Internal Anisotropy of Collision Cascades

TL;DR

This paper explores the internal anisotropy of collision cascades, introducing an angular correlation function to better describe their directional structure beyond traditional fractal measures.

Contribution

It proposes a new angular correlation function to quantify the internal anisotropy and directionality of collision cascades, addressing limitations of the fractal dimension.

Findings

Angular correlation function decays as a power law.

Angular correlation length differs from radius of gyration.

Overlapping subcascades significantly affect angular correlation.

Abstract

We investigate the internal anisotropy of collision cascades arising from the branching structure. We show that the global fractal dimension cannot give an adequate description of the geometrical structure of cascades because it is insensitive to the internal anisotropy. In order to give a more elaborate description we introduce an angular correlation function, which takes into account the direction of the local growth of the branches of the cascades. It is demonstrated that the angular correlation function gives a quantitative description of the directionality and the interrelation of branches. The power law decay of the angular correlation is evidenced and characterized by an exponent and an angular correlation length different from the radius of gyration. It is demonstrated that the overlapping of subcascades has a strong effect on the angular correlation.