Analytic Reductions for Transmission and Leakage Probabilities in Finite Tubes and Hexahedra

Analytic reductions are used to simplify evaluation of the transmission probabilities in a hexahedron and of the five independent probabilities (two transmission and three leakage probabilities) that are required for a finite tube. The four- and five-dimensional numerical integrations required for transmission and leakage probabilities are reduced to one and two dimensions, respectively.