On the mean number of collisions suffered by neutrons in bounded domains

The mean number of collisions suffered by monoenergetic neutrons starting from a random point on or inside a purely scattering bounded convex or non-convex domain is derived. For trajectories starting on the surface and entering the body with an isotropic uniform incidence, the average number of collisions is independent of the scattering law. Monte-Carlo simulations illustrate our results in two- and three-dimensions.