A New statistical model and a redefinition of isotopic ratio; Correction and evaluation in ultra-microanalysis

Osawa, Takahito  

A decrease in the number of measured atoms reveals a serious problem in the concept of isotopic ratio. The first fundamental defect of the isotopic ratio concept is imperfect reversibility of numerator and denominator, leading to two isotopic compositions inconsistent with each other. Secondly, the probability distribution of isotopic ratio is not the same as the binominal distribution, indicating that the mean isotopic ratio is systematically higher than the true isotopic ratio. The potential uncertainty of isotopic ratio and the gap between the obtained isotopic ratio and the true one deriving from the number of sampling atoms and the isotopic ratio are vigorously evaluated here. Isotopic ratio must be below 1, to reduce the effects of distorted probability distribution of isotopic ratio. In the precise measurement of isotopes, the potential error and disagreement with the true value must be tested when the number of sampled atoms is extremely few.