Use of a correlated compound-binomial model to assess absence of non-counting noise in Pu-isotope ratios measured by AMS at LLNL

Abstract

Methods for error analysis pertaining to isotopic ratio measures made by accelerator mass spectrometry (AMS) typically focus on accuracy/precision of detected counts of a single rare isotope (e.g. 14C), relative to a current strength indicating the abundance of an isotope present in far greater amounts (e.g. 13C). Because AMS analysis of the relative abundance of actinide isotopes involves comparing detected counts that each correspond to a relatively rarely occurring isotope, error analysis is complicated by correlations between isotope-specific counts and by isotope-specific dead times, that affect each pair of isotope-specific counts. A new method of error analysis described here was developed specifically to estimate and characterize error in AMS measures of actinide isotope ratios. The method models a series of detected pairs of isotope counts as correlated compound-binomial (censored trinomial contingency) data, provides an approximately unbiased moment-method estimator of a common isotopic proportion (or ratio) corresponding to any data-pair series, and provides a corresponding homogeneity test for isotopic proportions observed within any data-pair series. Applications of this method to AMS measures of the relative abundance of plutonium isotopes, in samples analyzed at the Lawrence Livermore National Laboratory Center for AMS, revealed that observed measurement errors were nearly all attributable to modeled counting errors.