Approximated total and full energy peak intrinsic efficiencies of gamma detectors for measuring systems design

Functions characterizing the performance of gauges based on gamma radiation correlate the design parameters and the variables to be measured. The radiation detector is a major component of the gauge. Analytic expressions for the total and full energy peak efficiencies were derived using the mean chord length in the detector's sensitive volume. The errors associated with this approximation were estimated from the distribution of the chord length. The uncertainties found in the determined total intrinsic efficiency are in the range of a few percent for most practical industrial gauges, and up to about 20% in the worst cases. The approximate values are higher than the experimental or theoretical results. The intrinsic full energy peak efficiency determined by the analytic expression is compared with experimental results for NaI 1″ × 1″ and 3″ × 3″ with ¹³⁷Cs and ⁶⁰Co sources. Results from Monte Carlo calculations agree within 10% with the determination. These errors are acceptable at the design state, as later both source activity and counting time may be adjusted to yield the required statistical uncertainty.