Cox, M G; Michotte, C*; Pearce, A (2007) Measurement modelling of the International Reference System (SIR) for gamma emitting radionuclides. Technical Report. BIPM.

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Abstract

The photon and beta effciency curves of an ionization chamber, as part of the SIR (International Reference System for activity measurements of gamma-ray emitting radionuclides), have historically been determined using an iterative approach. That approach accounts for the influence of gamm-ray-emitting impurities on the SIR measurement data based on experimental knowledge of the contributing effects or using the effciency curves during the iterative process.
Extrapolation of the curves is needed at the ends of the energy range to cover all photon and beta-particle energies of interest. The approach described here is based on a model that at the outset accounts for all available information, including impurity corrections and beta spectrum shapes. It also accounts for the uncertainties and known corrections associated with the SIR measurement data, the nuclear reference data and other effects. The only empirical parts of the model are the mathematical forms selected for the efficiency curves. Rather than using conventional functions such as polynomials, the approach works with the exponentials of polynomials. These forms are capable of exhibiting physically feasible behaviour throughout the energy range, even though there is relatively sparse radionuclide data available at high energies.
Rather than correcting the measurement data for impurities, as is conventional in this area, the model itself is adjusted. The benefit of this approach is that the polynomial coefficients can be determined using generalized non-linear least-squares minimization. The adjusted model matches the SIR measurement data as closely as possible, taking account of the uncertainties and correlations indicated above. Although the solution to this least-squares formulation requires iterative solution algorithmically, it is not iterative in the sense of previous methods.
This process provides estimates of the effciency values of the ionization chamber, and the associated uncertainties, at any photon or beta energy. The uncertainties associated with the response of the ionization chamber for all radionuclides of interest are also evaluated.

Item Type:	Report/Guide (Technical Report)
Keywords:	modelling, uncertainties, numerical methods
Subjects:	Mathematics and Scientific Computing Mathematics and Scientific Computing > Modelling
Publisher:	BIPM
Last Modified:	02 Feb 2018 13:15
URI:	http://eprintspublications.npl.co.uk/id/eprint/4297

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