Fractal dimension of collision cascades

The geometrical structure of the vacancy distribution in collision cascades is studied using Monte Carlo simulations. Based on a Flory-de Gennes-type approach, a relation of the fractal dimension, the self-similarity dimension, and the dimension of the embedding space is established. It is shown that, varying the parameter of the interaction potential, a structural transition takes place in the cascade from an open branching structure to a space-filling one. Based on the results the spike condition of Cheng, Nicolet, and Johnson [Phys. Rev. Lett. 58, 2083 (1987)] is revisited.