Error-systematics of determining simultaneously the isotopic abundance ratios of natural lithium and natural boron as Li2BO2+

Abstract

Recently, we have shown how the errors delta(j) and delta(k), that occur when measuring the two different isotopic molecular abundance ratios required for analysis, are transformed into the actual errors of elemental isotopic analysis, (deltaEi/Ei)'s. With a view to gain further understanding as to how the errors (deltaEi/Ei)'s are governed, we now evaluate theoretically the effects of selecting different isotopic molecular pairs as the monitor pairs (j and k) for measurements, and of the measurement errors (delta(j) and delta(k)), on the results of analysis (the 6Li/7Li and the 10B/11B abundance ratios), by considering all the constituent elements of Li2BO2+ at their natural isotopic abundances. It is shown that the ratio of measurement errors, delta(j)/delta(k), is a more fundamental parameter than either the individual errors (delta(j) and delta(k)), or their sum, absolute value(delta(j)) + absolute value(delta(k)), in governing deltaEi/Ei. The important implication of this observation is that it reveals the possibility of achieving not only a desired level of accuracy in analysis, but even absolute accuracy (i.e. deltaEi/Ei = 0) by causing mutual cancellation of the effects of individual measurement errors delta(j) and delta(k), through proper regulation of measurement parameters. However, as the measurement errors cannot be pre-set, it is shown how selection of proper monitor pairs (j and k) can help achieve the desired accuracy in analysis. The present work sets guidelines for the more general problem of selecting monitor pairs to avoid larger errors in analysis.