Empirical efficiency and volume relationships for HPGe detectors

We have extended the empirical work of Vano et al.[1] relating the slope of the detector efficiency curve to the active volume for Ge detectors. The analysis was carried out using Monte Carlo techniques and covered a wide range of incident energies (200 keV-20 MeV) and active volumes (19.6 cm³–396 cm³). It is shown that the expression of Vano et al.[1] is only valid over the energy range 200 keV-3 MeV for active volumes <50 cm³. The upper bound decreases to 2 MeV for volumes of a few hundred cm³. The usable energy range can, however, be extended to 6 MeV by introducing higher order terms into the polynomial. Above this energy, the shape of the efficiency curve is better described by a non-linear function since linear forms fail simultaneously to fit large active volumes and high energies. We therefore propose a composite function which reduces to the form given in Vano et al. in the low energy/active volume limit. By comparison with the Monte Carlo results, it is estimated that relative efficiencies can be calculated to within 6% over the energy range 200 keV-20 MeV and active volumes 20 cm³–400 cm³. Since the largest errors occur for the smallest volumes, we recommend that for energies <3 MeV a two-fold approach be followed, i.e. using the expression of Vano et al.[1] for active volumes less than 50 cm³ and the proposed non-linear form for larger volumes. For high energy work (E > 3 MeV), we advocate the non-linear form. In this way, average errors can be kept 3%. Finally, we point out that the real power of the expression of Vano et al. lies not in predicting efficiencies, but active volumes.