The Calculation of Self Attenuation Factors for Simple Bodies in the Far Field Approximation

ABSTRACT

Microsoft Excel spreadsheet functions have been developed for the calculation of the self attenuation of gamma-rays in simple bodies viewed from afar. The cases are a uniform rod viewed along its axis, a sphere viewed along a diameter and a cylinder (or disk) viewed along a mid-plane diameter. The results for the former two cases can be expressed in closed form while the algorithm used for the third is described. We also develop useful expressions for small and large lump cases. The self attenuation functions have been used along with other numerical methods to generate and validate test data for exercising a proposed new lump correction algorithm based on exploiting the differential attenuation of different energy g -rays emitted by an item.

INTRODUCTION

The measurement of special nuclear materials such as ²³⁵U and ²³⁹Pu, in radioactive waste by the application of high resolution gamma-ray spectrometry is a widely used technique [1]. If the nuclides are present the form of “lumps” (such as shavings, chips, pellets, foundry spills, crevice accumulations and the like) rather than as dilutely distributed activity in and on the bulk waste matrix, then self attenuation may occur. Self attenuation is not accounted for by the usual transmission source and weight based matrix correction factor methods. This is because dense lumps of significant size, sufficient to affect the assay result, are still physically small in relation to the overall size of most waste container types [2]. Therefore, traditional gross matrix correction methods are not sensitive to the presence of lumps.

If the presence of lumps goes unrecognized then an assay system calibrated using dilute (minimally absorbing) standards will underreport when put into operation. This is because the number of g-rays emerging from the lump per unit mass of nuclide present will be less than assumed.

In order to examine the importance of self attenuation by numerical simulation it is desirable to have a simple way to calculate the attenuation factor for lumps in a variety of shapes. In essence, a shape defines a particular distribution of emergent path lengths. By using a given lump shape or combination of shapes various measurement scenarios can be played out to examine the impact of self attenuation as a function of photon energy and nuclide mass given assumptions on the nature (chemical composition, density, enrichment) of the lumps. This is important to do as part of the assessment of a reasonable and justifiable total measurement uncertainty and also when bounding or limiting assay results are to be reported.