Fractionation Corrections in Radiocarbon Dating

Abstract

Recent experimental work has suggested that the relative fractionation of 14C to 13C may differ from the accepted value of b = 2. In order to explore the implications of this possibility, the standard formulae for correcting radiocarbon dates for fractionation effects are rederived, but without making any of the usual assumptions or approximations. A generalized dating equation A(SN) = Beta {[R(ST)^(o)]/[R(ST)]}^(b) A(ON)exp(-t(cal)/8267) is derived (where A(SN) and A(ON) are normalized sample and standard activities, Beta is a factor which reflects changes in atmospheric 13C and 14C content, {[R(ST)^(o)]/[R(ST)]}^(b) accounts for post-depositional changes in sample 13C ratio, and tcal is calendar age in years before ad 1950. The errors in calculated ages which might arise from different b values are estimated and shown to be small relative to other dating uncertainties. The effect of b as unequal to 2 may be important in the calibration of radiocarbon dates using tree-ring samples of known age. A theoretical analysis suggests that b as unequal to 2 effects may result in a correlation between age anomaly (ie, the difference between radiocarbon age and calendar age) and sample 13C data. However, an analysis of published data reveals no meaningful correlation. This result, while not eliminating the possibility that b does not equal 2, highlights its unimportance even in this high-precision application of radiocarbon dating.