The systematics of double spiking

Abstract

It is known that the addition to a sample of a known isotopic mixture of the same element (the ‘double spike’) and the isotopic analysis of the resulting combination can be used to eliminate systematic discrimination during isotopic analysis. This paper presents a new formulation of the theory of double spiking, in which a geometrical representation is used. The criterion for absence of systematic discrimination is taken to be colinear points in a multidimensional diagram, representing spike, sample, and mixture. The condition is applied by requiring an appropriate vector product to be zero, with the result that explicit expressions are obtained for discrimination per unit mass in the form of ratios of two determinants of the order of three. The solutions so obtained were used to determine the propagation of errors in sample and mixture analyses, and it was shown that the presence of Pb206 and Pb208 in those double spikes which have been used for lead isotope analyses makes a very minor contribution to error propagation. Therefore, little can be gained by preparing the spike from purer separated isotopes.