A NUMERICAL APPROACH TO PU GAMMA-RAY SELF-ABSORPTION CORRECTION

Abstract

Self absorption is a significant source of error in the assay of Pu-bearing waste by gamma-ray spectrometry. Differential absorption of the 129keV and 414keV lines can be used as a means of determining self-absorption and applying a correction. With a view to refining this technique, the behaviour of the 129keV and 414keV lines from ²³⁹Pu as they emerge from lumps of Pu has been studied using a point-kernel point-detector theoretical model for a range of lump shapes, densities and masses. The shapes include right circular cylinders, rods and rotating square plates and the densities range from those typical of PuO₂ to pure metal. The mass ranged studied covers 1 mg to 350g.

Variation in shape and density for Pu lumps may be expected to complicate any correction method. However, from inspection of 3D plots of total lump mass against apparent 129keV and 414keV masses it is observed that points on a plot of apparent masses of the 129keV against the 414keV line of constant total mass lie on continuous curves, irrespective of the shape or density of the lump. This observation has been used to derive a lump correction approach by a 3D fitting algorithm to the computed apparent mass data.

A model has been devised to determine the self-absorption corrected mass from the observed apparent 129keV and 414keV line masses. The paper will present a description of the model, results in the form of 3D plots, a description of the fitting method and results obtained for the corrected mass for theoretical samples and for real samples of known total Pu mass for which the 129keV and 414keV lines have been measured. A discussion of the applicability of this method for multiple lumps is presented.

Keywords: NDA, Plutonium, Self-Absorption

Introduction

During previous tests at Canberra an issue with the plutonium self-absorption correction was highlighted; for our AE 4043/5 Pu sample [1], a consistent over-correction of 50% was observed. The possibility of inaccurate measured line intensities as the source of the problem was ruled-out by comparing uncorrected 129keV and 414keV assay results with calculated SAC (self absorption corrected) emission rates for this sample. This prompted detailed analysis of the Pu self-absorption behaviour for various lump shapes and materials (densities) and hence the search for a more accurate method. One resolution to this problem is to calculate self-absorption factors using analytical methods [2]. Due to the extreme non-linearity in the nature of gamma attenuation these methods generally require some degree of approximation.

The standard SAC algorithm offered in the NDA2000 data acquisition and analysis suite [3] was developed empirically for the assay of canned radioactive waste containing a distribution of lump sizes. The nature of the empirical approach involved comparing gamma-assay result against calorimetric based assays of the same item. The form of the correction is shown below:

where M _i and E _i are the activity and energy of the i’th line, M^o is the corrected activity of the nuclide and â is a model parameter. This correction can be derived from first principles under the assumptions that the self-absorption is not severe and therefore the method may be less appropriate for single, mass and encapsulated sources. An option to the engine allows for the possibility that only a fraction of the Pu is affected. A further obvious limitation of the NDA2000 approach which shall not be addressed further here is the embedded 1/E dependence appearing in the exponent. The motivation behind the present study was to find a more generic approach with broader applicability.