A numerical method for the calibration of in situ gamma ray spectroscopy systems

High purity germanium in situ gamma ray spectroscopy systems are typically calibrated using pre-calculated tables and empirical formulas to estimate the response of a detector to an exponentially distributed source in a soil matrix. Although this method is effective, it has estimated uncertainties of 10-15%, is limited to only a restricted set of measurement scenarios, and the approach only applies to an exponentially distributed source. In addition, the only soil parameters that can be varied are density and moisture content, while soil attenuation properties are fixed. This paper presents a more flexible method for performing such calibrations. For this new method, a three- or four-dimensional analytical expression is derived that is a combination of a theoretical equation and experimentally measured data. Numerical methods are used to integrate this expression, which approximates the response of a detector to a large variety of source distributions within any soil, concrete, or other matrix. The calculation method is flexible enough to allow for the variation of multiple parameters, including media attenuation properties and the measurement geometry. The method could easily be adapted to horizontally non-uniform sources as well. Detector responses are calculated analytically and Monte Carlo radiation transport simulations are used to verify the results. Results indicate that the method adds an uncertainty of only approximately 5% to the other uncertainties typically associated with the calibration of a detector system.