ASSAY ERRORS INTRODUCED BY MATRIX CORRECTION USING TRANSMISSIONS DETERMINED BY THE MATERIAL BASIS SET METHOD

ABSTRACT

Nondestructive assay instruments such as segmented gamma scanners and tomographic gamma scanners generally use measured transmission values to calculate correction factors for attenuation effects. Current practice is to use one or more transmission sources with peak energies close to the assay energy and to use interpolation techniques to obtain transmissions at each assay energy. This practice limits the source radioisotopes that are useful for each assay radioisotope and can lead to using isotopes that are expensive or have half-lives so short as to require frequent replacement. Use of the Material Basis Set (MBS) approach to perform the transmission interpolation or extrapolation provides more flexibility in choice of transmission sources and provides transmission values over a wider range of assay energies. A previous computational study by the authors [1] quantified assay errors introduced by the MBS method for four radioactive sources and eight diverse matrix types assuming exact values of measured transmissions. The present study includes the effect of statistical uncertainties in measured transmissions. To determine the effect of these uncertainties on the MBS-determined values, measured transmission uncertainties were corrected for intensity and attenuation to estimate measured transmission uncertainties for the different assay scenarios. Using these estimated uncertainties, the assay bias and random error introduced by the MBS method plus transmission measurement uncertainties was determined. Particular attention was given to extrapolation to low transmission values at low gamma ray energy (60 keV), where the energy variation is the steepest.

INTRODUCTION

The measurement of the quantity of one or more radioisotopes in a container by detection of the emitted gamma rays generally requires that a correction be made for attenuation of the gamma rays by the material containing the radioisotopes. The correction can be calculated directly if the composition, density, and uniformity of the material are known along with the activity distribution. Most often this is not the case, and the correction is made based on measured transmissions of gamma rays through the container. The usual method is to use a separate “transmission” gamma ray source that emits gamma rays at one or more energies near the assay energy. Transmissions through the container are measured at the transmission source energies, and then these values are interpolated or extrapolated to the assay energy or energies using exponential, linear, or quadratic functions or polynomials in logarithm-logarithm space. Sources with energies most appropriate for assay of some important radioisotopes, such as ²³⁵U and ²³⁹Pu, have relatively short half lives and require frequent replacement. Also, a single transmission source used with traditional interpolation and extrapolation methods is not well suited for attenuation correction over a wide range of energies, as needed for an assay instrument that quantifies many radioisotopes with each assay sequence. Use of the MBS method determines the transmission through a container over a wide range of energies based on measured transmissions at only a few strong, disparate energies. Also, this method can be applied using transmission sources having multi-year half-lives and needing replacement at no less than 7-year intervals. The calculation-based study presented here quantifies the assay bias and random errors for each assay scenario due to attenuation-correction using the MBS and provides guidance for its use.