The Extrapolation Distance at the Surface of a Grey Cylindrical Control Rod

The extrapolation distance ϵ at the surface of a grey cylindrical control rod of given size is found in terms of the blackness β of the rod and in terms of the extrapolation distance ϵ_b at the surface of a black rod of the same size. The formula is where λ_e is the transport mean free path in the region external to the rod. Tables are provided for β and an empirical expression for ϵ_b/λ_e is given.