Statistical properties of etched nuclear tracks

Abstract

Abstract Statistical distributions of quadratic holes of uniform shape on a planar surface are investigated. Analytical calculations give expressions for the effective porosity, and the probability and areal dispersion of multiple holes of multiplicity n ≤ 2 as function of nominal porosity. Computer simulations give a simple expression for the effective porosity due to hole overlap, further the probability of multiple holes of multiplicity n ≲ 50, and the areal dispersion of holes of multiplicity n ≲ 7, taking into account closed rings of multiple holes forming islands. The results apply directly to nuclear tracks of rhom-boidal cross section as found in mica. They give a good approximation for convex holes with inversion symmetry as e.g. circular holes. They can be interpreted in terms of the multiple hit theory in radiation biology. The range of porosity investigated reaches beyond the realm of mechanically stable nuclear track filters into the realm relevant for surface micromachining.