A Modified Wigner Rational Approximation for Neutron Collision Escape Probability from Bare Homogeneous Reactor Assemblies

The neutron collision escape probability from a medium depends on the shape of spatial distribution of the source. The case of a uniform or flat source distribution has been investigated extensively from time to time. In the present work, the case of bare homogeneous reactor assemblies having a centrally peaked neutron source distribution has been analyzed for predicting collision escape probability as a function of assembly size measured in terms of the optical mean chord length . An approximation, known as the modified Wigner rational approximation, is derived and is given by where p_E(W) stands for the collision escape probability from a bare homogeneous reactor assembly; ϵ₁ and ϵ₂ are geometry-dependent parameters. These parameters have been determined for infinite slab, infinite cylinder, sphere, cube, and finite cylinders of height-to-diameter ratio varying from 0.1 to 20. It is shown that it is possible to predict the collision escape probability within approximately ±2% of the exact value for , ranging from 0 to 20 mean-free-paths (mfp). Generally, for a given the collision escape probability value for the centrally peaked source is lower than that for the uniform source. But it is found that for very thin infinite slab assemblies of optical mean chord length 1.5 mfp, the collision escape probability for centrally peaked source distribution is higher than that for uniform source distribution. The reason for this anomaly is discussed.