A Semiempirical Method for Calculating Detector Efficiency as a Function of Distance

The assumption that the efficiency of a detector varies as the inverse square of the distance is valid only for a point source and a point detector in vacuum. To account for the finite size of the detector, we use the idea of an effective interaction center for that detector. The detector efficiency can then be described as varying with the inverse square of the distance between the source and the energy-dependent location of the effective interaction center. We present two simple expressions, one for the location of the effective interaction center and one for a normalization parameter. The expressions were obtained by a two-stage fitting procedure and are valid for gamma-ray energies between 60 keV and 2.615 MeV at distances of 10 cm or greater. The efficiencies so obtained agree with measurements to about 5%.