FRACTAL DIMENSION OF COLLISION CASCADES

The geometrical structure of the vacancy distribution in collision cas cades is studied using Monte Carlo simulations. Based on a Flory-de Ge nnes-type approach, a relation of the fractal dimension, the self-simi larity dimension, and the dimension of the embedding space is establis hed. It is shown that, varying the parameter of the interaction potent ial, a structural transition takes place in the cascade from an open b ranching structure to a space-filling one. Based on the results the sp ike condition of Cheng, Nicolet, and Johnson [Phys. Rev. Lett. 58, 208 3 (1987)] is revisited.