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 approximately 200 keV-3 MeV for active volumes < 50 cm3. The upper bound decreases to approximately 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 approximately 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.