Description of high energy collision cascades within the multifractal theory framework

The random nature of both the energy lost during a collision event and the length traveled by a particle between two successive collisions leads to introduce probability density functions (pdf) to define their evolution in a displacement cascade. Using the Hard Sphere approximation to describe the collision cross section as a toy model to handle the physics of energy dissipation in a displacement cascade, analytical expressions for these pdf can be calculated within the BCA. As these functions exhibit long tails, a description of a collision cascade by a deterministic fractal is not able to capture physical key parameters associated with the energy dissipation. The multifractal formalism is then the only natural framework to define the fractal feature of a displacement cascade. Applying such a formalism, the bifractal behavior of displacement cascade has been clearly pointed out. This feature is clearly due to the long tails of pdf describing collision events. (c) 2008 Published by Elsevier B.V.