.5, 122, 662, 835, 1173, and 1332 keV, respectively, and one measurement of radioactive waste drum for 662, 1173, and 1332 keV.