Approximate Methods for Calculation of Intrinsic Total-Absorption-and Double-Escape-Peak Efficiencies for Ge(Li) Detectors

Approximate methods are presented for calculation of intrinsic total-absorption-and double-escape-peak efficiencies of Ge(Li) detectors. These methods utilize "average" characteristics of gamma-ray photon interactions with matter, and, while developed in this paper for specific application to the Ge(Li) detector efficiency problem, should be applicable to any gamma-ray detector or absorptive medium. The technique for total-absorption-peak efficiency determination includes the use of an "average-photon energy-degradation curve" and of the Dirac chord method for calculation of collision probabilities. The average-photon energy-degradation curve is obtained from differential Compton collision cross sections and detector material total-crosssection characteristics; it is independent of detector size and shape. The Dirac chord method is then used to determine the probability of further collisions for photons "generated" within the detector volume. In the model these probabilities are functions only of a characteristic detector dimension, s??, where s is the average chord length and ?? is the total linear attenuation coefficient. Double-escape-peak efficiencies are determined through the calculation of the average probability of occurrence of the following three phenomena: (1) pair production, (2) electron-positron absorption, and (3) annihilation-photon double escape. Complete working curves and expressions are included to enable convenient utilization of these techniques. Example results are compared with efficiency determinations made experimentally and by Monte Carlo calculations.