Modeling the heavy ion upset cross section

The standard Rectangular Parallelepiped (RPP) construct is used to derive a closed form expression for, bar σ(θ,φ,L) the directional-spectral heavy ion upset cross section. This is an expected value model obtained by integrating the point-value cross section model, σ(θ,φ,L,E), also developed here, with the Weibull density function, f(E), assumed to govern the stochastic behavior of the upset threshold energy, E. A comparison of bar σ(θ,φ,L) with experimental data show good agreement, lending strong credibility to the hypothesis that E-randomness is responsible for the shape of the upset cross section curve. The expected value model is used as the basis for a new, rigorous mathematical formulation of the effective cross section concept. The generalized formulation unifies previous corrections to the inverse cosine scaling, collapsing to Petersen's correction, [cosθ - (h/l)sinθ]-1, near threshold and Sexton's, [cosθ + (h/l)sinθ]-1, near saturation. The expected value cross section model therefore has useful applications in both upset rate prediction and test data analysis