Binomial distribution function for intuitive understanding of fluence dependence of non-amorphized ion-track area

We propose the binomial distribution function is a useful function to describe the fluence dependence of overlapped and non-overlapped area of ion-tracks created by high-energy heavy ions. The validity of the function has been proven by simple computer simulation assuming that ion-tracks are introduced at random positions of two-dimentional grid. In order to test the applicability of the function for describing accumulation behavior of non-amorphized ion-tracks, asymmetric X-ray diffraction peak observed for CeO2 irradiated with 200-MeV 197Au ions has been analyzed. The asymmetric peak observed after the irradiations can be explained by the sum of the original peak attributed to the matrix and the new peak partly attributed to non-overlapped area of ion-tracks. It has been found that the binomial distribution function is useful for explaining the fluence dependence of the non-overlapped area of ion-tracks.