An empirical equation between track radii and melting temperatures and its consequences for insulators irradiated by swift heavy ions

A universal function Θ(r) describes the empirical relationship between track radii Re and melting temperatures Tm without involving any other materials parameters. The precise form of the function Θ(r) is derived. Track radii Re for mica and NiFe2O4 are calculated from the experimental data of TeO2 and Y3Fe5O12 by using only the Tm values and Θ(r). The good agreement of the calculated values with the data for low and high velocity projectiles confirm the validity of Θ(r) in a broad range of the electronic stopping power Se. Consequences for the damage cross-section velocity effect are discussed. Equations are derived from Θ(r  ) for the track evolution Re2-Se and the threshold value of Se for track formation which agree with the basic equations of the analytical thermal spike model.