On the densities of etchable fission tracks in a mineral and co-irradiated external detector with reference to fission-track dating of minerals

Abstract

The ratio R of the densities of etchable fission tracks in a mineral and co-irradiated external detector is shown to depend on the length ratios of the latent ( L f/ L f′) and etched fission tracks ( L e/ L e′) in the two media. Calculations of L f for apatite, titanite zircon and L f′ for muscovite external detectors allow a precise determination of R, and confirm that neglecting R could constitute the most significant source of systematic error in fission-track dating with the external detector method. The ratios of the measured fission-track densities in an external and internal surface of apatite and a muscovite external detector are calculated from R and the track counting efficiencies ηq. The fact that the results are consistent with the experiment supports the accuracy of R and of the ηq-factors. The external detector ages of a basal and prismatic section of Durango apatite are consistent with its reference age, without the need for a length correction. A critical examination of the uncertainties related to the thermal neutron fluence measurements, fission-decay constant, calculated R-value, independently determined ηq-factors and the reference age of the standard, demonstrates that the assumption that a reduction of the confined track length of the spontaneous tracks in Durango apatite necessitates a proportional correction of its apparent fission-track age is the element most in question. Published U/Th–He ages lend support to the conclusion that such a correction is not required. The significance of R and of the ratio Q of the ηq-factors for the induced and spontaneous track counts leads us to propose a formalisation of the age equation, in which these are included, as well as a formal length correction L, which is, however, not set equal to the ratio of the confined track lengths of the induced and spontaneous tracks. The accuracy of the thermal neutron fluence and the decay constant leads us to propose a possible deconvolution of the ζ-calibration factor. If, for suitable age standards L=1, the proposed deconvoluted calibration factor ζ 0 is a function of R and Q, which can be determined in ways that are independent of the reference ages of the standards. This can either be interpreted as a multiple calibration or as establishing the fission-track method as an independent dating method.