Theoretical evaluation of error in the isotopic analysis of carbon and oxygen as CO (2)(+): considerations for determining two different isotopic abundance ratios simultaneously

The computations involved in the CO(2)(+) ion beam method of determining simultaneously a pair of constituent elemental isotopic abundance ratios P and Q (viz. (13)C/(12)C and (17)O/(16)O, or (13)C/(12)C and (18)O/(16)O, or (17)O/(16)O and (18)O/(16)O) are worked out, and the possible implications of their involvement as an analytical step are evaluated theoretically. It is shown, as an immediate consequence, that accurate measurements of the required isotopic CO(2)(+) abundance ratios (R(j) and R(k)) do not necessarily mean that the results (P; Q) are equally accurate. It is demonstrated that, and also explained why, the results can be far more inaccurate, or even in some cases more accurate, than the (R(j);R(k)) values themselves. It is clarified how the errors of analysis (delta(P) and delta(Q)) are actually governed, and elaborated further by evaluating their variations as a function of different possible parameters which control their magnitudes. The investigations thus help to predict the required analytical conditions for accurate isotopic analysis of carbon and/or oxygen samples of any origin as CO(2)(+). The considerations for the case of natural samples predict that, while it should be generally possible to simultaneously determine the isotopic abundance ratios of (13)C/(12)C and (18)O/(16)O with an accuracy better than the measurements themselves, the determination of either the ((13)C/(12)C and (17)O/(16)O) ratios or the ((17)O/(16)O and (18)O/(16)O) ratios, with an accuracy as good as that of the measurements, would be extremely difficult and may, in practice, be impossible.