Applications of collision probabilities in reactor physics

The traditional applications of collision probabilities in reactor physics are the solution of the integral form of the neutron transport equation and in the derivation of equivalence relations connecting heterogeneous and homogeneous resonance integrals. An alternative method of solving the multigroup flux equations is presented. The method is well suited to few region, many group condensation calculations particularly if the resonance treatment requires a group by group flux solution. A review is given of existing methods of computing collision probabilities in slab, annular and cluster geometry. Developments include anisotropic scattering representation, exp(iBz) leakage representation and a rapid approximate cluster geometry routine. Finally a method of computing heterogeneous resonance integrals is discussed. The method combines the Russian subgroup formulation of homogeneous resonance integrals and equivalence relations based entirely on numerical collision probabilities.