Empirical estimation of the gamma-ray full-energy absorption efficiency of cylinders and slabs from 0.14 to 2 MeV (2009)

We present an empirical formula for estimating the gamma-ray full-energy detection efficiency of slabs and cylinders from 140 keV to 2 MeV. It can be applied to any material whose chemical formula and density are known, from LiCaAlF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> to PbWO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> . Monte-Carlo calculations can be used for this purpose, but they require more computer time and resources than the formulas presented here. To provide control points for the empirical fitting procedure, we used Geant4 to track the interactions of 10 million gamma rays and determine the fraction that are fully absorbed in the cylinder or slab. The control points (a total of 780) included cylinders and slabs of five different thicknesses from 1 cm to 100 cm; six gammaray energies from 0.14 to 2 MeV; and 13 materials (BaF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , Bi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> , CaF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , CsI, Cd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.9</sub> Zn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.1</sub> Te, Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> , Ge, LaBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , LiCaLaF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> , Lu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> , NaI, PbWO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , YAlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ). An empirical formula containing 30 free parameters was separately fit to the Monte Carlo control points for the cylinders and the fit was repeated for the slabs. The rms deviations between the formula and the control points was 0.0184 for the cylinders and 0.0198 for the slabs. The reliability of the empirical model was checked by deleting each compound in turn, fitting the model to the remaining 12, using that model to estimate the efficiencies of the deleted material, and then computing the rms deviation between that those efficiencies and the calculated efficiencies. The average of the 13 standard deviations was 0.0202 for the cylinders and 0.0205 for the slabs. This shows that if any compound is omitted from the fit, it could be reliably calculated from the best-fit formula that used only the other 12 compounds.