Evaluation of an Exponential Model for Germanium Detector Efficiencies

Germanium detector efficiencies for vial geometries are modeled as ε = k[1- exp(-bh)]/bh, where h is the sample fill-level of the vial and k and b are constants relative to h. The model is tested against experimental data generated with 6 germanium detectors (8.8 to 90% standard efficiencies), 3 vials (24- to 64-mm diameters, 4- to 65-mm fill-levels), and 11 gamma energies (88 to 1836 keV). These data represent over 1000 comparisons between the model and experimental measurements. The overall agreement is within a few percent, with average deviations <1.0% and root-mean-square deviations <3%. For typical applications, the model requires only a few (2 to 3) vial calibration measurements, as opposed to the larger number (6 to 8) typically used for empirical data fitting. Methods and examples are discussed for use of the general model. Limits of the gen eral model, attenuation corrections for different sample media, and nondestructive assay calibrations for slab samples are also discussed. Also, possible model extensions are discussed for including gamma-energy dependence and Marinelli counting geometries.