Synthetic ion beams with instantaneous and temporal characteristics appropriate to thermal ionization mass spectrometry (TIMS) were mathematically generated and analyzed to determine the effects of using a mixed (sup 233)U-(sup 236)U spike (double-spike) in the analysis of uranium isotopes. The instantaneous beam characteristics are the intensities (e.g., counts per second) modeled with a Poisson distribution plus a component of random noise that simulates the detection processes. Several beam intensity and mass fractionation vs. time functions were modeled to simulate a range of sample sizes and the commonly employed methods of data collection. These beam profiles were also generated with different noise levels, and signal-to-noise vs. analytical precision diagrams are presented. Modeling focused on natural uranium, where (sup 238)U/(sup 235)U = 137.88, and on the ability of a given method to determine precisely and accurately small variations in this ratio. Practical limits on precision were determined to be 20-30 ppm, which is consistent with precision seen for other elements by state-of-the-art TIMS. The TIMS total evaporation method was compared directly with the double-spike method. While similar analytical precisions are obtained with either method, the double-spike method of correcting for analytical bias gives more accurate results. The results of a total evaporation analysis will deviate from true by more than the analytical precision if as little as 0.05% of the signal is not integrated, whereas the accuracy and precision of the double-spiked analyses are always linked.
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