The Thermal Diffusion Length Problem in an Array of Plates

An exact solution is developed for a plane source of thermal neutrons embedded in an infinite array of absorbing plates. Using methods based on generating functions and the theory of complex variables, we can obtain explicit values for the flux at the plate surfaces and hence at any position within the lattice.

The effect on the flux distribution of allowing the plate absorption parameter (Galanin's constant) to be a random variable, uniformly distributed between an upper and lower limit, is calculated. It is found that randomness leads to a reduced rate of decay with distance from the source, in agreement with other theories concerning this problem.