Thermal significance of fission-track length distributions

The semi-analytical solution of an equation describing the production and shortening of fission tracks in apatite suggests that certain thermal histories have unique length-distribution 'signatures'. Isothermal-heating histories should be characterized by flattened, length-shortened distributions; step-heating histories should be characterized by bimodal track length distributions; and linear-cooling histories should be characterized by negatively skewed, length-shortened distributions. The model formulated here to investigate track length distributions can be used to constrain the thermal histories of natural samples for which unbiased track length data are available - provided that the geologic history of the system of interest can be used to partially constrain one of the unknowns in the model equations, time or temperature. (author)