FRAM’s Isotopic Uncertainty Analysis

The Fixed-Energy Response-Function Analysis with Multiple Efficiency (FRAM) code was developed at Los Alamos National Laboratory to measure the gamma-ray spectrometry of the isotopic composition of plutonium, uranium, and other actinides. We have studied and identified two different kinds of errors from FRAM analysis: random and systematic. The random errors come mainly from statistics and are easily determined. The systematic errors can come from a variety of sources and can be very difficult to determine. We carefully examined the FRAM analytical results of the archival plutonium data and of the data specifically acquired for this isotopic uncertainty analysis project, and found the relationship between the systematic errors and other parameters. We determined that the FRAM’s systematic errors could be expressed as functions of the peak resolution and shape, region of analysis, and burnup (for plutonium) or enrichment (for uranium). All other parameters such as weight, matrix material, shape, size, container, electronics, detector, input rate, etc., contribute little to the systematic error or they contribute to the peak resolution and shape and then their contributions can be determined from the peak resolution and shape. A. INTRODUCTION The Fixed-Energy Response-Function Analysis with Multiple Efficiency (FRAM) software has been developed and is continuing to be refined at the Los Alamos National Laboratory for the gamma-ray spectrometry measurement of the isotopic composition of plutonium, uranium, and other actinides [1–2]. FRAM can obtain a complete plutonium or uranium isotopic analysis using either a single planar or coaxial germanium detector or a CdTe detector. The actual detector type is not really important; what matters most are the resolution and the shapes of the peaks in the spectrum. The current version of FRAM (v4) can analyze a plutonium or uranium spectrum with a maximum peak resolution of 1.8 keV FWHM (full width at half maximum) at 122 keV for analysis of the 100-keV region, 2.2 keV at 122 keV for analysis of the low-energy region above 120 keV, and 3 keV at 1.3 MeV for analysis of the energy region above 500 keV. As for the peak shape, FRAM requires that the fraction of the peak area that is present in the low-energy tail of the peak must be less than 0.20 for all the peaks in the spectrum. Note that FRAM can analyze a peak with a large tail on the low-energy side of the peak. However, it cannot determine the tail on the highenergy side of a peak. Therefore, in spectra with peaks that have large high-energy tails, FRAM will not be able to accurately determine the isotopic compositions of the plutonium or uranium. Although FRAM can analyze spectra with very broad peaks and with large-tail peaks, such as those near the limits just mentioned, common sense would tell us that the results from those