A Numerical Method for the Calibration of in Situ Gamma Ray Spectroscopy Systems

Abstract

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.

A method for determining the analytical form of a radionuclide depth distribution using multiple gamma spectrometry measurements

“…However, if f(t,x 1 ,x 2 ,., x n ) and its parameters are known, then Eq. (4) can be solved numerically using an adaptive Simpson's quadrature (Dewey et al, 2010).…”

“…Multiple measurements can be made using an adjustable cylindrical collimator and circular lead shield described elsewhere (Dewey et al, 2010). The geometry is shown in Fig.…”

“…Additionally, a lead circular center shield may be used. Details concerning the t geometries and the techniques used to calculate the detector response are reported elsewhere (Dewey et al, 2010). For each t geometry used, the following is generated:…”

“…Further research is required before this method can be applied with confidence to an actual measurement scenario. How input errors affect the selected parameters for each possible distribution has been examined in previous papers for some of the distributions presented (Dewey et al, 2010); however, some of the distributions error properties need to be further investigated. Also, how input errors affect how the output distribution is selected should be examined more thoroughly.…”

Integration of Ground- Penetrating Radar and Gamma-Ray Detectors for Nonintrusive Characterisation of Buried Radioactive Objects

“…For a radioactive point source buried in an air-soil half-space as shown in Figure 1, the flux Fp measured by the detector placed above the ground is given by [20]: Fp=SpAr(E,θ)Ce(E)4πh+dprefixcosθ2e−μm(E)ρahprefixcosθe−μm(E)ρbdprefixcosθ where E is the energy of the point source (keV), θ is the angle of incidence of the source with the detector (radians), d is the depth of the source in the soil (cm), Sp is the activity of the source (Bq) and Ar(E,θ) is the angular response of the detector to a point source of energy E incident at angle θ. This is a dimensionless quantity and is obtained by measuring the response of the detector to a point source at angles varying from 0–π/2.…”