A Monte-Carlo calculation of the size distribution of latent alpha-recoil tracks

Abstract

This paper proposes a Monte-Carlo method for calculating the time-dependent size distribution of alpha-recoil tracks in minerals. The results show that, in the case of recoil tracks in phlogopite, produced by the uranium-series isotopes in the time interval between 0 and 1 Ma, the size distribution comprises two distinct track-populations. The first has a mean size of ∼30 nm and standard deviation of ∼5 nm and consists of tracks that are the result of a single alpha decay. The second has a broad range of sizes with a mean of ∼125 nm and standard deviation ∼50 nm and consists of tracks that, for the most part, result from complete decay of 238 U and 234 U to stable 206 Pb . The first population saturates at around ∼1 Ma, whereas the second shows approximately linear growth. On the basis of the present results, it becomes possible to calculate both the number of recoil tracks intersecting a unit surface of natural minerals and the interconnectedness of recoil damage as a function of time, which has direct implications for alpha-recoil track dating of mica and for the prediction of the long-term behaviour of mineral host phases for the disposal of high-level nuclear waste.